BRIGHAM EXPLORATION CO
10-K, 1999-03-31
CRUDE PETROLEUM & NATURAL GAS
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                UNITED STATES SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                            -------------------------

                                    FORM 10-K

                            -------------------------

          (Mark One)
            [X] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                SECURITIES EXCHANGE ACT OF 1934 
                    FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998

                OR

            [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE 
                SECURITIES EXCHANGE ACT OF 1934 
                    FOR THE TRANSITION PERIOD FROM ___________ TO _____________

                             COMMISSION FILE NUMBER:

                           BRIGHAM EXPLORATION COMPANY
             (Exact name of Registrant as Specified in its Charter)


                DELAWARE                                75-2692967
     (State or other jurisdiction of                 (I.R.S. Employer
     incorporation or organization)                 Identification No.)

        6300 BRIDGE POINT PARKWAY
          BUILDING 2, SUITE 500                            78730
             AUSTIN, TEXAS                              (Zip Code)
(Address of principal executive offices)

                                 (512) 427-3300
              (Registrant's telephone number, including area code)

                                 ---------------
           Securities registered pursuant to Section 12(b) of the Act:

                                                 NAME OF EACH EXCHANGE ON
           TITLE OF EACH CLASS                       WHICH REGISTERED
           -------------------                   ------------------------
                  None                                     None

           Securities registered pursuant to Section 12(g) of the Act:

                          COMMON STOCK, $.01 PAR VALUE
                                (Title of Class)

     Indicate by check mark whether the Registrant: (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes  X  No
                                              ---    ---

     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of Registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. [ ]

     As of March 26, 1999, the Registrant had outstanding 13,306,206 shares of
Common Stock. The aggregate market value of the Common Stock held by
non-affiliates of the Registrant, based upon the closing sale price of the
Common Stock on March 26, 1999, as reported on The Nasdaq Stock Market(sm), was
approximately $18 million.

     Pursuant to Rule 12b-25 under the Act, (1) combined financial statements of
the Registrant's subsidiaries whose securities are pledged as collateral for the
Registrant's Senior Subordinated Secured Notes and (2) certain exhibits have
been omitted from this Form 10-K.

                       DOCUMENTS INCORPORATED BY REFERENCE

     Portions of the definitive proxy statement for the Registrant's 1999 Annual
Meeting of Stockholders to be held on May 13, 1999, are incorporated by
reference in Part III of this Form 10-K. Such definitive proxy statement will be
filed with the Securities and Exchange Commission not later than 120 days
subsequent to December 31, 1998.

================================================================================


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                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                              PAGE
                                                                                              ----
                                                      PART I
<S>               <C>                                                                         <C>
     ITEM 1.      BUSINESS.......................................................................1

     ITEM 2.      PROPERTIES.....................................................................9

     ITEM 3.      LEGAL PROCEEDINGS.............................................................18

     ITEM 4.      SUBMISSION OF MATTERS TO A VOTE OF SECURITYHOLDERS............................18

     EXECUTIVE OFFICERS OF THE REGISTRANT.......................................................19

                                                      PART II

     ITEM 5.      MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED
                  STOCKHOLDER MATTERS...........................................................20

     ITEM 6.      SELECTED FINANCIAL DATA.......................................................21

     ITEM 7.      MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
                  AND RESULTS OF OPERATIONS.....................................................22

     ITEM 7A.     QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK....................39

     ITEM 8.      FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA...................................39

     ITEM 9.      CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING
                  AND FINANCIAL DISCLOSURE......................................................39

                                                     PART III

     ITEM 10.     DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT............................40

     ITEM 11.     EXECUTIVE COMPENSATION........................................................40

     ITEM 12.     SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND
                  MANAGEMENT....................................................................40

     ITEM 13.     CERTAIN RELATIONSHIPS AND RELATED PARTY TRANSACTIONS..........................40

                                                      PART IV

     ITEM 14.     EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K...............41

     GLOSSARY OF OIL AND GAS TERMS..............................................................47

     SIGNATURES.................................................................................51

     INDEX TO FINANCIAL STATEMENTS............................................................F1-1
</TABLE>

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                           BRIGHAM EXPLORATION COMPANY

                         1998 ANNUAL REPORT ON FORM 10-K


                                     PART I

ITEM 1.     BUSINESS

OVERVIEW

     Brigham Exploration Company ("Brigham" or the "Company") is an independent
exploration and production company that applies 3-D seismic imaging and other
advanced technologies to systematically explore and develop onshore oil and
natural gas provinces in the United States. The Company focuses its 3-D seismic
activity in provinces where it believes 3-D technology may be effectively
applied to generate relatively large potential reserve volumes per well and per
field, high potential production rates and multiple producing objectives. The
Company's exploration activities are concentrated primarily in three core
provinces: the Anadarko Basin of western Oklahoma and the Texas Panhandle; the
onshore Gulf Coast of south Texas and, to a lesser extent, the transition zone
of Louisiana; and West Texas.

     The Company pioneered the acquisition of large scale onshore 3-D seismic
surveys for exploration, obtaining extensive 3-D seismic data and experience in
capturing undiscovered oil and natural gas reserves. As of December 31, 1998,
Brigham has acquired 5,236 square miles (3.3 million acres) of 3-D seismic data
and has identified an estimated 1,140 potential drilling locations, of which the
Company has drilled 442. The Company generates most of its exploratory projects
and, therefore, has the ability to retain a sizeable working interest to the
extent that it decides not to place interests with industry participants.

     From inception in 1990 through 1998, Brigham has drilled 378 exploratory
and 64 development wells on its 3-D generated prospects with an aggregate 64%
success rate and an average working interest of 29%. As of December 31, 1998,
the Company has added 114 Bcfe of net proved reserves to its reserve base,
approximately 92 net Bcfe of which were discovered by Brigham through its
systematic 3-D exploration drilling activities at an average net drilling cost
of $0.82 per Mcfe. The Company's estimated net proved reserves as of December
31, 1998 were 97.8 Bcfe having an aggregate Present Value of Future Net Revenues
of $81.7 million, compared to estimated net proved reserves as of December 31,
1996 of 21.9 Bcfe having an aggregate Present Value of Future Net Revenues of
$44.5 million. The Company's net proved reserve volumes at December 31, 1998 are
73% natural gas and 57% proved developed reserves.

BUSINESS STRATEGY

     Brigham's principal objective and business strategy is to achieve superior
growth in shareholder value through the application of its systematic
exploration approach, which emphasizes the integrated use of 3-D seismic imaging
and other advanced technologies to reduce drilling risks and finding costs.
Since its inception in 1990, the Company has achieved rapid growth in its
acquisition of 3-D seismic data, identification of potential drilling locations,
discovery of proved reserves and production volumes.

     Brigham completed its initial public offering of common stock in May 1997,
raising approximately $24 million to fund the Company's accelerated 3-D seismic
acquisition and exploration drilling activities. Key elements of the Company's
long-term growth strategy at its initial public offering and continuing today
include: (i) acquiring 3-D seismic data in proven producing trends to identify
and capture potential drilling locations; (ii) retaining significant working
interests in its exploration projects to capture a greater share of the reserves
that the Company discovers; (iii) identifying higher potential, higher impact
prospects; and (iv) monetizing the value of its 3-D seismic investments by
drilling its inventory of 3-D seismic delineated locations.


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     Since its initial public offering in early 1997, Brigham has been effective
in the implementation of its long-term growth strategy. During 1997 and 1998,
the Company acquired 2,475 square miles of 3-D seismic data at an average
working interest of 73%, which nearly doubled its inventory of gross onshore 3-D
seismic data to 5,236 square miles as compared to year-end 1996 and increased
its net onshore 3-D seismic data in inventory more than three-fold from 780
square miles at year-end 1996 to 2,590 square miles at year-end 1998. Brigham's
overall level of 3-D seismic acquisition during the past two years represents
the most active in the Company's history, and 90% of the recently acquired data
is located in Brigham's higher potential Anadarko Basin and Gulf Coast provinces
where it has achieved historically lower finding costs for drilling than in its
West Texas province. As a result of these significant investments in 3-D seismic
acquisition and interpretation in proven natural gas producing trends, the
Company believes it has assembled a significant competitive knowledge base and
strategic position in each of its two active exploration provinces. Brigham
further believes it has captured a high quality inventory of 3-D delineated
potential drilling locations that can be monetized through the drillbit at
profitable finding costs over the next several years, thereby providing
opportunities for future reserve, production and cash flow growth.

     Brigham has substantially reduced its planned capital expenditure budget
for 1999 and has undertaken a number of strategic initiatives in an effort to
improve and preserve its capital liquidity in the current environment. While the
Company remains focused on its long-term growth objectives and the continuation
of its established business model for 3-D seismic-based exploration, Brigham has
adapted its business strategy in the near-term in an effort to maximize value
for its shareholders on a long-term basis through the implementation of the
following principal strategic initiatives: (i) focusing all of the Company's
planned exploration efforts in 1999 toward the drilling of its highest- grade
3-D prospects identified in its Anadarko Basin and Gulf Coast projects,
concentrated primarily in trends where Brigham has achieved exploration success,
(ii) eliminating substantially all planned seismic and land expenditures for new
projects until its capital resources can support such additional activity, (iii)
seeking to divest certain producing natural gas and oil properties in an effort
to raise capital to reduce debt borrowings and to redirect capital to drilling
projects that have the potential to generate higher investment returns, (iv)
restructuring its outstanding senior and subordinated debt agreements to provide
the Company with flexibility needed to preserve cash flow to fund its expected
near-term exploration activities, (v) implementing an overhead reduction plan to
reduce general and administrative expenses, and (vi) evaluating opportunities to
raise additional equity capital either through the sales of interests in certain
of its seismic projects or the issuance of equity securities. The Company
believes that the successful execution of these strategic initiatives will
provide Brigham with sufficient capital resources to execute its planned 1999
exploration program and position the Company to realize the significant value it
believes it has captured in its inventory of 3-D seismic projects and delineated
drilling locations. See "Item 7. Management's Discussion and Analysis of
Financial Condition and Operating Results -- Liquidity" and "-- Capital
Resources."

EXPLORATION AND OPERATING APPROACH

     The Company has acquired 3-D seismic data covering 5,236 square miles (3.3
million acres) in over 20 geologic trends in seven basins and seven states.
Through this activity, the Company has developed expertise in the selection of
geologic trends that are suitable for 3-D seismic exploration. Brigham uses
experience that it gains within a trend to enhance the quality of subsequent
projects in the same trend and other analogous trends, contributing to lower
finding and development costs, compressed project cycle times and increased
project rates of return.

     The Company typically acquires 3-D seismic data in and around existing
production where the Company can benefit from the imaging of producing analogs.
These 3-D defined analogs, combined with the Company's experience in drilling
442 wells, provide the Company with a knowledge base to evaluate other potential
geologic trends, 3-D seismic projects within trends and 3-D delineated potential
drilling locations. The Company's knowledge base assists in identifying geologic
trends where Brigham believes it can find and develop economic volumes of oil
and natural gas.

     The Company has experience exploring with 3-D seismic in a wide range of
reservoir types and geologic trapping styles, both stratigraphic and structural
(including reefs, salt domes, channel sands, complex faulted and fractured
reservoirs and pinchout plays). The Company seeks to supplement its knowledge
base with the best local geologic expertise available for a particular geologic
trend. In addition, the Company typically acquires digital data bases for

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integration on the Company's CAEX workstations, including digital land grids,
well information, log curves, production information, geologic studies, geologic
top data bases and existing 2-D seismic data.

     The Company uses its knowledge base, local geological expertise and digital
data bases integrated with 3-D seismic to create maps of producing and
potentially productive reservoirs. The Company believes its 3-D generated maps
are more accurate than previous reservoir maps (which generally were based on
subsurface geological information and 2-D seismic surveys), enabling the Company
to more precisely evaluate recoverable reserves and the economic feasibility of
projects and drilling locations.

     Brigham acquires most of its raw 3-D seismic data using seismic acquisition
vendors on either a proprietary basis or through alliances affording it the
exclusive right to interpret and use data for extended periods of time. In
addition, the Company participates in non-proprietary group shoots of 3-D data
when it believes the expected full cycle project economics are justified. In its
proprietary acquisitions and alliances, Brigham selects the sites of projects,
primarily guided by its knowledge and experience in the core provinces it
explores; establishes and monitors the seismic parameters of each project for
which data is shot; and typically selects the equipment that will be used. Data
is generally priced on the basis of square miles shot. See "Item 1. Business --
Industry Alliances."

EXPLORATION STAFF

     Over the last eight years the Company has assembled an exploration staff
that includes ten geophysicists, ten geologists, four petroleum engineers, five
computer applications specialists, five geophysical/geological/engineering
technicians, six landmen and six lease and division order analysts. Brigham's
ten geophysicists have different but complementary backgrounds, and their
diversity of experience in varied geological and geophysical settings, combined
with various technical specializations (from hardware and systems to software
and seismic data processing), provide the Company with valuable technical
intellectual resources. The Company's team of explorationists has over 310 years
of exploration experience and more than 85 years of 3-D CAEX workstation
experience, most of which was acquired at Brigham and various major and large
independent oil companies. Occasionally, the Company complements and leverages
its exploration staff by seeking out alliances or retainer relationships with
geologists having extensive experience in a particular area of interest.

3-D SEISMIC TECHNOLOGY

     The Company's strategy is to use 3-D seismic and other advanced
technologies, including CAEX, to systematically explore and develop domestic
onshore oil and natural gas provinces. In general, 3-D seismic is the process of
acquiring seismic data along multiple lines and grids. The primary advantage of
3-D seismic over 2-D seismic is that it provides information with respect to
multiple horizontal and vertical points within a geologic formation instead of
information on a single vertical line or multiple vertical lines within the
formation. Acquiring larger amounts of data relating to a geologic formation
allows a user to better correlate the data and, in some cases, obtain a greater
understanding and image of the formation. Although it is impossible to predict
with certainty the specific configuration or composition of any underground
geologic formation, the use of 3-D seismic data provides clearer and more
accurate projected images of complex geologic formations, which can assist a
user in evaluating whether to drill for oil and natural gas reserves. If a
decision to drill is made, 3-D seismic data can also help in determining the
optimal location to drill.

     CAEX is the process of accumulating and analyzing the various seismic,
production and other data obtained relating to a geographic area. In general,
CAEX involves accumulating various 2-D and 3-D seismic data with respect to a
potential drilling location, correlating that data with historical well control
and production data from similar properties and analyzing the available data
through computer programs and modeling techniques to project the likely geologic
composition of a potential drilling location and potential locations of
undiscovered oil and natural gas reserves. This process relies on a comparison
of data with respect to the potential drilling location and historical data with
respect to the density and sonic characteristics of different types of rock
formations, hydrocarbons and other subsurface minerals, resulting in a projected
three dimensional image of the subsurface. This modeling is performed through
the use of advanced interactive computer workstations and various combinations
of available computer programs that have been developed solely for this
application.

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     Brigham has invested extensively in the advanced computer hardware and
software necessary for 3-D seismic exploration. The Company has both Landmark
and Geoquest CAEX workstations. This workstation flexibility provides the
Company the opportunity to interpret a project on the particular CAEX
workstation that it believes is best suited for defining those particular
geologic objectives. Brigham's explorationists can access a diverse software
tool kit including SeisWorks, StratWorks, EarthCube, OpenVision, Open Explorer,
ZAP, Zmap+, ARIES, SynTool, Poststack, TDQ, AutoPix, MapView, GeoViz, Voxels,
SynView, CSA (Computed Seismic Attributes), Surface Slice, Hampson -- Russell
AVO Analysis and Modeling and ZEH Graphics CGMage Builder (graphics montage
tool).

     The Company believes that its use of 3-D seismic technology provides it
with a number of benefits in the exploration, delineation and development
process that are not generally available to those who only use 2-D seismic data
and conventional processing methods. In particular, the Company believes that it
obtains clearer and more accurate projected images of underground formations
through computer modeling, and is therefore better able to identify potential
locations of hydrocarbon accumulations based on the characteristics of the
formations and analogies made with nearby fields and formations where
hydrocarbons have been found. This enhanced data has been used to assist the
Company in eliminating potential drilling locations that might otherwise have
been drilled had the Company relied solely on 2-D seismic data. This data has
also been used to assist the Company in attempting to identify the most
desirable location for the wellbore to increase the prospects of a successful
exploratory or development well and production from the reservoir.

INDUSTRY ALLIANCES

     Veritas Anadarko Basin Acquisition Alliances. Pursuant to certain alliances
with Veritas DGC Land Ltd. ("Veritas"), Brigham has acquired approximately 1,460
square miles of 3-D seismic in the Anadarko Basin through December 31, 1998 and
has agreed to acquire from 165 to 265 additional square miles of data to be
divided among individual projects in that province. In exchange for the
Company's commitment to Veritas, the Company and its assignees only pay a
portion of the 3-D seismic acquisition costs as the data is acquired. As the
Company leases acreage or drills wells, it pays Veritas the balance of the
deferred costs in the form of leasing and drilling fees until such deferred
costs are repaid or until certain time periods have occurred. In addition, in
the event that the outstanding balance of deferred seismic acquisition costs
exceeds certain threshold amounts, the Company must pre-pay part of the leasing
and drilling fees to cause the outstanding balance to fall below the current
threshold amount. These arrangements afford the Company access to 3-D seismic
acquisition in a compressed cycle time, providing the Company with significant
operational efficiencies.

     In addition, Veritas Geoservices, Ltd. provides employees that maintain and
operate seismic data processing workstations in Brigham's offices. Supervised by
Brigham's geophysicists, the vendor's employees process most of the Company's
3-D seismic. The associated improvement in communication and integration, from
field data acquisition to processing, reduces project cycle times, and therefore
costs, while improving the quality of the data for Brigham's subsequent
interpretation.

     Anadarko Basin Alliance I. The Company has entered into alliances with
Vintage Petroleum, Inc. ("Vintage") and Stephens Production Company ("Stephens")
which provided for their participation with Brigham in all of the projects that
the Company conducted within a 625 square mile 3-D seismic program that was
completed in 1997 with Veritas in the Anadarko Basin. Vintage and Stephens
incurred a disproportionate share of all pre-seismic and certain seismic costs
on all projects in the program. Net of the interests of Vintage and Stephens,
the Company holds a 37.5% interest in the program. The Company believes that
this leveraging of its costs was possible because of the expertise and knowledge
that the Company has developed, enabling the Company to build its revenue and
cash flow base at a time when it has been capital constrained.

     Anadarko Basin Alliance II. Upon completion of data acquisition in its
Alliance I program, Brigham began acquiring 3-D seismic under a second alliance
with Veritas in the Anadarko Basin. From August 1997 through November 1998, the
Company acquired approximately 835 square miles of 3-D seismic under this
alliance with a 100% working interest. Pursuant to the terms of its acquisition
agreement with Veritas, Brigham ceased acquisition of 3-D seismic data in the
Alliance II program in early November 1998, and the Company will consider
acquiring the balance of the data contemplated in this program when it
determines that its capital resources are sufficient to incur such

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expenditures. The Company currently intends to retain a majority working
interest in its Alliance II seismic projects subsequent to the sale and
potential future sales of a portion of its working interests in certain of these
projects. See "-- Duke Project Financing."

     Carry-to-Casing Point Programs. From 1996 through 1998, Brigham has entered
into annual agreements with certain industry parties to participate in all of
the wells drilled by the Company during the term of the agreement on a promoted
drilling cost basis. For example, in order to participate in wells drilled by
the Company between April 1, 1998 and March 31, 1999, Gasco Limited Partnership
("Gasco") agreed to fund 8% of the Company's drilling costs and 4% of its
completion costs for each well. In return, the Company agreed to assign to Gasco
an undivided 4% of the Company's interest in the leasehold allocated to the
production unit for each completed well. As a result, the Company pays for 92%
of costs attributable to its working interest to casing point, and 96% of its
completion costs, for 96% of its original working interest for each well funded
during the term of the agreement.

     Brigham entered into a carry-to-casing point agreement in late 1998 with a
major drilling contractor to participate in four wells drilled by the Company.
Pursuant to the agreement, the drilling contractor agreed to fund 25% of the
Company's drilling costs and 12.5% of its completion costs for each of these
four wells. In return, the Company agreed to utilize the drilling contractor's
services for the drilling of the wells and to assign to the drilling contractor
an undivided 12.5% of the Company's interest in the leasehold allocated to the
production unit for each completed well. As a result, the Company pays for 75%
of costs attributable to its working interest to casing point, and 87.5% of its
completion costs, for 87.5% of its original working interest for each well
drilled under the agreement. Brigham is currently in discussions with the
drilling contractor to extend this arrangement to provide for the participation
in all of the wells spud by the Company over an annual term. However, there can
be no assurance that such an arrangement will be reached or that the terms of
any such arrangement will not differ from those in its prior agreements. The
Company believes that current industry conditions have provided it with the
opportunity to seek such arrangements with industry service providers to fund a
portion of its capital expenditures in exchange for service commitments with
such providers at competitive prices.

     The Company believes that its carry-to-casing point agreements have been
beneficial because they have allowed the Company to leverage its working
interests in its properties by requiring it to bear a disproportionately smaller
share of drilling costs, thereby enhancing its returns on drilling capital
investments. Depending on future conditions, the Company may seek to enter into
similar types of arrangements with industry or financial participants. To the
extent that the Company does seek to enter into such future arrangements, the
terms of these arrangements, including the percentages of costs borne and
interests assigned, may vary from those in the Company's past and present
arrangements.

     Duke Project Financing. In February 1999, the Company entered into a
project financing arrangement with Duke Energy Financial Services, Inc. ("Duke")
to fund the continued exploration of five projects covered by approximately 200
square miles of 3-D seismic data acquired in 1998 as part of its Anadarko Basin
Alliance II program. In this transaction, the Company conveyed 100% of its
working interest (land and seismic) in these project areas to a newly formed
limited liability company (the "Duke LLC") for total consideration of $10
million. The Company is the managing member of the Duke LLC with a 1% interest,
and Duke is the sole remaining member with a 99% interest. Pursuant to the terms
of the Duke LLC agreement, Brigham pays 100% of the drilling and completion
costs for all wells drilled by the Duke LLC within the designated project areas
in exchange for a 70% working interest in the wells (and their allocable
drilling and spacing units), with the remaining 30% working interest remaining
in the Duke LLC, subject in each instance to proportionate reduction by any
ownership rights held by third parties. Upon 100% project payout, the Company
has the right to back-in for 80% of the Duke LLC's working interest in all of
the then producing wells (and their allocable drilling and spacing units) and a
96% working interest in any wells (and their allocable drilling and spacing
units) drilled after payout within the designated project areas governed by the
Duke LLC agreement, thereby increasing the Company's effective working interest
in the Duke LLC wells from 70% to 94%. The Company believes this project
financing arrangement to be beneficial as it enabled Brigham to recoup
substantially all of its pre-seismic land and seismic data acquisition costs
incurred in these project areas and provided capital to drill the first six
wells within these projects.


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NATURAL GAS AND OIL MARKETING AND MAJOR CUSTOMERS

     Most of the Company's natural gas and oil production is sold under price
sensitive or spot market contracts. The revenues generated by the Company's
operations are highly dependent upon the prices of and demand for natural gas
and oil. The price received by the Company for its natural gas and oil
production depends on numerous factors beyond the Company's control, including
seasonality, competition, the condition of the United States economy, foreign
imports, political conditions in other oil-producing and natural gas-producing
countries, the actions of the Organization of Petroleum Exporting Countries, and
domestic government regulation, legislation and policies. Decreases in the
prices of natural gas and oil could have an adverse effect on the carrying value
of the Company's proved reserves and the Company's revenues, profitability and
cash flow. Although the Company is not currently experiencing any significant
involuntary curtailment of its natural gas or oil production, market, economic
and regulatory factors may in the future materially affect the Company's ability
to sell its natural gas or oil production. See "Item 7. Management's Discussion
and Analysis of Financial Condition and Results of Operations", "--Risk Factors
- -- Volatility of Natural Gas and Oil Prices" and "--Risk Factors --
Marketability of Production." For the year ended December 31, 1998, sales to
Highland Energy Company, Ward Petroleum Corporation, Lantern Petroleum
Corporation and Louis Dreyfus Natural Gas Corporation were approximately 25%,
15%, 11% and 11%, respectively, of the Company's natural gas and oil revenues.
Due to the availability of other markets and pipeline connections, the Company
does not believe that the loss of any single natural gas or oil customer would
have a material adverse effect on the Company's results of operations.

COMPETITION

     The oil and gas industry is highly competitive in all of its phases. The
Company encounters competition from other oil and gas companies in all areas of
its operations, including the acquisition of seismic and leasing options and oil
and natural gas leases on properties. The Company's competitors include major
integrated oil and natural gas companies and numerous independent oil and
natural gas companies, individuals and drilling and income programs. Many of its
competitors are large, well established companies with substantially larger
operating staffs and greater capital resources than the Company's. Such
companies may be able to pay more for seismic and lease options on oil and
natural gas properties and exploratory prospects and to define, evaluate, bid
for and purchase a greater number of properties and prospects than the Company's
financial or human resources permit. The Company's ability to acquire additional
properties and to discover reserves in the future will be dependent upon its
ability to evaluate and select suitable properties and to consummate
transactions in a highly competitive environment. See "Item 7. Management's
Discussion and Analysis of Risk Factors -- Competition" and "-- Risk Factors --
Substantial Capital Requirements."

OPERATING HAZARDS AND UNINSURED RISKS

     Drilling activities are subject to many risks, including the risk that no
commercially productive reservoirs will be encountered. There can be no
assurance that new wells drilled by the Company will be productive or that the
Company will recover all or any portion of its investment. Drilling for oil and
natural gas may involve unprofitable efforts, not only from dry wells, but also
from wells that are productive but do not produce sufficient net revenues to
return a profit after drilling, operating and other costs. The cost of drilling,
completing and operating wells is often uncertain. The Company's drilling
operations may be curtailed, delayed or canceled as a result of numerous
factors, many of which are beyond the Company's control, including title
problems, weather conditions, compliance with governmental requirements and
shortages or delays in the delivery of equipment and services. The Company's
future drilling activities may not be successful and, if unsuccessful, such
failure may have a material adverse effect on the Company's business, financial
condition or results of operations. See "Item 7. Management's Discussion and
Analysis of Financial Condition and Results of Operations -- Risk Factors --
Dependence on Exploratory Drilling Activities." In addition, use of 3-D seismic
technology requires greater pre-drilling expenditures than traditional drilling
strategies. Although the Company believes that its use of 3-D seismic technology
will increase the probability of drilling success, some unsuccessful wells are
likely, and there can be no assurance unsuccessful drilling efforts will not
have a material adverse effect on the Company's business, financial condition or
results of operations.


                                      - 6 -

<PAGE>   9





     The Company's operations are subject to hazards and risks inherent in
drilling for and producing and transporting oil and natural gas, such as fires,
natural disasters, explosions, encountering formations with abnormal pressures,
blowouts, cratering, pipeline ruptures and spills, any of which can result in
the loss of hydrocarbons, environmental pollution, personal injury claims and
other damage to properties of the Company and others. The Company maintains
insurance against some but not all of the risks described above. In particular,
the insurance maintained by the Company does not cover claims relating to
failure of title to oil and natural gas leases, trespass during 3-D survey
acquisition or surface change attributable to seismic operations, business
interruption or loss of revenues due to well failure. In certain circumstances
in which insurance is available the Company may not purchase it. The occurrence
of an event that is not covered, or not fully covered, by insurance could have a
material adverse effect on the Company's business, financial condition and
results of operations.

EMPLOYEES

     On March 26, 1999, the Company had 66 full-time employees. None is
represented by any labor union. The Company believes its relations with its
employees are good. The Company also relies on several regional consulting
service companies to provide field landmen to support the Company on a
project-by-project basis. One of these companies, Brigham Land Management, is
owned by Vincent M. Brigham, who is the brother of Ben M. Brigham, the Company's
Chief Executive Officer, President and Chairman of the Board.

FACILITIES

     The Company's principal executive offices are located in Austin, Texas,
where it leases approximately 34,330 square feet of office space at 6300 Bridge
Point Parkway, Building 2, Suite 500, Austin, Texas 78730. The Company also
leases a 4,100 square foot office at 450 Gears Road, Suite 240, Houston, Texas
77067.

TITLE TO PROPERTIES

     The Company believes it has satisfactory title, in all material respects,
to substantially all of its producing properties in accordance with standards
generally accepted in the oil and gas industry. The Company's properties are
subject to royalty interests, standard liens incident to operating agreements,
liens for current taxes and other inchoate burdens which the Company believes do
not materially interfere with the use of or affect the value of such properties.
The Company's Credit Facility (as defined) is secured by a first lien against
substantially all of the Company's oil and natural gas properties and other
tangible assets, and the Company's Subordinated Notes (as defined) are secured
by a second lien against all collateral pledged by the Company as security under
its Credit Facility. See "Item 7. Management's Discussion and Analysis of
Financial Condition and Results of Operations."

GOVERNMENTAL REGULATION

     The Company's oil and natural gas exploration, production and marketing
activities are subject to extensive laws, rules and regulations promulgated by
federal and state legislatures and agencies. Failure to comply with such laws,
rules and regulations can result in substantial penalties. The legislative and
regulatory burden on the oil and gas industry increases the Company's cost of
doing business and affects its profitability. Although the Company believes it
is in substantial compliance with all applicable laws and regulations, because
those laws and regulations are frequently amended, interpreted and
reinterpreted, the Company is unable to predict the future cost or impact of
complying with such laws and regulations.

     The State of Texas and many other states require permits for drilling
operations, drilling bonds and reports concerning operations and impose other
requirements relating to the exploration and production of natural gas and oil.
These states also have statutes or regulations addressing conservation matters,
including provisions for the unitization or pooling of natural gas and oil
properties, the establishment of maximum rates of production from wells and the
regulation of spacing, plugging and abandonment of such wells.


                                      - 7 -

<PAGE>   10


ENVIRONMENTAL MATTERS

     The Company's operations and properties are, like the oil and gas industry
in general, subject to extensive and changing federal, state and local laws and
regulations relating to environmental protection, including the generation,
storage, handling, emission, transportation and discharge of materials into the
environment, and relating to safety and health. The recent trend in
environmental legislation and regulation generally is toward stricter standards,
and this trend will likely continue. These laws and regulations may require the
acquisition of a permit or other authorization before construction or drilling
commences and for certain other activities; limit or prohibit seismic
acquisition, construction, drilling and other activities on certain lands lying
within wilderness and other protected areas; and impose substantial liabilities
for pollution resulting from the Company's operations. The permits required for
various of the Company's operations are subject to revocation, modification and
renewal by issuing authorities. Governmental authorities have the power to
enforce compliance with their regulations, and violations are subject to fines
or injunction, or both. In the opinion of management, the Company is in
substantial compliance with current applicable environmental laws and
regulations, and the Company has no material commitments for capital
expenditures to comply with existing environmental requirements. Nevertheless,
changes in existing environmental laws and regulations or in interpretations
thereof could have a significant impact on the Company, as well as the oil and
gas industry in general. The Comprehensive Environmental Response, Compensation
and Liability Act ("CERCLA") and comparable state statutes impose strict and
arguably joint and several liability on owners and operators of certain sites
and on persons who disposed of or arranged for the disposal of "hazardous
substances" found at such sites. It is not uncommon for the neighboring land
owners and other third parties to file claims for personal injury and property
damage allegedly caused by the hazardous substances released into the
environment. The Resource Conservation and Recovery Act ("RCRA") and comparable
state statutes govern the disposal of "solid waste" and "hazardous waste" and
authorize imposition of substantial fines and penalties for noncompliance.
Although CERCLA currently excludes petroleum from its definition of "hazardous
substance," state laws affecting the Company's operations impose clean-up
liability relating to petroleum and petroleum related products. In addition,
although RCRA classifies certain oil field wastes as "non-hazardous," such
exploration and production wastes could be reclassified as hazardous wastes
thereby making such wastes subject to more stringent handling and disposal
requirements.

     Federal regulations require certain owners or operators of facilities that
store or otherwise handle oil, such as the Company, to prepare and implement
spill prevention, control countermeasure and response plans relating to the
possible discharge of oil into surface waters. The Oil Pollution Act of 1990
("OPA") contains numerous requirements relating to the prevention of and
response to oil spills into waters of the United States. For onshore and
offshore facilities that may affect waters of the United States, the OPA
requires an operator to demonstrate financial responsibility. Regulations are
currently being developed under federal and state laws concerning oil pollution
prevention and other matters that may impose additional regulatory burdens on
the Company. In addition, the Clean Water Act and analogous state laws require
permits to be obtained to authorize discharge into surface waters or to
construct facilities in wetland areas. With respect to certain of its
operations, the Company is required to maintain such permits or meet general
permit requirements. The Environmental Protection Agency ("EPA") recently
adopted regulations concerning discharges of storm water runoff. This program
requires covered facilities to obtain individual permits, participate in a group
or seek coverage under an EPA general permit. The Company believes that it will
be able to obtain, or be included under, such permits, where necessary, and to
make minor modifications to existing facilities and operations that would not
have a material effect on the Company.

     The Company has acquired leasehold interests in numerous properties that
for many years have produced natural gas and oil. Although the Company believes
that the previous owners of these interests have used operating and disposal
practices that were standard in the industry at the time, hydrocarbons or other
wastes may have been disposed of or released on or under the properties. In
addition, some of the Company's properties are operated by third parties over
whom the Company has no control. See "Item 7. Management's Discussion and
Analysis of Financial Condition and Results of Operations -- Other Matters" and
"-- Risk Factors -- Compliance with Environmental Regulations."


                                      - 8 -

<PAGE>   11


ITEM 2.     PROPERTIES

PRIMARY EXPLORATION PROVINCES

     Brigham focuses its 3-D seismic exploration efforts in natural gas and oil
producing provinces where it believes 3-D technology may be effectively applied
to generate relatively large potential reserve volumes per well and per field,
high potential production rates and multiple producing objectives. Brigham's
exploration activities are concentrated primarily in three core provinces: the
Anadarko Basin of western Oklahoma and the Texas Panhandle; the onshore Gulf
Coast of south Texas and, to a lesser extent, the transition zone of Louisiana;
and West Texas. Brigham is concentrating substantially all of its current 3-D
seismic and drilling activities on its natural gas projects in its Anadarko
Basin and Gulf Coast provinces primarily due to the continuation of historically
low oil prices which has made its inventory of potential drilling locations in
its West Texas province less economically attractive.

     Brigham has made significant investments in 3-D seismic and prospective
acreage in its Anadarko Basin and Gulf Coast provinces during the past three
years. Through these investments, the Company believes it has assembled an
inventory of potential drilling locations that will support a multi-year
drilling program, thereby providing attractive opportunities for long-term
growth. Based upon the interpreted portion of its 3-D seismic data as of
December 31, 1998, the Company estimates that it has identified approximately
700 potential undrilled locations within its three core exploration provinces.
From inception in 1990 through 1998, Brigham has achieved net drilling costs of
$0.82 per Mcfe added through its 3-D seismic exploration efforts. In addition,
over 500 of Brigham's estimated potential drilling locations are in its
currently active Anadarko Basin and Gulf Coast provinces where the Company has
achieved inception-to-date net drilling costs of $0.68 and $0.59 per Mcfe,
respectively. Furthermore, the Company estimates that approximately 800 square
miles of its 1,213 total square miles of 3-D seismic data acquired in 1998 had
either not been interpreted or only partially interpreted at December 31, 1998,
which should provide additional potential drilling locations.

     As a result of the Company's substantial investments to identify potential
drilling locations and its currently limited capital resources, Brigham intends
to devote substantially all of its efforts and available capital resources in
1999 to the drilling and monetization of its highest grade prospects identified
or to be identified from its over 5,000 square mile inventory of 3-D seismic
data. The Company's current 1999 capital budget is estimated to be $17.5
million, which represents a significant reduction from 1998 expenditures and its
previously anticipated 1999 levels in an effort to match Brigham's current and
expected future capital resources. The Company's budgeted 1999 capital
expenditures consist of approximately $10 million to drill an estimated 20 to 25
gross wells, $3.5 million for seismic and land costs (primarily previous
commitments and obligations to acquire 3-D data and acreage), and $4 million for
capitalized general and administrative expenses and other fixed asset
expenditures. Brigham expects that its 1999 drilling expenditures will be
allocated approximately 50% to its Anadarko Basin province and 50% to its Gulf
Coast province, and such expenditures will be devoted to the drilling of the
highest grade prospects in the Company's inventory of identified potential
drilling locations. Additionally, Brigham's 1999 drilling program will be
concentrated within trends where the Company has experienced exploration success
to date. Management believes that the Company has an attractive opportunity to
profitably drill its highest grade 3-D delineated locations due to its
historical drilling costs and the currently low cost drilling environment.
Therefore, management's goal is to access additional capital to further monetize
its prospect inventory. As a result, the Company's actual capital expenditures
in 1999 may differ significantly from these estimates based upon capital
availability during the year. See "Item 7. Management's Discussion and Analysis
of Financial Condition and Results of Operations -- Liquidity" and "-- Capital
Resources".

     Although the Company is interpreting 3-D seismic data within the provinces
discussed below and has identified an estimated 700 potential drilling locations
yet to be drilled in those provinces, there can be no assurance that any of the
remaining seismic data will be interpreted or will generate additional drilling
locations or that any potential drilling locations will be drilled at all or
within the expected time frame. The final determination with respect to the
drilling of any well, including those currently budgeted, will depend on a
number of factors, including (i) the results of exploration efforts and the
review and analysis of the seismic data, (ii) the availability of sufficient
capital resources by the Company and other participants for drilling prospects,
(iii) economic and industry conditions at the time of drilling, including
prevailing and anticipated prices for oil and natural gas and the availability
of drilling rigs and crews, (iv) the financial resources and results of the
Company and (v) the availability of leases on reasonable terms

                                      - 9 -

<PAGE>   12


and permitting for the potential drilling location. There can be no assurance
that the budgeted wells will, if drilled, encounter reservoirs of commercial
quantities of natural gas or oil.

Anadarko Basin

     The Anadarko Basin is a prolific natural gas province that the Company
believes offers a combination of lower risk exploration and development
opportunities in shallower horizons and deeper, higher potential objectives that
have been relatively under explored. This province has produced in excess of 90
Tcfe to date from numerous, historically elusive stratigraphic targets, such as
the Red Fork, Upper Morrow and Springer channel sands, as well as from deeper,
higher potential structural objectives, such the Lower Morrow sandstones and the
Hunton and Arbuckle carbonates. In some cases, these objectives have produced in
excess of 30 Bcf of natural gas from a single well at rates of up to 30 MMcf of
natural gas per day. In addition, drilling economics in the Anadarko Basin are
enhanced by the multi-pay nature of many of the prospects in this province, with
secondary or tertiary targets serving as either incremental value or bailout
potential relative to the primary target zone.

     Each of the stratigraphic and structural objectives in the Anadarko Basin
can provide excellent targets for 3-D seismic imaging. The Company has assembled
an extensive digital data base in this province, including geologic studies,
basin wide geologic tops, production data, well data, geographic data and over
8,400 miles of 2-D seismic data. Working with its team of in-house geologists
and supplemented by consulting geologists, the Company's explorationists
integrate this data with their extensive expertise and knowledge base to
generate 3-D projects in the Anadarko Basin.

     Following its initial 3-D seismic acquisition in the province in 1991 (12.5
square miles), the Company acquired 51 square miles of 3-D seismic in the
Anadarko Basin in 1993. Over the last several years the Company has accelerated
its activity in the Anadarko Basin, acquiring 151 square miles of 3-D seismic in
1994, 195 square miles in 1995, 457 square miles in 1996, 675 square miles in
1997 and 583 square miles in 1998. The Company retained a 75% average working
interest in its 1997 and 1998 Anadarko Basin 3-D seismic projects which
consisted of an aggregate of 1,258 square miles of 3-D seismic data.

     As of December 31, 1998, the Company had acquired 2,124 square miles (1.4
million acres) of 3-D seismic data in the Anadarko Basin, of which an estimated
300 square miles had either not been interpreted or only partially interpreted.
The Company does not currently intend to acquire additional 3-D seismic data in
this province in 1999. As of December 31, 1998, Brigham had completed 71 wells
in 95 attempts (75% success rate) in the Anadarko Basin and had found cumulative
net proved reserves of 48 Bcfe at an average net drilling cost of $0.68 per
Mcfe. In addition to its drilling activity in this province, the Company
acquired 21.5 Bcfe of net proved reserves in the Anadarko Basin in late 1997 at
a cost of $0.63 per Mcfe in an effort to capture additional prospects for future
potential drilling. In its Anadarko Basin drilling program in 1998, the Company
completed 27 wells in 40 attempts (68% success rate) with an average working
interest of 50%, resulting in the addition of 9.5 net Bcfe of proved reserves
(including revisions to prior years' estimates) at an average net drilling cost
of $1.93 per Mcfe. Brigham's Anadarko Basin net drilling costs per Mcfe in 1998
were negatively impacted by the unsuccessful drilling of several proved
undeveloped locations booked during 1997, particularly three high equity
interest direct offset locations to the Company's Christopher 84 #1 Lower Morrow
discovery in Hemphill County, Texas, and by several unsuccessful exploratory
wells with high equity interests that were drilled late in the year. Despite the
disappointing drilling costs realized in 1998, the Company has achieved average
net drilling costs of $0.68 per Mcfe in its Anadarko Basin province from 1994 to
1998. As of December 31, 1998, the Company had identified an estimated 430 3-D
delineated potential drilling locations in the Anadarko Basin, of which the
Company intends to drill 10 to 15 gross wells in 1999 with an estimated average
working interest of 40%.

     As part of its strategic initiatives to improve its capital resources and
liquidity in 1999, Brigham is currently marketing three producing property
packages among its Anadarko Basin province reserve base. These three packages
consist of proved reserves totaling approximately 41 net Bcfe as of December 31,
1998. The Company may or may not divest all or a portion these reserves,
depending primarily upon the offers received during the marketing process.


                                     - 10 -

<PAGE>   13





     Brigham intends to focus its 1999 exploration activities in its Anadarko
Basin province in the following key project areas:

     Arnett Project

     Brigham's Arnett Project covers approximately 129,000 acres in Ellis
County, Oklahoma, and targets Morrow and Hunton producing horizons at depths of
10,000 to 14,000 feet. In 1997 and 1998, the Company acquired 127 square miles
of 3-D seismic in the first three of four planned phases of this project.
Following seismic interpretation and initial prospect delineation on this data,
Brigham began drilling in the Arnett Project in late 1998. While two of the
first three exploration wells in this project were unsuccessful, the Company was
completing a fourth well in mid- March 1999 in the primary objectives, the
Hunton and Morrow, and has logged additional pay behind pipe in a secondary pay
zone, the Tonkawa. Successful completion and production results from this well
could provide offset development drilling opportunities particularly for the
Morrow which is productive in the immediate area. In mid- March 1999, a fifth
well was drilling in this project, also targeting the Hunton and Morrow as
primary objectives. Following the sale of a portion of its interest in this
project in early 1999, Brigham retains a 70% effective working interest in its
Arnett Project. See "Item 1. Business -- Industry Alliances -- Duke Project
Financing".

     Falcon Project

     Brigham's Falcon Project covers approximately 43,500 acres in the
northeastern portion of the Texas Panhandle in Lipscomb County, Texas. This
project is located in an area which produces from a number of Pennsylvanian-aged
sands, with primary targets in the Upper and Lower Morrow and secondary targets
in the shallower Tonkawa and Cleveland sands. The Upper and Lower Morrow zones
produce from horizons in the area at depths ranging from 9,000 to 12,000 feet.
The Falcon Project is located within a trend where Brigham has considerable
exploration history having acquired over 280 miles of 3-D seismic and discovered
over 37 Bcfe of gross reserves in the Upper and Lower Morrow reservoirs. Based
on this historical success, the Company acquired an additional 68 square miles
of 3-D seismic data in its Falcon Project during the second half of 1998 and has
already delineated several Upper and Lower Morrow prospects in the early stages
of interpretation. Brigham spud the first exploration well in its Falcon Project
in March 1999 to test a potentially significant Lower Morrow sand structural
feature with associated upside potential in the shallower Tonkawa sands. Based
on predrill estimates, gross unrisked reserve potential for this structural
prospect is over 5 Bcfe. Following the sale of a portion of its interest in this
project in early 1999, Brigham retains a 70% effective working interest in its
Falcon Project. See "Item 1. Business -- Industry Alliances -- Duke Project
Financing".

     Gold Project

     The Gold Project is located in Dewey and Blaine Counties, Oklahoma, and
targets dual natural gas producing objectives in the Morrow sandstones and
Hunton carbonates at depths of 9,500 to 11,500 feet. The initial acquisition of
89 square miles of 3-D seismic data covering the project acreage was completed
in 1996 and drilling activity commenced in 1998 resulting in two Hunton and one
Morrow discovery. The Thomas #2 well (Brigham 34% working interest) discovered
2.4 gross Bcfe of proved reserves in the Hunton formation at a depth of 11,450
feet and was producing 2.5 MMcf of natural gas per day in mid-March 1999. The
Thomas #2 is producing from a location which is believed to be associated with a
potentially larger Hunton natural gas accumulation which could lead to several
development locations. The Willie Porter #1 well (Brigham 34% working interest)
found 2.3 gross Bcfe of proved reserves in the Hunton formation at 12,250 feet
and was producing at a rate of 570 Mcf of natural gas per day in mid- March
1999. In late 1998, the Sturgeon State #1 (Brigham 34% working interest) was
completed in a Morrow sand zone and was producing 70 Bbls of oil per day in
mid-March 1999 before stimulation of the well. The Company and its participants
have a number of additional Hunton and Morrow locations, mostly extensional and
developmental in nature, planned for drilling in the Gold Project in 1999.
Brigham has a 37.5% working interest in its Gold Project.

     Huskie and Boilermaker Projects

     Brigham's Huskie and Boilermaker Projects consist of 103 and 96 square
miles, respectively, of continuous 3-D seismic data covering approximately
127,000 acres in Blaine County, Oklahoma. These projects target stratigraphic

                                     - 11 -

<PAGE>   14


sand channels in the Springer with additional stratigraphic sand objectives in
the Red Fork and Morrow in several identified prospects. Brigham initiated
acquisition of data in its Huskie Project in 1996 where it retained a 37.5%
working interest and, based upon the prospect density and reserve potential
interpreted from this initial data set, the Company subsequently acquired data
in its adjacent Boilermaker Project in 1998 where it retained a 100% working
interest. The Company assembled acreage over a number of potential drilling
locations in these project areas during 1998 and has at least one exploratory
well planned for each project in 1999. An exploratory well in the Huskie Project
will test a prospect with greater than 15 Bcfe of gross unrisked reserve
potential which is an extension to a prolific Springer channel that has produced
over 128 Bcfe of natural gas. Success from this initial exploratory well would
likely establish several development locations.

     Wildcat and Panther Projects

     The Company's Wildcat and Panther Projects consist of 50 and 99 square
miles, respectively, of continuous 3-D seismic data covering approximately
95,000 acres in the southern portion of the Texas Panhandle in Wheeler County,
Texas and Beckham County, Oklahoma. The primary exploration targets within these
projects are high potential, structural features at depths ranging from 7,500 to
21,000 feet. Brigham initiated acquisition of data in its Wildcat Project in
1997 where it retained a 37.5% working interest. Based upon the interpretation
of this initial data set, the Company subsequently acquired data in its adjacent
Panther Project in 1998 where it retained a 100% working interest. In its
Wildcat Project, the Company has a deep 21,000 foot exploratory well planned for
the second half of 1999 to drill an updip location to a Hunton well that has
produced over 14.5 Bcfe since 1981 and was still producing in mid-March 1999.
The Company believes successful completion of this exploratory test could prove
up an additional 27 Bcfe of remaining gross unrisked reserves in the attic of
this producing structure. Also in the second half of 1999, the Company plans to
drill a 7,500 foot test for 17 Bcfe of gross unrisked potential reserves in a
dual objective Brown Dolomite/Granite Wash structure.

     Chitwood Project

     Brigham's Chitwood Project consists of approximately 13 square miles of 3-D
seismic data located in the prolific Carter Knox anticline in Grady County,
Oklahoma. This project targets a mix of intermediate and deep prospects that
range from lower risk, development locations to higher risk, exploratory
objectives. Brigham initially entered this area with its 24 square mile West
Bradley Project acquired in 1994. In November 1997, the Company acquired an
interest in the producing Chitwood properties and undeveloped acreage which is
located adjacent to the West Bradley Project area. During 1998, as part of a
larger 142 square mile non-proprietary 3-D survey, Brigham and its project
participant acquired 13 square miles of 3-D seismic data over the entire
Chitwood Project, which led to the delineation of a number of prospects in the
Springer, Big Four, and Bromide that are developmental and extensional in
nature. In addition, the Company also imaged a large Arbuckle structure with in
excess of 100 Bcfe of gross unrisked reserve potential which has not been
optimally tested. The targeted objectives in the Chitwood Project range in depth
from 12,000 to 19,000 feet. In March 1999, the Company and its project
participant drilled the first well in the Chitwood Project based upon
interpretation of the recently acquired 3-D seismic data. The Chitwood
Boatwright Sand Unit #9 (Brigham working interest 50%) was completed in the
Springer formation at a depth of 11,970 feet and was testing 300 Bbls of oil and
500 Mcf gas per day in mid-March 1999. Brigham and its project participant have
delineated over 25 potential 3-D drilling locations among the four primary
objectives within the Chitwood Project. Brigham has retained a 50% working
interest in its Chitwood Project.

     As part of its strategic initiatives to raise capital for its 1999
exploration program, the Company is marketing its 50% working interest in
acreage and producing wells in the Chitwood Project. To the extent that the
Company does not receive adequate offers for its interest in this project,
Brigham may retain its interest and engage in further drilling of its identified
locations in the Chitwood Project during 1999.

Gulf Coast

     The onshore Gulf Coast region of Texas and South Louisiana is a high
potential, multi-pay province that lends itself to 3-D seismic exploration due
to its substantial structural and stratigraphic complexity. The Company has
assembled a digital data base including geographical, production, geophysical
and geological information that the

                                     - 12 -

<PAGE>   15


Company evaluates on its CAEX workstations. Working with a team of in-house
geologists supplemented by consultants, the Company integrates this data with
their extensive expertise and knowledge base to generate 3-D projects in the
Gulf Coast. The Company has assembled projects in the Expanded Wilcox and
Expanded Vicksburg trends in South Texas, the Miocene and Upper, Middle, and
Lower Frio trends of the mid-to-southern regions of Texas, and the Lower Miocene
trend in the transition zone of South Louisiana, each of which are active 3-D
seismic exploration trends.

     Brigham was attracted to the Gulf Coast province because of the opportunity
to apply the Company's established 3-D seismic exploration approach and its
staff's extensive Gulf Coast experience to a prolific, highly complex structural
province with potential to discover significant natural gas reserves and
production. The Company initiated its Gulf Coast effort in 1995 with the
acquisition of 39 square miles of seismic data in its Esperson Dome Project in
which the Company retained a small net profits interest that converts to a
variable back-in working interest of 12% to 20% upon project payout. Brigham's
exploration efforts in its Esperson Dome Project to date have yielded the
discovery of approximately 22 Bcfe of gross proved reserves from 11 wells,
mostly from objectives above 6,000 feet, with a number of prospects still
remaining to be drilled. Over the last three years the Company has accelerated
its activity in the Gulf Coast, acquiring 115 square miles of 3-D seismic in
1996, 404 square miles in 1997, and 590 square miles in 1998. The Company
retained a 77% average working interest in its Gulf Coast 3-D seismic projects
acquired from 1996 through 1998 which consisted of an aggregate of 1,109 square
miles of 3-D seismic data. Brigham anticipates that its increased project
assemblage and 3-D seismic acquisition activity in the Gulf Coast will result in
the allocation of a higher percentage of its drilling budget to this province in
1999, and will be a significant factor in the Company's future growth.

     A portion of Brigham's 3-D seismic data acquisition in the Gulf Coast has
been accomplished by the Company's participation in certain non-proprietary, or
speculative, seismic programs. By converting certain of the Company's
proprietary seismic projects in core exploration areas to speculative data, the
Company was able to leverage these proprietary projects for access to
substantially larger non-proprietary speculative data for minimal or no
additional cost to the Company. The Company believes this 3-D seismic
acquisition strategy in the Gulf Coast, in certain circumstances, can accelerate
the addition of attractive potential drilling locations in targeted trends at
costs that are considerably less than those associated with proprietary 3-D
seismic programs, thereby enhancing expected project rates of return.

     As of December 31, 1998, the Company had acquired 1,148 square miles
(734,720 acres) of 3-D seismic data in its Gulf Coast province, of which an
estimated 470 square miles had either not been interpreted or only partially
interpreted. The Company does not currently intend to acquire additional 3-D
seismic data in this province in 1999. As of December 31, 1998, Brigham had
completed 25 wells in 32 attempts (78% success rate) in the Gulf Coast and had
found cumulative proved reserves of 24 net Bcfe at an average net drilling cost
of $0.59 per Mcfe. In its Gulf Coast drilling program in 1998, the Company
completed 17 wells in 21 attempts with an average working interest of 59% adding
21 net Bcfe of proved reserves (including revisions to prior years' estimates)
at an average net drilling cost of $0.64 per Mcfe. As of December 31, 1998, the
Company had identified an estimated 120 3-D delineated potential drilling
locations in the Gulf Coast province, of which the Company intends to drill 10
gross wells in 1999 with an estimated average working interest of 55%.

     Brigham intends to focus its 1999 exploration activities in its Gulf Coast
province in the following key project areas:

     Diablo Project

     Brigham's Diablo Project covers 57 square miles in Brooks County, Texas,
and targets shallow Frio and deep Vicksburg producing horizons. The Company has
entered into a venture with a major integrated oil company that controls
adjoining acreage to explore on the combined acreage for potential below 10,000
feet in the Vicksburg formation. Brigham has retained a 34% working interest in
this joint exploration project. However, in prospective zones above 10,000 feet,
primarily the Frio, Brigham has retained a 100% working interest in its original
4,000 acre lease block. The Company initially acquired 25 square miles of
proprietary 3-D seismic in this project in 1997, and

                                     - 13 -

<PAGE>   16


acquired an additional 33 square miles in 1998 in its Diablo Project. The
Company and its participant control approximately 12,000 net acres of leasehold
in this project area.

     In the fourth quarter of 1998, Brigham made a potentially significant Lower
Vicksburg discovery in its Diablo Project with the completion of the Brigham
Palmer State #1 well (Brigham 33% working interest). The Palmer State #1 was
successfully completed in three of five possible Lower Vicksburg pay zones at a
depths ranging from 9,600 to 12,800 feet and had initially tested at a rate of
2.8 MMcf of natural gas and 668 Bbls of condensate per day. This discovery well
appears to be located on the downdip flank of a structure which exceeds 800
acres in closure and contains potential reserves exceeding 50 Bcfe. A minimum of
five potential development locations have been identified on the crest of the
structure which are updip to the Palmer State #1 discovery well, the first of
which is expected to spud in the late second or early third quarter of 1999. In
addition, the Company has identified a large, downthrown, four-way closure in an
adjacent fault block which has produced over 86 Bcfe from the Frio formation,
but which has not been tested in the equivalent Vicksburg sands that produce in
the Company's Palmer State #1 well. Brigham plans to spud an exploratory well to
test this high potential faulted closure in mid-1999.

     Southwest Danbury Project

     Located in Brazoria County, Texas, Brigham's Southwest Danbury Project is
an approximate 29 square mile 3-D project targeting a series of pressured Lower
Frio sands at depths ranging from 12,000 to 13,000 feet. In the first half of
1998, the Brigham Nold Gas Unit #1 (Brigham working interest 46%) was drilled to
a depth of approximately 12,700 feet to test a Lower Frio amplitude, or bright
spot, and encountered 29 feet of net pay in the Rucks interval of the Lower Frio
sands. This well has produced at an average daily rate of 2.6 MMcf of natural
gas with 17 Bbls of condensate and 13 Bbls of water since August 1998. Based on
the results from this initial well, the Company spud the Brigham Renn Gas Unit
#1 (Brigham working interest 83.5%) in December 1998 to test another Lower Frio
3-D bright spot prospect with over 6 Bcfe gross unrisked reserve potential. This
well reached total depth and was in the process of completing in late March
1999. In addition, Brigham is evaluating several additional Lower Frio prospects
in its Southwest Danbury Project which could expose the Company to significant
upside potential.

     Hawkins Ranch Project

     Brigham's Hawkins Ranch Project is a 160 square mile 3-D seismic program in
the Miocene/Frio trend located in Matagorda County, Texas. In 1998, the Company
acquired approximately 85 square miles of new proprietary 3-D seismic that was
converted to speculative data and merged with 65 square miles of adjacent
speculative 3-D data already in inventory. The Hawkins Ranch Project targets
potential in the shallow, nonpressured Miocene and Frio sands as well as the
deeper, pressured Frio sands. In addition to the shallow Miocene potential, the
Company has identified a number of prospects targeting deeper Frio objectives in
its Hawkins Ranch Project. The first exploratory Frio well is planned to spud
during the second half of 1999. This well is a 14,000 foot pressured test of a
500 acre structure with associated gross unrisked reserve potential exceeding 33
Bcfe. Brigham retains a 60% working interest in this project, following the sale
of a 15% interest in the project to an industry participant for $1.5 million in
early 1999.

     El Sauz Project

     In May 1997, Brigham initiated its El Sauz Project with a seismic option
covering approximately 94,000 acres in Willacy and Kennedy Counties, Texas. In
1998, the Company acquired 200 square miles of 3-D seismic data over this
acreage and sold a 45% working interest in the project to two industry
participants which provided the Company with significant carry on the
pre-seismic land and seismic acquisition costs of the project. The El Sauz
Project is an underexplored area which is bordered on three sides by Miocene and
Frio fields which have in aggregate produced over 740 Bcf of natural gas and 94
MMBbls of oil. Primary targets in the El Sauz Project are expected to be in
Miocene and Frio sands at depths of 4,500 to 10,000 feet, with additional
potential as deep as 18,000 feet in the Lower Frio. Reserve targets range from 5
to 20 Bcf per well. Three prospects are planned for drilling in 1999, two of
which target the Frio at depths of 9,300 feet and 9,800 feet and one of which is
a Miocene test at 4,500 feet. Brigham retained a 55% working interest in its El
Sauz Project.


                                     - 14 -

<PAGE>   17


West Texas

     The Company's limited drilling activity in the West Texas region in 1998
was focused in the Horseshoe Atoll, the Midland Basin and the Eastern Shelf of
the Permian Basin. Due to a combination of continuing low oil prices and less
than anticipated drilling results in its recent exploratory activity in this
province, the Company has ceased all 3-D seismic and drilling activities in its
West Texas projects and intends to focus substantially all of its exploration
efforts in 1999 on its predominately natural gas prospects in its Anadarko Basin
and Gulf Coast provinces. To the extent that oil prices improve in the future
from current levels, the Company would resume selective drilling of its
remaining undrilled locations in its West Texas province if such projects are
competitive with its Anadarko Basin and Gulf Coast projects based on estimated
risk adjusted, pre-drill economic return analysis.

     As of December 31, 1998, the Company had acquired 1,689 square miles (1.1
million acres) in the West Texas region, the vast majority of which has been
interpreted. The Company does not currently intend to acquire additional 3-D
seismic data in this province for the foreseeable future. As of December 31,
1998, Brigham had completed 185 wells in 298 attempts (62% success rate) with an
average working interest of 23% in its West Texas province and had found
cumulative proved reserves of 20 net Bcfe at an average net drilling cost of
$1.39 per Mcfe. In its West Texas drilling program in 1998, the Company
completed 6 wells in 11 attempts with an average working interest of 45% adding
0.5 net Bcfe of proved reserves (including revisions to prior years' estimates)
at an average net drilling cost of $9.06 per Mcfe. As of December 31, 1998, the
Company had an estimated 140 3-D delineated potential drilling locations in the
West Texas region. The Company does not currently plan to drill any wells in its
West Texas province in 1999.

NATURAL GAS AND OIL RESERVES

     The Company's estimated total net proved reserves of natural gas and oil as
of December 31, 1996, 1997 and 1998 and the present values attributable to these
reserves as of those dates were as follows:


<TABLE>
<CAPTION>
                                                     AS OF DECEMBER 31,
                                                ------------------------------
                                                 1996(1)     1997       1998
                                                --------   --------   --------
<S>                                             <C>        <C>        <C>   
Estimated net proved reserves:
    Natural gas (MMcf) .......................    10,257     53,230     71,166
    Oil (MBbls) ..............................     1,940      3,181      4,433
    Natural gas equivalent (MMcfe) ...........    21,897     72,316     97,764
Proved developed reserves as a percentage
    of proved reserves .......................        67%        65%        57%
Present Value of Future Net Revenues
    (in thousands) ...........................  $ 44,506   $ 69,249   $ 81,741
Standardized Measure (in thousands) ..........  $ 44,506   $ 64,274   $ 81,649
</TABLE>

- -------------------------

(1)      Prior to the Exchange consummated in February 1997, the Company was a
         partnership and not subject to income taxes. Had the Company been a
         taxable corporation at December 31, 1996, the Standardized Measure
         would have been $32.4 million, reflecting a pro forma estimate for the
         discounted value of future income taxes.

     The reserve estimates reflected above were prepared by Cawley, Gillespie &
Associates, Inc. ("Cawley Gillespie"), the Company's petroleum consultants, and
are part of reports on the Company's oil and natural gas properties prepared by
Cawley Gillespie. The base sales prices for the Company's reserves were $3.71
per Mcf for natural gas and $25.37 per Bbl for oil as of December 31, 1996,
$2.27 per Mcf for natural gas and $15.50 per Bbl for oil as of December 31,
1997, and $2.12 per Mcf for natural gas and $9.50 per Bbl for oil as of December
31, 1998. These base prices were adjusted to reflect applicable transportation
and quality differentials on a well-by-well basis to arrive at realized sales
prices used to estimate the Company's reserves at these dates.


                                     - 15 -

<PAGE>   18


     In accordance with applicable requirements of the SEC, estimates of the
Company's proved reserves and future net revenues are made using sales prices
estimated to be in effect as of the date of such reserve estimates and are held
constant throughout the life of the properties (except to the extent a contract
specifically provides for escalation). Estimated quantities of proved reserves
and future net revenues therefrom are affected by oil and natural gas prices,
which have fluctuated widely in recent years. There are numerous uncertainties
inherent in estimating oil and natural gas reserves and their estimated values,
including many factors beyond the control of the Company. The reserve data set
forth in this Form 10-K represents only estimates. Reservoir engineering is a
subjective process of estimating underground accumulations of oil and natural
gas that cannot be measured in an exact manner. The accuracy of any reserve
estimate is a function of the quality of available data and of engineering and
geologic interpretation and judgment. As a result, estimates of different
engineers, including those used by the Company, may vary. In addition, estimates
of reserves are subject to revision based upon actual production, results of
future development and exploration activities, prevailing oil and natural gas
prices, operating costs and other factors. The revisions may be material.
Accordingly, reserve estimates are often different from the quantities of oil
and natural gas that are ultimately recovered and are highly dependent upon the
accuracy of the assumptions upon which they are based. The Company's estimated
proved reserves have not been filed with or included in reports to any federal
agency. See "Item 7. Management's Discussion and Analysis of Financial Condition
and Results of Operations -- Risk Factors -- Uncertainty of Reserve Information
and Future Net Revenue Estimates."

     Estimates with respect to proved reserves that may be developed and
produced in the future are often based upon volumetric calculations and upon
analogy to similar types of reserves rather than actual production history.
Estimates based on these methods are generally less reliable than those based on
actual production history. Subsequent evaluation of the same reserves based upon
production history will result in variations in the estimated reserves that may
be substantial.

DRILLING ACTIVITIES

     The Company drilled, or participated in the drilling of, the following
number of wells during the periods indicated:


<TABLE>
<CAPTION>
                                                                               YEAR ENDED DECEMBER 31,
                                                                   1996                 1997                 1998
                                                           -------------------- -------------------- --------------------
                                                             GROSS       NET      GROSS       NET      GROSS       NET
                                                           --------- ---------- --------- ---------- --------- ----------
<S>                                                        <C>       <C>        <C>       <C>        <C>       <C> 
Exploratory Wells:
  Natural gas.............................................         5        1.2        15        6.5        30       15.6
  Oil.....................................................        22        5.2        21        7.9         7        2.5
  Non-productive .........................................        24        7.0        26        9.8        17        8.0
                                                           --------- ---------- --------- ---------- --------- ----------
     Total................................................        51       13.4        62       24.2        54       26.1
                                                           ========= ========== ========= ========== ========= ==========

Development Wells:
  Natural gas.............................................        10        1.3         4        1.6        10        6.6
  Oil.....................................................         5        1.0         5        1.6         3        1.5
  Non-productive .........................................         1        0.2         2        0.9         5        3.4
                                                           --------- ---------- --------- ---------- --------- ----------
     Total................................................        16        2.5        11        4.1        18       11.5
                                                           ========= ========== ========= ========== ========= ==========
</TABLE>


     The Company does not own any drilling rigs, and the majority of its
drilling activities have been conducted by industry participant operators or
independent contractors under standard drilling contracts. Consistent with its
business strategy, the Company has continued to retain operations of an
increasing number of the wells it drills. Brigham operated 57% of the gross and
76% of the net wells it participated in during 1998.


                                     - 16 -

<PAGE>   19





PRODUCTIVE WELLS AND ACREAGE

Productive Wells

     The following table sets forth the Company's ownership interest as of
December 31, 1998 in productive natural gas and oil wells in the areas
indicated.


<TABLE>
<CAPTION>
                                              NATURAL GAS              OIL                 TOTAL
                                            ---------------      ----------------     ---------------
PROVINCE                                    GROSS      NET       GROSS       NET      GROSS     NET
- --------                                    -----     -----      -----      -----     -----    ------
<S>                                         <C>       <C>        <C>        <C>       <C>      <C> 
Anadarko Basin............................     66      21.8         18        2.1        84      23.9
Gulf Coast................................     15       5.7          8        3.0        23       8.7
West Texas ...............................      4       1.0         86       24.5        90      25.5
Other.....................................     --        --          5        0.8         5       0.8
                                            -----     -----      -----     ------     -----    ------
     Total................................     85      28.5        117       30.4       202      58.9
                                            =====     =====      =====     ======     =====    ======
</TABLE>

     Productive wells consist of producing wells and wells capable of
production, including wells waiting on pipeline connection. Wells that are
completed in more than one producing horizon are counted as one well. Of the
gross wells reported above, none had multiple completions.

Acreage

     Undeveloped acreage includes leased acres on which wells have not been
drilled or completed to a point that would permit the production of commercial
quantities of oil and natural gas, regardless of whether or not such acreage
contains proved reserves. A gross acre is an acre in which an interest is owned.
A net acre is deemed to exist when the sum of fractional ownership interests in
gross acres equals one. The number of net acres is the sum of the fractional
interests owned in gross acres expressed as whole numbers and fractions thereof.
The following table sets forth the approximate developed and undeveloped acreage
in which the Company held a leasehold, mineral or other interest at December 31,
1998:


<TABLE>
<CAPTION>
                                         DEVELOPED          UNDEVELOPED           TOTAL
                                     -----------------  -------------------  ------------------
PROVINCE                              GROSS      NET      GROSS       NET      GROSS      NET
- --------                             --------  -------  ---------  --------  --------  --------
<S>                                    <C>      <C>       <C>        <C>      <C>        <C>   
Anadarko Basin......................   26,751   13,411    116,546    60,627   143,297    74,038
Gulf Coast..........................    1,041      447     23,300    16,822    24,341    17,269
West Texas .........................    6,570    1,898     18,740     7,919    25,310     9,817
Other...............................      520      148     48,189    18,105    48,709    18,253
                                     --------  -------  ---------  --------  --------  --------
   Total............................   34,882   15,904    206,775   103,473   241,657   119,377
                                     ========  =======  =========  ========  ========  ========
</TABLE>

     All the leases for the undeveloped acreage summarized in the preceding
table will expire at the end of their respective primary terms unless the
existing leases are renewed, production has been obtained from the acreage
subject to the lease prior to that date, or some other "savings clause" is
implicated. The following table sets forth the minimum remaining terms of leases
for the gross and net undeveloped acreage:


<TABLE>
<CAPTION>
                                                              ACRES EXPIRING
                                                        -------------------------
                                                          GROSS            NET
                                                        ---------       ---------
<S>                                                     <C>             <C>   
Twelve Months Ending:
   December 31, 1999..............................         58,205          28,464
   December 31, 2000..............................         60,347          26,998
   December 31, 2001..............................         68,759          41,222
   Thereafter.....................................         19,464           6,789
                                                        ---------       ---------
        Total.....................................        206,775         103,473
                                                        =========       =========
</TABLE>


                                     - 17 -

<PAGE>   20


     In addition, the Company had lease options as of December 31, 1998 to
acquire an additional 173,670 gross (128,166 net) acres, substantially all of
which expire within eighteen months.

VOLUMES, PRICES AND PRODUCTION COSTS

     The following table sets forth the production volumes, average prices
received and average production costs associated with the Company's sale of oil
and natural gas for the periods indicated.



<TABLE>
<CAPTION>
                                                       YEAR ENDED DECEMBER 31,
                                                       -----------------------
                                                        1996    1997     1998
                                                       ------  ------   ------
<S>                                                    <C>     <C>      <C>  
Production:
   Natural gas (MMcf) ...............................     698   1,382    4,269
   Oil (MBbls) ......................................     227     291      396
   Natural gas equivalent (MMcfe) ...................   2,060   3,126    6,644
Average sales price:
   Natural gas (per Mcf) ............................  $ 2.30  $ 2.56   $ 2.04
   Oil (per Bbl) ....................................    9.98   19.40    12.85
Average production expenses and taxes (per Mcfe) ....  $ 0.53  $ 0.55   $ 0.46
</TABLE>


COSTS INCURRED AND CAPITALIZED COSTS

     The costs incurred in oil and natural gas acquisition, exploration and
development activities are as follows (in thousands):


<TABLE>
<CAPTION>
                                                       YEAR ENDED DECEMBER 31,
                                                    -----------------------------
                                                      1996       1997      1998
                                                    --------   --------  --------
<S>                                                 <C>        <C>       <C>     
Cost incurred for the year:
   Exploration..................................... $ 10,527   $ 29,516  $ 67,110
   Property acquisition............................    6,195     26,956    16,245
   Development.....................................    1,328      2,953    10,427
   Proceeds from participants......................   (4,111)      (319)  (10,502)
                                                    --------   --------  --------
                                                    $ 13,939   $ 59,106  $ 83,280
                                                    ========   ========  ========
</TABLE>

     Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive reimbursement of certain costs from participants in its projects
subsequent to project initiation in return for an interest in the project. These
payments are described as "Proceeds from participants" in the table above.


ITEM 3.      LEGAL PROCEEDINGS

     The Company is not a party to any material legal proceedings.


ITEM 4.      SUBMISSION OF MATTERS TO A VOTE OF SECURITYHOLDERS

     No matter was submitted to a vote of the Company's securityholders during
the fourth quarter of 1998.


                                     - 18 -

<PAGE>   21


EXECUTIVE OFFICERS OF THE REGISTRANT

     Pursuant to Instruction 3 to Item 401(b) of the Regulation S-K and General
Instruction G(3) to Form 10-K, the following information is included in Part I
of this report.

     The following table sets forth certain information concerning the executive
officers of the Company as of March 31, 1999:

<TABLE>
<CAPTION>
             NAME            AGE                     POSITION
             ----            ---                     --------
<S>                          <C>      <C>
     Ben M. Brigham          39       Chief Executive Officer and President
     Jon L. Glass            43       Vice President--Exploration
     Craig M. Fleming        41       Chief Financial Officer
     David T. Brigham        38       Vice President--Land and Administration, Corporate Secretary
     A. Lance Langford       36       Vice President--Operations
     Karen E. Lynch          37       Vice President and General Counsel
</TABLE>

     Set forth below is a description of the backgrounds of the executive
officers of the Company.

     Ben M. "Bud" Brigham has served as Chief Executive Officer, President and
Chairman of the Board of the Company since founding the Company in 1990. From
1984 to 1990, Mr. Brigham served as an exploration geophysicist with Rosewood
Resources, an independent oil and gas exploration and production company. Mr.
Brigham began his career in Houston as a seismic data processing geophysicist
for Western Geophysical, a provider of 3-D seismic services, after earning his
B.S. in Geophysics from the University of Texas. Mr. Brigham is the husband of
Anne L. Brigham, Director, and the brother of David T. Brigham, Vice
President--Land and Administration and Corporate Secretary.

     Jon L. Glass joined the Company in 1992 and has served as Vice President --
Exploration since 1994 and a Director of the Company since 1995. From 1984 to
1992, Mr. Glass served in various capacities with Santa Fe Minerals, an oil and
gas exploration company, in a variety of staff and managerial positions mainly
focused on Santa Fe Minerals' exploration activities in the midcontinent and
Gulf of Mexico (onshore and offshore). During this time Mr. Glass also assisted
in the development of exploration and acquisition opportunities for Santa Fe
Minerals in Canada and South America. Mr. Glass' early geological experience
includes three years with Mid-America Pipeline Company and two years with Texaco
USA, serving mainly as a midcontinent exploration geologist. Mr. Glass holds a
B.S. and an M.S. in Geology from Oklahoma State University and an M.B.A. from
the University of Tulsa.

     Craig M. Fleming has served as the Chief Financial Officer of the Company
since 1993. From 1990 to 1993, Mr. Fleming served as Controller of Odyssey
Petroleum Co., Ltd., an independent energy company. From 1988 to 1990, Mr.
Fleming served as Controller and Treasurer for Harken Exploration Company, an
independent energy company. Mr. Fleming began his career with Arthur Anderson &
Co. in the Oil and Gas Audit Division and is a Certified Public Accountant. Mr.
Fleming holds a B.B.A. in Accounting from Texas A&M University.

     David T. Brigham joined the Company in 1992 and has served as Vice
President -- Land and Administration and Corporate Secretary of the Company
since February 1998. Mr. Brigham served as Vice President -- Legal of the
Company from 1994 until February 1998. From 1987 to 1992, Mr. Brigham was an oil
and gas attorney with Worsham, Forsythe, Sampels & Wooldridge. Before attending
law school, Mr. Brigham was a landman for Wagner & Brown Oil and Gas Producers,
an independent oil and gas exploration and production company. Mr. Brigham holds
a B.B.A. in Petroleum Land Management from the University of Texas and a J.D.
from Texas Tech School of Law. Mr. Brigham is the brother of Ben M. Brigham,
Chief Executive Officer, President and Chairman of the Board.

     A. Lance Langford joined the Company as Manager of Operations in 1995 and
has served as Vice President -- Operations since January 1997. From 1987 to
1995, Mr. Langford served in various engineering capacities with Meridian Oil
Inc., handling a variety of reservoir, production and drilling responsibilities.
Mr. Langford holds a B.S. in Petroleum Engineering from Texas Tech University.

                                     - 19 -

<PAGE>   22





     Karen E. Lynch joined the Company in October 1997 as General Counsel and
has served as Vice President -- Legal and General Counsel of the Company since
February 1998. Prior to joining the Company, Ms. Lynch was a shareholder in the
Dallas-based law firm of Thompson & Knight, P.C., where she practiced in the
energy area since joining the firm in 1987. Ms. Lynch holds a B.B.A. in
Petroleum Land Management from the University of Texas and a J.D. from the
University of Oklahoma.

                                     PART II

ITEM 5.      MARKET FOR REGISTRANT'S COMMON EQUITY AND RELATED STOCKHOLDER
             MATTERS

     The Company's Common Stock (the "Common Stock") has been publicly traded on
The Nasdaq Stock Market(sm) under the symbol "BEXP" since the Company's initial
public offering effective May 8, 1997. The following table summarizes the high
and low last reported sales prices on Nasdaq for each quarterly period since the
Company's initial public offering:


<TABLE>
<CAPTION>
                                                                 COMMON STOCK
                                                               -----------------
                                                                HIGH       LOW
                                                               -------   -------
<S>                                                            <C>       <C>    
1997:
Second Quarter (from May 9, 1997)............................. $  8.75   $  7.00
Third Quarter................................................. $ 14.31   $  8.25
Fourth Quarter................................................ $ 17.13   $ 12.00

1998:
First Quarter................................................. $ 14.00   $ 10.50
Second Quarter................................................ $ 15.50   $  8.75
Third Quarter................................................. $ 10.25   $  5.13
Fourth Quarter................................................ $  9.50   $  4.75
</TABLE>



     The closing market price of the Company's Common Stock on March 26, 1999
was $3.50 per share. As of March 26, 1999, the Company estimates that there were
more than 80 record and 1,100 beneficial owners of the Company's Common Stock.

     No dividends have been declared or paid on the Company's Common Stock to
date. The Company intends to retain all future earnings for the development of
its business. In addition, the Credit Facility (as defined) and the Indenture
(as defined) restrict the Company's ability to pay dividends on the Company's
Common Stock.


                                     - 20 -

<PAGE>   23


ITEM 6.      SELECTED FINANCIAL DATA

     The following selected consolidated financial data should be read in
conjunction with "Item 7. Management's Discussion and Analysis of Financial
Condition and Results of Operations" and the Company's consolidated financial
statements and related notes included in "Item 8. Financial Statements and
Supplementary Data."


<TABLE>
<CAPTION>
                                                                    YEAR ENDED DECEMBER 31,
                                                      ----------------------------------------------------
STATEMENT OF OPERATIONS DATA:                           1994     1995      1996      1997          1998
                                                      --------  -------  --------  --------      ---------
<S>                                                   <C>       <C>      <C>       <C>           <C>      
     Revenues:
     Natural gas and oil sales....................... $  2,565  $ 3,578  $  6,141  $  9,184      $  13,799
     Workstation revenue.............................      815      635       627       637            390
                                                      --------  -------  --------  --------      ---------
         Total revenues..............................    3,380    4,213     6,768     9,821         14,189

     Costs and expenses:
     Lease operating.................................      491      761       726     1,151          2,172
     Production taxes................................      126      165       362       549            850
     General and administrative......................    1,785    1,897     2,199     3,570          4,672
     Depletion of oil and natural gas properties....      1,104   1,626     2,323     2,743          8,410
     Capitalized ceiling impairment.................       --        --        --        --         24,847
     Depreciation and amortization ..................      561      533       487       694            785
                                                      --------  -------  --------  --------      ---------
         Total costs and expenses....................    4,067    4,982     6,097     8,707         41,736
                                                      --------  -------  --------  --------      ---------

     Operating income (loss).........................     (687)    (769)      671     1,114        (27,547)

     Other income (expense):
     Interest income.................................       56      128        52       145            136
     Interest expense................................     (668)    (936)   (1,173)   (1,190)        (7,120)
                                                      --------  -------  --------  --------      ---------
         Total other income (expense)................     (612)    (808)   (1,121)   (1,045)        (6,984)

     Net income (loss) before income taxes...........   (1,299)  (1,577)     (450)       69        (34,531)
     Income tax expense, net.........................     --         --        --    (1,186)(1)      1,186
                                                      --------  -------  --------  --------      ---------
         Net loss.................................... $ (1,299) $(1,577) $   (450) $ (1,117)(1)  $ (33,345)
                                                      ========  =======  ========  ========      =========

     Net loss per share.............................. $  (0.15) $ (0.18) $  (0.05) $  (0.10)     $   (2.64)
                                                      ========  =======  ========  ========      =========

     Weighted average common shares outstanding......    8,929    8,929     8,929    11,081         12,626

STATEMENT OF CASH FLOWS DATA:
     Net cash provided by operating activities....... $    626  $ 1,383  $  3,710  $  9,806      $  13,622
     Net cash used in investing activities...........   (5,463)  (8,005)  (11,796)  (57,300)       (85,075)
     Net cash provided by financing activities.......    4,634    7,724     7,731    47,748         72,321

OTHER FINANCIAL DATA:
     Capital expenditures............................ $  5,445  $ 7,935  $ 13,612  $ 57,170      $  84,055
</TABLE>


<TABLE>
<CAPTION>
                                                                  AS OF DECEMBER 31,
                                                 ---------------------------------------------------
                                                   1994      1995       1996       1997       1998
                                                 -------   --------   --------   --------   --------
<S>                                              <C>       <C>        <C>        <C>        <C>     
BALANCE SHEET DATA:
     Cash and cash equivalents ..............    $   700   $  1,802   $  1,447   $  1,701   $  2,569
     Oil and natural gas properties, net ....     11,970     18,538     28,005     84,294    134,317
     Total assets ...........................     15,781     22,916     33,614     92,519    150,516
     Total debt .............................      7,950     16,000     24,000     32,000     94,786
     Total equity ...........................      5,271      3,694      3,244     43,313     24,681
</TABLE>


(1)      Includes a net $1.2 million ($0.10 per share) non-cash deferred income
         tax charge related to the Company's conversion from a partnership to a
         corporation in 1997.


                                     - 21 -

<PAGE>   24


ITEM 7.      MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
             RESULTS OF OPERATIONS

OVERVIEW

     The Company is an independent exploration and production company that
applies 3-D seismic imaging and other advanced technologies to systematically
explore and develop onshore oil and natural gas provinces in the United States.
From inception in 1990 through December 31, 1998, Brigham acquired 5,236 square
miles of 3-D seismic data, identified an estimated 1,140 potential drilling
locations and drilled 442 wells delineated by 3-D seismic analysis. Through its
3-D seismic-based drilling efforts, the Company had discovered an aggregate of
92 Bcfe of net proved reserves as of December 31, 1998. The Company believes
this performance demonstrates a systematic methodology for finding oil and
natural gas in onshore domestic oil and natural gas provinces.

     Combining its geologic and geophysical expertise with a sophisticated land
effort, the Company manages the majority of its projects from conception through
3-D acquisition, processing and interpretation and leasing. In addition, the
Company manages the negotiation and drafting of most of its geophysical
exploration agreements, resulting in reduced contract risk and more consistent
deal terms. Because it generates most of its projects, the Company can control
the size of the working interest that it retains as well as the selection of the
operator and the non-operating participants. Consistent with its business
strategy, Brigham has increased the working interest it retained in its
projects, based on capital availability and perceived risk. The Company's
average working interest in its 3-D seismic projects acquired during 1996, 1997
and 1998 was 37%, 67% and 80%, respectively, while its average working interest
in its wells drilled during this period was 24%, 39% and 52%, respectively.
Beginning in 1995, the Company has managed operations through the drilling and
production phases on an increasing portion of its 3-D seismic projects. Brigham
operated 57% of its gross wells and 76% of its net wells drilled in 1998 as
compared with 10% of its gross wells and 16% of its net wells drilled in 1996.

     Expenditures made in oil and natural gas exploration vary from project to
project depending primarily on the costs related to land, seismic acquisition,
drilling costs and the working interest retained by the Company. Historically,
the Company's participants have typically borne a disproportionate share of the
costs of optioning available acreage and acquiring, processing and interpreting
the 3-D seismic data, and the Company and its participants each typically
incurred leasing, drilling and completion costs in proportion to their ownership
interests. In recent years, Brigham has retained majority working interests in
its new 3-D seismic projects, and has thereby reduced the financial leverage it
has historically received on the costs of optioning available acreage and
acquiring, processing and interpreting the 3-D seismic data on its projects.

     From inception through 1996, the Company acquired 2,761 gross (781 net)
square miles of 3-D seismic data. Initially, the Company focused its efforts in
West Texas. In 1995, the Company began to devote substantial attention to the
Anadarko Basin, and since 1996 the Company has devoted the majority of its
resources to the Anadarko Basin and Gulf Coast. With this shift in regional
focus, the majority of the Company's production volumes has shifted from oil to
natural gas. To finance these project generation and drilling activities, the
Company supplemented cash flow from operations with private placements of debt
and equity, commercial bank credit facilities and placements of working
interests in projects with industry participants. As the Company's cash flows
from operations and other sources of capital have increased during this period,
it retained larger average working interests in its projects.

     In 1997 and 1998, the Company acquired 2,475 gross (1,810 net) square miles
of 3-D seismic and continued to focus the majority of its 3-D exploration
efforts in the Anadarko Basin and the Gulf Coast. During the past two years, the
Company acquired 1,258 square miles (51%) of 3-D seismic in the Anadarko Basin,
making this basin the most active 3-D seismic acquisition province for the
Company. Brigham also significantly increased its Gulf Coast activity, acquiring
994 square miles (40%) of 3-D seismic in this period. During 1997 and 1998, the
Company drilled 145 gross (65.9 net) wells based on its 3-D seismic data
analysis. In addition to its drilling activities, the Company acquired 21.3 net
Bcfe of proved reserves and an interest in undeveloped acreage (the "Chitwood
Acquisition") at the northern end of the Carter Knox anticline in Grady County,
Oklahoma for $13.4 million in November 1997. As a result of these activities,
the Company's net natural gas and oil production increased from 2.1 Bcfe in 1996
to 6.6 Bcfe

                                     - 22 -

<PAGE>   25


in 1998. The Company's net production volumes consisted of 79% natural gas on an
equivalent basis during the fourth quarter 1998 as compared with 36% during the
fourth quarter 1996. The Company supplemented cash flow from operations in 1997
and 1998 with borrowings under commercial bank credit facilities, $24 million
raised in its initial public offering of common stock in May 1997, $47.5 million
raised through the placement of debt and equity securities in August 1998 and
the placement of working interests in projects to industry participants to
finance its project generation, property acquisition and drilling activities.

     The Company uses the full-cost method of accounting for its natural gas and
oil properties. Under this method, all acquisition, exploration and development
costs, including certain internal costs that are directly attributable to the
Company's acquisition, exploration and development activities, are capitalized
in the amortizable base of the "full-cost pool" as incurred. Upon the
interpretation by the Company of the 3-D seismic associated with unproved
properties, the geological and geophysical costs of acreage that is not
specifically identified as prospective are transferred to the amortizable base
of the full-cost pool. Geological and geophysical costs associated with
prospective acreage, as well as leasehold costs, are transferred to the
amortizable base of the full-cost pool when the prospects are drilled. The
Company records depletion of its full-cost pool using the unit of production
method.

     To the extent that the costs capitalized in the full-cost pool (net of
depreciation, depletion and amortization and related deferred taxes) exceed the
present value (using a 10% discount rate and based on period-end natural gas and
oil prices) of estimated future net after-tax cash flows from proved natural gas
and oil reserves plus the capitalized cost of unproved properties, such costs
are charged to operations as a writedown of the carrying value of natural gas
and oil properties, or a "capitalized ceiling impairment" charge. The risk that
the Company will be required to write down the carrying value of its oil and gas
properties increases when oil and gas prices are depressed, even if such prices
are temporary. In addition, capitalized ceiling impairment charges may occur if
the Company experiences poor drilling results or has substantial downward
revisions in its estimated proved reserves. A capitalized ceiling impairment is
a charge to earnings that does not impact cash flows, but does impact operating
income and stockholders' equity. Once incurred, a capitalized ceiling impairment
charge to natural gas and oil properties cannot be reversed at a later date.
Primarily as a result of the significant declines in both oil and natural gas
prices at December 31, 1998 and disappointing drilling results on several of the
Company's high working interest wells in 1998, the Company recorded a
capitalized ceiling impairment charge at December 31, 1998 of $24.8 million (see
Note 2 of Notes to the December 31, 1998 Consolidated Financial Statements). No
assurance can be given that the Company will not experience a capitalized
ceiling impairment charge in future periods. See "-- Risk Factors -- Dependence
on Exploratory Drilling Activities"; "-- Risk Factors -- Volatility of Natural
Gas and Oil Prices"; and " -- Risk Factors -- Uncertainty of Reserve Information
and Future Net Revenue Estimates."

     In connection with the Exchange in 1997, the Company issued options to
purchase 644,097 shares of Common Stock to certain of its officers and
employees. The Company recorded an unearned stock compensation balance of $2.5
million in the first quarter 1997, of which approximately one-half will be added
to the amortizable base of the full-cost pool over the vesting period of the
options and the balance will be recorded as a noncash compensation expense over
the vesting period of the options. As a result, the Company expects to incur
unearned stock compensation amortization expenses of approximately $189,000 in
1999, $115,800 in 2000 and an aggregate of $111,000 in the three years
thereafter.

     The Company's predecessor was classified as a partnership for federal
income tax purposes. Therefore, no income taxes were paid or provided for by the
Company prior to the Exchange. The Company is a taxable entity. In connection
with the Exchange on February 27, 1997, the Company incurred a $5 million charge
to record a deferred income tax liability to recognize the differences between
the financial statement basis and tax basis of the Company's predecessor
partnership's natural gas and oil properties at the Exchange date, given the
provisions of enacted tax laws. During the fourth quarter 1997, the Company
elected to record a step-up in the basis of its assets for tax purposes as a
result of the Exchange. Due to this election, the Company recorded a $3.8
million non-cash deferred income tax benefit during the fourth quarter 1997,
which resulted in a net $1.2 million ($0.10 per dividend share) non-cash
deferred income tax charge for the year ended December 31, 1997.


                                     - 23 -

<PAGE>   26


RESULTS OF OPERATIONS

     The following table sets forth certain operating data for the periods
presented.


<TABLE>
<CAPTION>
                                                           YEAR ENDED DECEMBER 31,
                                                        ----------------------------
                                                         1996       1997      1998
                                                        -------    ------    -------
<S>                                                     <C>        <C>       <C>  
Production:
     Natural gas (MMcf) .............................       698     1,382      4,269
     Oil (MBbls) ....................................       227       291        396
     Natural gas equivalent (MMcfe) .................     2,060     3,126      6,644
     % Natural gas ..................................        34%       44%        64%
Average sales prices per unit (1):
     Natural gas (per Mcf) ..........................   $  2.30    $ 2.56    $  2.04
     Oil (per Bbl) ..................................     19.98     19.40      12.85
     Natural gas equivalent (per Mcfe) ..............      2.98      2.94       2.08
Costs and expenses per Mcfe:
     Lease operating ................................   $  0.35    $ 0.37    $  0.33
     Production taxes ...............................      0.18      0.18       0.13
     General and administrative .....................      1.07      1.14       0.70
     Depletion of natural gas and oil properties ....      1.13      0.88       1.27
</TABLE>

- ---------------

(1)      Reflects the effects of the Company's hedging activities. See "Item 7.
         Management's Discussion and Analysis of Financial Condition and Results
         of Operations -- Other Matters -- Hedging Activities."

Year Ended December 31, 1998 Compared to Year Ended December 31, 1997

     Natural gas and oil sales. Natural gas and oil sales increased 50% from
$9.2 million in 1997 to $13.8 million in 1998. Production volume increases
accounted for $9.4 million (204%) of this increase and were offset by $4.8
million (104%) from a decrease in the average sales price received for natural
gas and oil sales. Production volumes for natural gas increased 209% from 1,382
MMcf in 1997 to 4,269 MMcf in 1998. The average price received for natural gas
decreased 20% from $2.56 per Mcf in 1997 to $2.04 per Mcf in 1998. Production
volumes for oil increased 36% from 291 MBbls in 1997 to 396 MBbls in 1998. The
average price received for oil decreased 34% from $19.40 per Bbl in 1997 to
$12.85 per Bbl in 1998. Natural gas and oil sales in 1998 were increased by
production from wells completed and flowing to sales since December 31, 1997,
offset partially by the natural decline of existing production, and from certain
wells acquired in the Chitwood Acquisition which were included in the Company's
results of operations effective September 1, 1997. As a result of hedging
activities, natural gas revenues increased by $555,240 ($0.13 per Mcf) in 1998,
compared to a decrease in oil revenues of $6,191 ($0.02 per Bbl) in 1997. See
"-- Other Matters -- Hedging Activities."

     Workstation revenue. Workstation revenue decreased 39% from $637,000 in
1997 to $390,000 in 1998. Workstation revenue is recognized by the Company as
industry participants in the Company's seismic programs are charged an hourly
rate for the work performed by the Company on its 3-D seismic interpretation
workstations. This decrease is primarily attributable to the Company's increased
working interests in its recently acquired 3-D seismic data, which reduces the
amount of workstation interpretation costs that the Company can bill to its
participants. The Company expects workstation revenue to continue to decline in
1999 due to the Company's increased working interests in the square miles of 3-D
seismic it acquired in 1997 and 1998.

     Lease operating expenses. Lease operating expenses increased 89% from $1.2
million ($0.37 per Mcfe) in 1997 to $2.2 million ($0.33 per Mcfe) in 1998. This
increase was primarily due to an increase in the number of producing wells
during 1998 from those in 1997. The decrease in the per unit amount was
primarily due to an increase in natural gas production as a percentage of total
equivalent production (44% in 1997 and 64% in 1998) since a typical natural gas
well produces with lower average lease operating costs per unit of production
than a typical oil well.


                                     - 24 -

<PAGE>   27





     Production taxes. Production taxes increased 55% from $549,000 ($0.18 per
Mcfe) in 1997 to $850,000 ($0.13 per Mcfe) in 1998 as a direct result of
increased production volumes. The effective average production tax rate
increased from 6% of natural gas and oil sales revenues in 1997 to 6.2% in 1998
due to the increase in natural gas production as a percentage of total
equivalent production as natural gas is typically burdened with higher
production tax rates than oil. The decrease in the per unit amount was primarily
attributable to the decline in natural gas and oil sales prices in 1998 as
compared with 1997.

     General and administrative expenses. General and administrative expenses
increased 31% from $3.6 million ($1.14 per Mcfe) in 1997 to $4.7 million ($0.70
per Mcfe) in 1998. This increase was primarily attributable to the hiring of
additional personnel and related expenses necessary to manage the Company's
growing operations. The decrease in the per unit rate was a result of a greater
increase in natural gas and oil production volumes than general and
administrative expenses from 1997 to 1998 due to the aforementioned factors. The
Company has initiated an overhead reduction plan during 1999, consisting
primarily of a Company-wide salary reduction beginning in the second quarter of
1999 and the elimination or reduction of various other discretionary
administrative expenditures. The Company plans to continue to evaluate its
overhead cost structure during the course of 1999 and may take further steps to
reduce its administrative expenses depending upon the outcome of its various
strategic initiatives underway to improve its capital resources and liquidity.

     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 207% from $2.7 million ($0.88 per Mcfe) in 1997 to $8.4
million ($1.27 per Mcfe) in 1998. Of this increase, $4.5 million was
attributable to the increase in production volumes during the period and $1.2
million was due to the increase in the depletion rate per unit of production.
The increase in depletion rate per unit of production was primarily the result
of the addition of natural gas and oil reserves at higher average capital costs
due to a reduction in drilling performance and downward revisions to previous
reserve estimates.

     Interest expense. Interest expense increased from $1.2 million in 1997 to
$7.1 million in 1998 due to the Company's higher average outstanding debt
balance in 1998 combined with a higher average effective interest rate. The
Company's weighted average outstanding debt balance increased 450% from $12
million in 1997 to $66 million in 1998. This increase in debt was incurred
primarily to fund the Company's increased capital expenditures and working
capital needs, net of operating cash flow, during 1998. The effective annual
interest rate on the Company's outstanding indebtedness increased from 9.4% in
1997 to 10.6% in 1998, primarily due to the Company's issuance of $40 million of
Senior Subordinated Secured Notes due 2003 (the "Subordinated Notes") in August
1998, which bore interest at an annual rate of 12% from the date of issuance. In
addition, interest expense in 1998 included (i) approximately $1 million of
non-cash charges related to the amortization of deferred loan fees and the
amortization of discount on the Subordinated Notes, and (ii) $507,000 of
interest expenses related to the Subordinated Notes that was paid through the
issuance of additional Subordinated Notes in lieu of cash in February 1999.
Pursuant to the recently amended terms of the Credit Facility and the
Subordinated Notes, the Company expects to pay its interest obligations related
to the Subordinated Notes in 1999 through the issuance of additional
Subordinated Notes in lieu of cash in an effort to preserve cash flow to fund
capital expenditures and working capital. Borrowings under the Company's
commercial bank credit facility had an effective annual interest rate of 7.2% at
December 31, 1998. See "-- Liquidity" and "-- Capital Resources."

Year Ended December 31, 1997 Compared to Year Ended December 31, 1996

     Natural gas and oil sales. Natural gas and oil sales increased 50% from
$6.1 million in 1996 to $9.2 million in 1997. Production volume increases
accounted for $3.2 million (104%) of this increase and were offset by $134,000
(4%) from a decrease in the average sales price received for natural gas and oil
sales. Production volumes for natural gas increased 98% from 698,036 Mcf in 1996
to 1,381,996 Mcf in 1997. The average price received for natural gas increased
11% from $2.30 per Mcf in 1996 to $2.56 per Mcf in 1997. Production volumes for
oil increased 28% from 226,925 Bbls in 1996 to 290,624 Bbls in 1997. The average
price received for oil decreased 3% from $19.98 per Bbl in 1996 to $19.40 per
Bbl in 1997. Natural gas and oil sales were increased by production from 46
wells completed in 1997, which was partially offset by the natural decline of
existing production. Hedging activities in 1997 reduced the amount by which oil
revenues increased by $6,191, compared to a decrease in oil revenues of $301,280
as a result of hedging activities in 1996.

                                     - 25 -

<PAGE>   28





     Workstation revenue. Workstation revenue increased 2% from $627,000 in 1996
to $637,000 in 1997. Workstation revenue is recognized by the Company as
industry participants in the Company's seismic programs are charged an hourly
rate for the work performed by the Company on its 3-D seismic interpretation
workstations.

     Lease operating expenses. Lease operating expenses increased 59% from
$726,000 ($0.35 per Mcfe) in 1996 to $1.2 million ($0.37 per Mcfe) in 1997. The
increase was primarily due to an increase in producing wells during the year.

     Production taxes. Production taxes increased 52% from $362,000 ($0.18 per
Mcfe) in 1996 to $549,000 ($0.18 per Mcfe) in 1997 as a direct result of
increased production volumes. The effective average production tax rate remained
unchanged at 6% of natural gas and oil sales revenues for each period.

     General and administrative expenses. General and administrative expenses
increased 62% from $2.2 million ($1.07 per Mcfe) in 1996 to $3.6 million ($1.14
per Mcfe) in 1997. Approximately $300,000 of the increase in 1997 resulted from
nonrecurring expenses related to the Company's relocation of its corporate
headquarters from Dallas, Texas to Austin, Texas, and the balance was primarily
attributable to the hiring of additional personnel and related expenses
necessary to manage the Company's growing operations. The increase in the per
unit rate was a result of a greater increase in aggregate general and
administrative expenses than natural gas and oil production volumes from 1996 to
1997 due to the aforementioned factors.

     Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased 18% from $2.3 million ($1.13 per Mcfe) in 1996 to $2.7
million ($0.88 per Mcfe) in 1997 as a result of higher production volumes.
The per unit amount decreased due to the addition of proved reserves during
1997.

     Interest expense. Interest expense was essentially unchanged from 1996 to
1997 as the Company's lower average outstanding debt balance in 1997 was offset
by a higher effective average interest rate. The weighted average outstanding
debt balance decreased 39% from $19.7 million in 1996 to $12 million in 1997.
The effective interest rate increased 83% from 5.7% in 1996 to 10.5% in 1997.
The decrease in the weighted average outstanding debt balance and increase in
the effective average interest rate resulted primarily from the conversion to
equity of privately placed 5% notes in February 1997, the retirement of $13.3
million of borrowings under its previous credit facility in connection with the
Company's May 1997 initial public offering, and $32 million of borrowings
incurred under its previous credit facility subsequent to the Company's initial
public offering to fund the Company's increased exploration activity and its
$13.5 million acquisition of properties from Mobil adjacent to its West Bradley
3-D Project area. The Company's previous credit facility had an effective
interest rate of 8.8% at December 31, 1997.

LIQUIDITY

     Despite the Company's success in building its inventory of 3-D seismic data
and potential drilling locations, a number of key factors have recently
contributed to significantly limit the Company's capital resources available to
fund its continued long-term growth-oriented exploration strategy. Management
believes these principal factors include: (i) lower commodity sales prices,
which reduced revenues and cash flow from the Company's production volumes, (ii)
reduced access to public, private and industry sources of capital on
cost-effective terms due to the continuing low commodity price environment and
outlook, (iii) less than anticipated success in placing working interests with
industry or financial participants in certain of its high equity interest
projects, resulting in lower levels of project cost recoupment than budgeted,
(iv) high levels of expenditures for 3-D seismic and land activities that do not
generate proved reserves and cash flow until the drilling stage of the project
cycle, (v) the utilization of high levels of debt to fund its accelerating
exploration expenditures, and (vi) disappointing drilling results during 1998 on
a number of high equity interest exploratory and development wells, several of
which were completed and subsequently plugged and abandoned or otherwise
performed below expectations.

     As a result of these limiting factors and an expectation for continuing
difficult industry and capital markets conditions, Brigham has substantially
reduced its planned capital budget for 1999 and has undertaken a number of
strategic initiatives in an effort to improve and preserve its capital liquidity
in the current environment. While the Company remains focused on its long-term
growth objectives and the continuation of its established business model

                                     - 26 -

<PAGE>   29


for 3-D seismic-based exploration, Brigham has adapted its business strategy in
the near-term in an effort to maximize value for its shareholders on a long-term
basis through the implementation of the following principal strategic
initiatives: (i) focusing all of the Company's planned exploration efforts in
1999 toward the drilling of its highest- grade 3-D prospects identified in its
Anadarko Basin and Gulf Coast projects, concentrated primarily in trends where
Brigham has achieved exploration success, (ii) eliminating substantially all
planned seismic and land expenditures for new projects until its capital
resources can support such additional activity, (iii) seeking to divest certain
producing natural gas and oil properties in an effort to raise capital to reduce
debt borrowings and to redirect capital to drilling projects that have the
potential to generate higher investment returns, (iv) restructuring its
outstanding senior and subordinated debt agreements to provide the Company with
flexibility needed to preserve cash flow to fund its expected near-term
exploration activities, (v) implementing an overhead reduction plan to reduce
general and administrative expenses, and (vi) evaluating opportunities to raise
additional equity capital either through the sales of interests in certain of
its seismic projects or the issuance of equity securities. The Company believes
that the successful execution of these strategic initiatives will provide
Brigham with sufficient capital resources to execute its planned 1999
exploration program and position the Company to realize the significant value it
believes it has captured in its inventory of 3-D seismic projects and delineated
drilling locations. While the Company has initiated each of these strategic
directives in late 1998 and early 1999, and has effected certain of them to
date, the successful completion of any or all of these efforts to improve the
Company's capital availability within the expected timeframe is uncertain and
will likely have a material impact on the Company's near-term capital
expenditure levels and growth profile.

     On March 30, 1999, the Company entered into an agreement with Veritas DGC 
Land, Inc. ("Veritas") to exchange 1,002,865 shares of newly issued Brigham
common stock valued at $3.50 per share for approximately $3.5 million of payment
obligations due to Veritas in 1999 for certain seismic acquisition and
processing services previously performed.  In addition, this agreement provides
for the payment by Brigham of up to $1 million in future seismic processing
services to be performed by Veritas in newly issued shares of Brigham common
stock valued at $3.50 per share, in the event that the Company does not elect to
pay for such services in cash.  The settlement of these future seismic
processing services will be determined on a quarterly basis through December 31,
1999. Brigham considers this arrangement to be beneficial as it will enable the
Company to reduce its working capital commitments and preserve additional cash
flow and capital availability to fund its 1999 drilling program.

CAPITAL RESOURCES

     The Company's primary sources of capital have been revolving credit
facility and other debt borrowings, public and private equity financings, the
sale of interests in projects and funds generated by operations. The Company's
primary capital requirements are 3-D seismic acquisition, processing and
interpretation costs, land acquisition costs and drilling expenditures. During
May 1997, the Company completed an initial public offering of common stock of
the Company that generated proceeds of approximately $24 million, net of
offering costs, that were used to repay all outstanding debt ($13.3 million)
under the Company's then existing revolving credit facility and to fund capital
expenditures. In January 1998, the Company entered into a new revolving credit
facility that provided for borrowing availability of $75 million that was used
to repay its then outstanding borrowings under its previous credit facility and
to fund capital expenditures. In August 1998, the Company issued $50 million of
debt and equity securities, including the $40 million of Subordinated Notes,
that generated proceeds of approximately $47.5 million, net of offering costs,
that were used to repay a portion of then outstanding borrowings under the
Credit Facility, thereby increasing the Company's borrowing availability under
its Credit Facility to fund capital expenditures.

Revolving Credit Facility

     In January 1998, the Company entered into a new revolving credit agreement
(the "Credit Facility"), which provided for borrowing availability of $75
million. The Company used a portion of the funds available under the Credit
Facility to repay the $32 million in borrowings outstanding at December 31, 1997
under its previous commercial bank credit facility. Principal outstanding under
the Credit Facility is due at maturity on January 26, 2001 with interest due
monthly for base rate tranches or periodically as LIBOR tranches mature. The
annual interest rate for borrowings under the Credit Facility has been either
the lender's base rate or LIBOR plus 2.25%, at the Company's option. The Credit
Facility's borrowing availability was subsequently reduced from $75 million to
$65 million upon the Company's issuance of the Subordinated Notes in August
1998.

     In March 1999, the Company and its lenders entered into an amendment to the
Credit Facility. Pursuant to this amendment, the borrowing availability under
the Credit Facility will remain at $65 million until June 1, 1999, when the
borrowing availability will be redetermined by the lenders based on the
Company's then proved reserve value and cash flows. In addition, certain
financial covenants of the Credit Facility have been amended, additional
covenants have been included that place significant restrictions on the
Company's ability to incur certain capital expenditures, the annual interest
rate for borrowings under the Credit Facility has been amended to the lender's
base rate or LIBOR plus 3.00%, and the Company will pay the lenders a $500,000
transaction fee over a ten month period. The Company's obligations under the
Credit Facility are secured by substantially all of the natural gas and oil
properties

                                     - 27 -

<PAGE>   30


and other tangible assets of the Company. At March 26, 1999, the Company had $59
million in borrowings outstanding under the Credit Facility, which bear interest
at an annual rate of 7.4%. See Note 5 of Notes to the December 31, 1998
Consolidated Financial Statements.

     The Credit Facility has certain financial covenants including current and
interest coverage ratios, as defined. The Company and its lenders effected the
recent amendment to the Credit Facility to enable the Company to comply with
certain financial covenants of the Credit Facility, including the minimum
current ratio, minimum interest coverage ratio and the limitation on capital
expenditures related to seismic and land activities. The Company believes this
most recent amendment is indicative of its lenders' cooperation in the current
oil and natural gas pricing environment. If this pricing environment continues
or deteriorates further beyond the date of redetermination of borrowing
availability, the Company believes its lenders will expect the Company to
substantially reduce its level of borrowing under the Credit Facility. With this
in mind, the Company has initiated the business strategy noted above. Should the
Company be unable to comply with certain of the financial covenants, its lenders
may be unwilling to waive compliance or amend the covenants in the future. In
such instance, the Company's liquidity may be adversely affected, which could in
turn have an adverse impact on the Company's future financial position and
results of operations.

Subordinated Notes

     In August 1998, the Company issued $50 million of debt and equity
securities to affiliates of Enron Corp. ("Enron"). Securities issued by the
Company in connection with this financing transaction included: (i) $40 million
of Subordinated Notes, (ii) warrants to purchase 1,000,000 shares of the
Company's common stock at a price of $10.45 per share (the "Warrants"), and
(iii) 1,052,632 shares of the Company's common stock at a price of $9.50 per
share. The approximate $47.5 million in net proceeds received by the Company
from this financing transaction were used to repay a portion of outstanding
borrowings under its Credit Facility, which increased the Company's borrowing
availability under its Credit Facility to fund capital expenditures.

     Principal outstanding under the Subordinated Notes is due at maturity on
August 20, 2003. Interest on the Subordinated Notes is payable quarterly at
rates that vary depending upon whether accrued interest is paid in cash or "in
kind" through the issuance of additional Subordinated Notes ("PIK Interest").
Interest shall be paid in cash at interest rates of 12%, 13% and 14% per annum
during years one through three, year four and year five, respectively, of the
term of the Subordinated Notes; provided, however, that if the payment of
interest accrued on the Subordinated Notes in cash would cause a borrowing base
deficiency under the Credit Facility or would cause the Company to be in
violation of any covenant or other restriction set forth in any senior loan
document or any agreement entered into by the Company or subsidiary of the
Company in connection with the Subordinated Notes, the Company may pay PIK
Interest at interest rates of 13%, 14% and 15% per annum during years one
through three, year four and year five, respectively, of the term of the Notes.

     The Subordinated Notes rank subordinate in right of payment to Senior
Indebtedness (as defined) and senior to all other financings (other than any
allowed capital leases and purchase money financings) of the Company. The
Subordinated Notes are secured by a second lien against substantially all of the
natural gas and oil properties and other tangible assets of the Company. The
Subordinated Notes may be prepaid at any time, in whole or in part, without
premium or penalty, provided that all partial prepayments must be pro rata to
the various holders of the Subordinated Notes. The Subordinated Notes were
issued pursuant to an indenture (the "Indenture") that contains certain
covenants that, among other things, limit the ability of the Company and its
subsidiaries to incur additional indebtedness, pay dividends, make
distributions, enter into certain sale and leaseback transactions, enter into
certain transactions with affiliates, dispose of certain assets, incur liens,
and engage in mergers and consolidations.

     In March 1999, the Company and Chase Bank of Texas, National Association,
as trustee (the "Trustee") for the holders of the Subordinated Notes, entered
into an amendment to the Indenture. This amendment provides the Company with the
option to pay interest due on the Subordinated Notes in kind, for any reason,
through the second quarter of 2000. In addition, certain financial and other
covenants were amended. The amendment also provides for a reduction in the
exercise price per share of the Warrants from $10.45 per share to $3.50 per
share.


                                     - 28 -

<PAGE>   31


     The Indenture governing the Subordinated Notes has certain financial
covenants including current and interest coverage ratios, as defined. The
Company and the holders of the Subordinated Notes effected the recent amendment
to the Indenture to enable the Company to comply with certain financial
covenants of the Indenture that parallel those of the Credit Facility, including
the minimum current ratio and the minimum interest coverage ratio. Should the
Company be unable to comply with certain of the financial covenants, the holders
of the Subordinated Notes may be unwilling to waive compliance or amend the
covenants in the future. In such instance, the Company's liquidity may be
adversely affected, which could in turn have an adverse impact on the Company's
future financial position and results of operations.

Cash Flow Analysis

     Cash Flows from Operating Activities. Cash flows provided by operating
activities were $13.6 million in 1998, $9.8 million in 1997, and $3.7 million in
1996. The increase in cash flows for 1998 compared to 1997 was due primarily to
an increase in natural gas and oil revenues, net of lease operating expenses,
production taxes and general and administrative expenses, and net changes in
working capital items. The increase in cash flows for 1997 compared to 1996 was
due primarily to an increase in natural gas and oil revenues, net of lease
operating expenses, production taxes and general and administrative expenses.

     Cash Flows from Investing Activities. Cash flows used in investing
activities increased to $85.1 million in 1998 compared to $57.3 million in 1997
and $11.8 million in 1996. These increases are directly related to an increase
in capital expenditures related to the Company's exploration and development
activities. Capital expenditures were $84.1 million in 1998, $57.2 million in
1997 and $13.6 million in 1996.

     The Company acquired 1,213 gross (968 net) square miles of 3-D seismic in
1998, 1,262 gross (842 net) square miles in 1997, and 655 gross (241 net) square
miles in 1996. The Company's drilling efforts resulted in the completion of 50
wells (26.3 net) in 1998, 45 wells (17.6 net) in 1997 and 42 wells (8.7 net) in
1996, which resulted in aggregate net increases in proved reserve volumes (net
of revisions to previous estimates) of 31.2 Bcfe in 1998, 32.4 Bcfe in 1997, and
11.3 Bcfe in 1996. In addition, the Company sold certain producing properties in
1996 for $2.1 million and acquired certain producing properties and related
interests for $13.5 million in 1997 and $1.0 million in 1998.

     Cash Flows from Financing Activities. Cash flows provided by financing
activities for 1998 were $72.3 million, primarily as a result of borrowings
under the Credit Facility, the issuance of the Subordinated Notes and the sale
of $10 million of common stock. Cash flows from financing activities for 1997
were $47.7 million, primarily as a result of borrowings under the Company's
previous credit facility and proceeds from the common stock sold in the
Company's initial public offering. Cash flows from financing activities for 1996
were $7.7 million, primarily as a result of borrowings under the Company's
previous credit facility.

Capital Expenditures

     As a result of the Company's limited available capital resources, Brigham
has significantly reduced its planned capital expenditure budget for 1999 from
the Company's previously anticipated levels in an effort to match the its
current and expected future capital resources. The Company's current 1999
capital budget is estimated to be $17.5 million, or approximately 21% of 1998
expenditures. The Company's budgeted 1999 capital expenditures consist of
approximately $10 million to drill an estimated 20 to 25 gross wells, $3.5
million for seismic and land costs, consisting primarily of previous year
commitments and obligations to acquire 3-D data and acreage, and $4 million for
capitalized general and administrative expenses and other fixed asset
expenditures. Brigham expects that its 1999 drilling expenditures will be
allocated approximately 50% to its Anadarko Basin province and 50% to its Gulf
Coast province, and such expenditures will be devoted to the drilling of the
highest grade prospects in the Company's inventory of identified potential
drilling locations. The Company intends to fund these budgeted capital
expenditures through a combination of cash flow from operations, available
borrowings under its Credit Facility and the sales of certain assets (including
the potential divestitures of certain producing property packages from among its
Anadarko Basin properties and interests in certain 3-D seismic projects). In
addition to these sources of capital, the Company is also evaluating
opportunities to raise additional capital to enable it to increase its planned
capital expenditures for drilling in 1999. However, since the Company's capital
availability during 1999 will depend to a large extent on the

                                     - 29 -

<PAGE>   32


Company's success raising additional financing through its planned and potential
strategic initiatives, the Company's actual 1999 capital expenditures may differ
from its current estimates. In the event additional financing is not available
in the amounts or timing needed, the Company may be required to curtail its
planned exploration activities in 1999 and take further measures to reduce the
size and scope of its business. See "Item 2. Properties -- Primary Exploration
Provinces."

OTHER MATTERS

Hedging Activities

     The Company believes that hedging, although not free of risk, allows the
Company to reduce its exposure to natural gas and oil sales price fluctuations
and thereby to achieve more predictable cash flows. However, hedging
arrangements, when utilized, limit the benefit to the Company of increases in
the prices of the hedged commodity. Moreover, the Company's hedging arrangements
apply only to a portion of its production and provide only partial price
protection against declines in commodity prices. The Company expects that the
amount of its hedges will vary from time to time. See "-- Risk Factors -- Risk
of Hedging Activities" and "Item 7A. Quantitative and Qualitative Disclosures
About Market Risk."

     In 1995 the Company, in an attempt to reduce its sensitivity to volatile
commodity prices, began using crude oil swap arrangements resulting in a fixed
price over a period of six months. Total oil purchased and sold subject to swap
arrangements entered into by the Company was 118,150 Bbls in 1996 and 54,900
Bbls in 1995. The Company accounts for all these transactions as hedging
activities and, accordingly, adjusts the price received for natural gas and oil
production during the period the hedged transactions occur. Adjustments to the
price received for oil under these swap arrangements resulted in an increase in
oil revenues of $40,849 in 1995 and decreases in oil revenues of $301,280 in
1996 and $6,191 in 1997. As of December 31, 1997, the Company had no hedging
contracts outstanding.

     In 1998, the Company began using natural gas swap arrangements in an
attempt to reduce its sensitivity to volatile commodity prices as its production
base became increasingly weighted toward natural gas. Pursuant to these
arrangements the Company exchanges a floating market price for a fixed contract
price. Payments are made by the Company when the floating price exceeds the
fixed price for a contract month and payments are received by the Company when
the fixed price exceeds the floating price. Settlements of these swaps are based
on the difference between the ANR Pipeline Co.-Oklahoma index price (as
published in Inside FERC's Gas Market Report) for a contract month and the fixed
contract price for the same month.

     The following table summarizes the Company's natural gas swap arrangements
entered into from February 1998 through March 1999:


<TABLE>
<CAPTION>
               DAILY                                                                                         
               DAILY                                                                                   AVERAGE   
              VOLUMES                                           TOTAL VOLUMES HEDGED (MMBTU)            FIXED    
              HEDGED                                 --------------------------------------------- CONTRACT PRICE
              (MMBTU)          MONTHLY TERM            1998        1999         2000      2001      ($/MMBTU)(1)
             --------   --------------------------   ---------  ----------   ---------- ---------- --------------
<S>          <C>        <C>                          <C>        <C>          <C>        <C>        <C>
Contract #1    10,000    April 1998 - October 1999   2,750,000   3,040,000                             $2.163
Contract #2     5,000    April 1999 - October 1999               1,070,000                             $2.015
Contract #3    15,000   November 1999 - April 2001                 915,000    5,490,000  1,800,000     $2.065
</TABLE>

- -----------------
(1) Based on the ANR Pipeline Co.-Oklahoma index price as published in Inside
    FERC's Gas Market Report.


     For the year ended December 31, 1998, the Company realized an increase in
revenues attributable to natural gas hedges of $555,240.


                                     - 30 -

<PAGE>   33


Effects of Inflation and Changes in Prices

     The Company's results of operations and cash flows are affected by changing
natural gas and oil prices. If the price of natural gas and oil increases
(decreases), there could be a corresponding increase (decrease) in revenues as
well as the operating costs that the Company is required to bear for operations.
Inflation has had a minimal effect on the Company.

Environmental and Other Regulatory Matters

     The Company's business is subject to certain federal, state and local laws
and regulations relating to the exploration for and the development, production
and marketing of natural gas and oil, as well as environmental and safety
matters. Many of these laws and regulations have become more stringent in recent
years, often imposing greater liability on a larger number of potentially
responsible parties. Although the Company believes it is in substantial
compliance with all applicable laws and regulations, the requirements imposed by
laws and regulations are frequently changed and subject to interpretation, and
the Company is unable to predict the ultimate cost of compliance with these
requirements or their effect on its operations. Any suspensions, terminations or
inability to meet applicable bonding requirements could materially adversely
affect the Company's financial condition and operations. Although significant
expenditures may be required to comply with governmental laws and regulations
applicable to the Company, compliance has not had a material adverse effect on
the earnings or competitive position of the Company. Future regulations may add
to the cost of, or significantly limit, drilling activity. See "-- Risk Factors
- -- Compliance with Environmental Regulations," "Item 1. Business -- Governmental
Regulation" and "Item 1. Business -- Environmental Matters."

Year 2000 Issues

     Many computer software systems, as well as certain hardware and equipment
using date-sensitive data, were structured to use a two-digit date field meaning
that they may not be able to properly recognize dates in the year 2000. The
Company has developed a plan to address this issue and is taking steps to review
its information technology systems, such as computer hardware and software, as
well as non information technology systems, including computer controlled
equipment and electronic devices used to operate equipment involved in
processing and interpreting 3-D seismic data.

     The Company has completed the initial phases of its plan by identifying all
computerized systems and substantially completing an inventory of its equipment
and component parts. Both information technology and non information technology
systems may contain embedded technology, which complicates the Company's Year
2000 identification, assessment, remediation and testing efforts. The Company
continues to inventory its equipment and facilities to determine if they contain
embedded date-sensitive technology. The Company is currently reviewing all of
its systems to determine which are not Year 2000 compliant and will need to be
replaced or modified. This current phase includes comparisons of inventory to
manufacturer's information and/or performance testing. If problems are
identified, the Company will undertake remediation, replacement or alternative
procedures for non-compliant equipment or facilities on a business priority
basis. The Company's identification and assessment efforts to date have not
identified any computer equipment or software it currently uses which will
require replacement or modification, except that one of the word processing
software programs the Company uses may be non-compliant and may need to be
discontinued or upgraded. In addition, in the ordinary course of replacing
computer equipment and software, the Company attempts to obtain replacements
that are Year 2000 compliant. The Company currently anticipates that its
identification, assessment, remediation and testing efforts will continue and,
depending upon the results of the assessment efforts, be completed during the
first three quarters of 1999.

     As of December 31, 1998, all costs incurred by the Company in connection
with its Year 2000 compliance efforts were included within the Company's normal
general and administrative expenses (for example, regular maintenance of
software programs). The Company is currently expensing as incurred all costs
related to the assessment and remediation of the Year 2000 issue, and these
costs are being funded through operating cash flow. However, in certain
instances the Company may determine that replacing existing equipment may be
appropriate and may capitalize such replacements. The Company is unable
currently to estimate the amount of its total out-of-pocket costs to become

                                     - 31 -

<PAGE>   34


Year 2000 compliant, but the Company currently expects that such costs will not
have a material adverse effect on the Company's financial condition, operations
or liquidity.

     The foregoing timetable and assessment of costs to become Year 2000
compliant reflect management's current best estimates. These estimates are based
on many assumptions, including assumptions about the cost, availability and
ability of resources to locate, remediate and modify affected systems, equipment
and facilities. Based upon its activities to date, the Company does not
currently believe that these factors will cause results to differ significantly
from those estimated. However, the Company cannot reasonably estimate the
potential impact on its financial condition and operations if key third parties
including, among others, suppliers, contractors, joint venture partners,
financial institutions, customers and governments do not become Year 2000
compliant on a timely basis. The Company is currently identifying third parties
whose business significantly impacts the Company, has contacted some significant
third parties to determine the extent to which interfaces with such entities are
vulnerable to Year 2000 issues, and will contact others as it completes the
identification phase.

     In the event that the Company is unable to complete the remediation or
replacement of its critical systems, facilities and equipment, establish
alternative procedures in a timely manner, or if those with whom the Company
conducts business are unsuccessful in implementing timely solutions, Year 2000
issues could have a material adverse effect on the Company's liquidity and
results of operations. At this time, the potential effect in the event the
Company and/or third parties are unable to timely resolve their Year 2000
problems is not determinable. A contingency plan has not been developed for
dealing with the most reasonably likely worst case scenario, and such scenario
has not yet been clearly identified. However, the Company currently believes
that it will be able to resolve its own Year 2000 issues in a timely manner.

     The disclosure set forth in this section is provided pursuant to Securities
Act Release No. 33-7558. As such it is protected as a forward-looking statement
under the Private Securities Litigation Reform Act of 1995. See "Forward-Looking
Statements." This disclosure is also subject to protection under the Year 2000
Information and Readiness Disclosure Act of 1998, Public Law 105-271, as a "Year
2000 Statement" and "Year 2000 Readiness Disclosure" as defined therein.

Recent Accounting Pronouncements

     In June 1997, the Financial Accounting Standards Board (the "FASB") issued
SFAS No. 130, "Reporting Comprehensive Income" which established standards for
reporting, in addition to net income, comprehensive income and its components.
Adoption of this standard has no impact on the Company's financial statements.

     In June 1997, the FASB issued SFAS No. 131, "Disclosure about Segments of
an Enterprise and Related Information," which the Company adopted in the first
quarter of 1998. As all of the Company's natural gas and oil properties and
related operations are located in the United States, management has determined
that the Company has one reportable segment.

     In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities," which is effective for fiscal years
beginning after June 15, 1999. The Company is currently assessing the impact
adoption of this standard will have on its financial statement presentation.

FORWARD LOOKING INFORMATION

     Brigham or its representatives may make forward looking statements, oral or
written, including statements in this report, press releases and filings with
the SEC, regarding estimated future net revenues from oil and natural gas
reserves and the present value thereof, planned capital expenditures (including
the amount and nature thereof), increases in oil and gas production, the number
of wells the Company anticipates drilling through 1999 and the Company's
financial position, business strategy and other plans and objectives for future
operations. Although the Company believes that the expectations reflected in
these forward looking statements are reasonable, there can be no assurance that
the actual results or developments anticipated by the Company will be realized
or, even if substantially realized, that they will have the expected effects on
its business or operations. Among the factors that could cause

                                     - 32 -

<PAGE>   35


actual results to differ materially from the Company's expectations are general
economic conditions, inherent uncertainties in interpreting engineering data,
operating hazards, delays or cancellations of drilling operations for a variety
of reasons, competition, fluctuations in oil and gas prices, the ability of the
Company to successfully integrate the business and operations of acquired
companies, government regulations and other factors set forth among the risk
factors noted below or in the description of the Company's business in Item 1 of
this report. All subsequent oral and written forward looking statements
attributable to the Company or persons acting on its behalf are expressly
qualified in their entirety by these factors. The Company assumes no obligation
to update any of these statements.

RISK FACTORS

     Effects of Leverage. The Company had long-term debt outstanding of $99
million (principal amount) as of December 31, 1998 and $100.3 million (principal
amount) as of March 26, 1999. The Indenture limits the amounts of additional
debt borrowings, including borrowings under the Credit Facility or other Senior
Indebtedness (as defined). However, the Indenture permits the Company to borrow
under the Credit Facility up to the lesser of $75 million or the borrowing base
under the Credit Facility ($65 million as of December 31, 1998 and March 26,
1999), which would provide the Company with the ability to borrow up to $6
million of additional indebtedness under its Credit Facility as of December 31,
1998 and March 26, 1999. In addition, the Indenture allows the Company to borrow
up to $25 million of future subordinated indebtedness that is pari passu in
right of payment with the Subordinated Notes if the holders of the Subordinated
Notes have been given a first look and right to make a proposal for such
subordinated indebtedness.

     The Company's level of indebtedness will have several important effects on
its operations, including (i) a substantial portion of the Company's cash flow
from operations will be dedicated to the payment of interest on its indebtedness
and will not be available for other purposes; (ii) the covenants contained in
the Credit Facility and the Indenture limit its ability to borrow additional
funds or to dispose of assets and may affect the Company's flexibility in
planning for, and reacting to, changes in business conditions and (iii) the
Company's ability to obtain additional financing in the future for working
capital, capital expenditures, acquisitions, general corporate purposes or other
purposes may be impaired. Moreover, future exploration, development or
acquisition activities may require the Company to alter its capitalization
significantly. These changes in capitalization may significantly alter the
leverage of the Company. The Company's ability to meet its debt service
obligations and to reduce its total indebtedness will be dependent upon the
Company's future performance, which will be subject to general economic
conditions and to financial, business and other factors affecting the operations
of the Company, many of which are beyond its control. There can be no assurance
that the Company's future performance will not be adversely affected by such
economic conditions and financial, business and other factors. See "Item 7.
Management's Discussion and Analysis of Financial Condition and Results of
Operations -- Liquidity" and "-- Capital Resources."

     Substantial Capital Requirements; Limited Current Liquidity. The Company
makes and will continue to make substantial capital expenditures in its
exploration and development projects. The Company's available capital resources
at March 26, 1999 are limited and not sufficient to fund its planned working
capital needs and capital expenditures for 1999. The Company intends to finance
these working capital needs and planned capital expenditures with cash flow from
operations, borrowings available under the Credit Facility, the potential sales
of interests in certain producing properties and 3-D seismic projects and the
potential issuance of additional equity securities. Additional financing will be
required in the future to fund the Company's exploratory and developmental
drilling and 3-D seismic acquisition activities at currently budgeted levels. No
assurance can be given as to the availability or terms of any such additional
financing that may be required or that financing will continue to be available
under the existing or new financing arrangements. If additional capital
resources are not available to the Company, its drilling and other activities
may be curtailed and its business, financial condition and results of operations
could be materially adversely affected. See "Item 7. Management's Discussion and
Analysis of Financial Condition and Results of Operations -- Liquidity" and " --
Capital Resources."

     Dependence on Exploratory Drilling Activities. The Company's revenues,
operating results and future rate of growth are highly dependent upon the
success of its exploratory drilling program. Exploratory drilling involves
numerous risks, including the risk that no commercially productive natural gas
or oil reservoirs will be encountered. The cost of drilling, completing and
operating wells is often uncertain, and drilling operations may be curtailed,
delayed or canceled as a result of a variety of factors, including unexpected
drilling conditions, pressure or

                                     - 33 -

<PAGE>   36


irregularities in formations, equipment failures or accidents, adverse weather
conditions, compliance with governmental requirements and shortages or delays in
the availability of drilling rigs and the delivery of equipment. Despite the use
of 3-D seismic and other advanced technologies, exploratory drilling remains a
speculative activity. Even when fully utilized and properly interpreted, 3-D
seismic data and other advanced technologies only assist geoscientists in
identifying subsurface structures and do not enable the interpreter to know
whether hydrocarbons are in fact present in those structures. In addition, the
use of 3-D seismic data and other advanced technologies requires greater
predrilling expenditures than traditional drilling strategies, and the Company
could incur losses as a result of such expenditures. The Company's future
drilling activities may not be successful. There can be no assurance that the
Company's overall drilling success rate or its drilling success rate for
activity within a particular province will not decline. Unsuccessful drilling
activities could have a material adverse effect on the Company's results of
operations and financial condition. The Company often gathers 3-D seismic data
over large areas. The Company's interpretation of data delineates those portions
of an area desirable for drilling. Therefore, the Company may choose not to
acquire option and lease rights prior to acquiring seismic and, in many cases,
the Company may identify a drilling location before seeking option or lease
rights in the location. Although the Company has identified numerous potential
drilling locations, there can be no assurance that they will ever be leased or
drilled or that natural gas or oil will be produced from these or any other
potential drilling locations.

     Volatility of Oil and Natural Gas Prices. The Company's revenues, operating
results and future rate of growth are highly dependent upon the prices received
for the Company's oil and natural gas. Historically, the markets for oil and
natural gas have been volatile and are likely to continue to be volatile in the
future. Various factors beyond the control of the Company will affect prices of
its oil and natural gas, including worldwide and domestic supplies of oil and
natural gas, the ability of the members of the Organization of Petroleum
Exporting Countries to agree to and maintain oil price and production controls,
political instability or armed conflict in oil-producing regions, the price and
level of foreign imports, the level of consumer demand, the price and
availability of alternative fuels, the availability of pipeline capacity,
weather conditions, domestic and foreign governmental regulations and taxes, and
the overall economic environment. During 1998, the high and low prices for oil
on the NYMEX were $17.82 per Bbl and $10.72 per Bbl, and the high and low prices
for natural gas on the NYMEX were $2.69 per MMBtu and $1.65 per MMBtu. The
recent decline in oil prices is generally thought to be caused primarily by an
oversupply of worldwide crude oil inventory created, in part, by unusually warm
winters in the United States and Europe in 1997 and 1998, an announced increase
in crude oil production quotas for OPEC countries in late 1997 and a possible
decline in demand in certain Asian markets. The recent decline in natural gas
prices is generally thought to be caused primarily by an oversupply of domestic
natural gas inventory created, in part, by reduced demand for natural gas due to
unusually warm winters in the United States in 1997 and 1998. It is impossible
to predict future oil and natural gas price movements with certainty. If such
declines in the NYMEX crude oil or natural gas prices worsen or persist for a
protracted period, it would adversely affect the Company's revenues, net income
and cash flows from operations. Also, if these prices maintain their present
level for an extended time period or decline further, the Company may delay or
postpone certain of its capital projects. Declines in oil and natural gas prices
may materially adversely affect the Company's financial condition, liquidity,
ability to finance planned capital expenditures and results of operations. Lower
oil and natural gas prices also may reduce the amount of oil and natural gas
that the Company can produce economically. Any significant decline in the price
of natural gas or oil would adversely affect the Company's revenues and
operating income and may require a reduction in the carrying value of the
Company's oil and natural gas properties. See "Item 1. Business -- Competition"
and "Item 7. Management's Discussion and Analysis of Financial Condition and
Results of Operations".

     Historical Operating Losses and Variability of Operating Results. The
Company had net losses of approximately $1.3 million in 1994, $1.6 million in
1995, $450,000 in 1996, $1.1 million (including a net $1.2 million non-cash
deferred income tax charge incurred in connection with the Company's conversion
from a partnership to a corporation) in 1997, and $33.3 million (including a
$24.8 million non-cash writedown in the carrying value of its natural gas and
oil properties) in 1998. The Company has incurred net losses in each year of
operation, and there can be no assurance that the Company will be profitable in
the future. At December 31, 1998, the Company's accumulated earnings were a
deficit of $33.4 million and its total stockholders' equity was $24.7 million.
In addition, the Company's future operating results may fluctuate significantly
depending upon a number of factors, including industry conditions, prices of oil
and natural gas, rates of drilling success, rates of production from completed
wells and the timing and amount of capital expenditures. This variability could
have a material adverse effect on the Company's business, financial

                                     - 34 -

<PAGE>   37


condition and results of operations. In addition, any failure or delay in the
realization of expected cash flows from operating activities could limit the
Company's ability to invest and participate in economically attractive projects.
See "Item 6. Selected Financial Data" and "Item 7. Management's Discussion and
Analysis of Financial Condition and Results of Operations."

     Reserve Replacement Risk. In general, production from oil and natural gas
properties declines as reserves are depleted, with the rate of decline depending
on reservoir characteristics. Except to the extent the Company conducts
successful exploration and development activities or acquires properties
containing proved reserves, or both, the proved reserves of the Company will
decline as reserves are produced. The Company's future oil and natural gas
production is highly dependent upon its ability to economically find, develop or
acquire reserves in commercial quantities. The business of exploring for or
developing reserves is capital intensive. To the extent cash flow from
operations is reduced and external sources of capital become limited or
unavailable, the Company's ability to make the necessary capital investment to
maintain or expand its asset base of oil and natural gas reserves would be
impaired. The Company participates in a percentage of its wells as a
non-operator. The failure of an operator of the Company's wells to adequately
perform operations, or an operator's breach of the applicable agreements, could
adversely impact the Company. In addition, there can be no assurance that the
Company's future exploration and development activities will result in
additional proved reserves or that the Company will be able to drill productive
wells at acceptable costs. Furthermore, although the Company's revenues could
increase if prevailing prices for oil and natural gas increase significantly,
the Company's finding and development costs could also increase. See "Item 7.
Management's Discussion and Analysis of Financial Condition and Results of
Operations."

     Operating Hazards and Uninsured Risks. The Company's operations are subject
to hazards and risks inherent in drilling for and producing and transporting oil
and natural gas, such as fires, natural disasters, explosions, encountering
formations with abnormal pressures, blowouts, cratering, pipeline ruptures and
spills, any of which can result in the loss of hydrocarbons, environmental
pollution, personal injury claims and other damage to properties of the Company
and others. As protection against operating hazards, the Company maintains
insurance coverage against some, but not all, potential losses. The Company may
elect to self-insure if management believes that the cost of insurance, although
available, is excessive relative to the risks presented. The Company generally
maintains insurance for the hazards and risks inherent in drilling for and
producing and transporting oil and natural gas and believes this insurance is
adequate. Nevertheless, the occurrence of an event that is not covered, or not
fully covered, by insurance could have a material adverse effect on the
Company's financial condition and results of operations. In addition, pollution
and environmental risks generally are not fully insurable. See "Item 2. Business
and Properties -- Operating Hazards and Uninsured Risks" and "

     Uncertainty of Reserve Information and Future Net Revenue Estimates.
Numerous uncertainties are inherent in estimating quantities of proved reserves
and their values, including many factors beyond the Company's control. The
reserve information in herein is an estimate only. Although the Company believes
these estimates are reasonable, reserve estimates are imprecise and are expected
to change as additional information becomes available. Estimates of oil and
natural gas reserves by necessity are projections based on engineering data, and
uncertainties are inherent in the interpretation of this data, the projection of
future rates of production and the timing of development expenditures. Reserve
engineering is a subjective process of estimating underground accumulations of
oil and natural gas that are difficult to measure. The accuracy of any reserve
estimate is a function of the quality of available data, engineering and
geologic interpretation, and judgment. Estimates of economically recoverable oil
and natural gas reserves and of future net cash flows depend upon a number of
variable factors and assumptions, such as historical production from the area
compared with production from other producing areas, the assumed effects of
regulations by governmental agencies, and assumptions concerning future oil and
natural gas prices, future operating costs, severance and excise taxes,
development costs and workover and remedial costs, all of which may in fact vary
considerably from actual results. For these reasons, estimates of the
economically recoverable quantities of oil and natural gas attributable to any
particular group of properties, classifications of reserves based on risk of
recovery, and estimates of the future net cash flows may vary substantially.
Moreover, there can be no assurance that the Company's reserves will ultimately
be produced or that the Company's proved undeveloped reserves will be developed
within the periods anticipated. Any significant variance in the assumptions
could materially affect the estimated quantity and value of the Company's
reserves. Actual production, revenues and expenditures with respect to the

                                     - 35 -

<PAGE>   38



Company's reserves will likely vary from estimates, and such variances may be
material. See "Item 2. Business and Properties -- Oil and Natural Gas Reserves."

     The Present Value of Future Net Revenues referred to herein should not be
construed as the current market value of the estimated oil and natural gas
reserves attributable to the Company's properties. In accordance with applicable
requirements of the SEC, the estimated discounted future net cash flows from
proved reserves are generally based on prices and costs as of the date of the
estimate, whereas actual future prices and costs may be materially higher or
lower. Actual future net cash flows also will be affected by factors such as the
amount and timing of actual production, supply and demand for oil and natural
gas, curtailments or increases in consumption by gas purchasers, and changes in
governmental regulations or taxation. The timing of actual future net cash flows
from proved reserves, and thus their actual present value, will be affected by
the timing of both the production and the incurrence of expenses in connection
with development and production of oil and natural gas properties. In addition,
the 10% discount factor, which must be used to calculate discounted future net
cash flows for SEC reporting purposes, is not necessarily the most appropriate
discount factor based on interest rates in effect from time to time and risks
associated with the Company or the oil and gas industry in general.

     Competition. The Company operates in the highly competitive areas of oil
and natural gas exploration, exploitation, acquisition and production with other
companies. In seeking to acquire desirable producing properties or new leases
for future exploration and in marketing its oil and natural gas production, as
well as in seeking to acquire the equipment and expertise necessary to operate
and develop those properties, the Company faces intense competition from a large
number of independent, technology-driven companies as well as both major and
other independent oil and natural gas companies. Many of these competitors have
financial and other resources substantially in excess of those available to the
Company. The effects of this highly competitive environment could have a
material adverse effect on the Company. See "Item 1. Business -- Competition."

     Compliance with Government Regulations. The Company's business is subject
to federal, state and local laws and regulations relating to the exploration
for, and the development, production and marketing of, oil and natural gas, as
well as safety matters. Although the Company believes it is in substantial
compliance with all applicable laws and regulations, legal requirements are
frequently changed and subject to interpretation, and the Company is unable to
predict the ultimate cost of compliance with these requirements or their effect
on its operations. Significant expenditures may be required to comply with
governmental laws and regulations. See "Item 1. Business -- Governmental
Regulation."

     Compliance with Environmental Regulations. The Company's operations are
subject to complex environmental laws and regulations adopted by federal, state
and local governmental authorities. Environmental laws and regulations are
frequently changed. The implementation of new, or the modification of existing,
laws or regulations could have a material adverse effect on the Company. The
discharge of natural gas, oil, or other pollutants into the air, soil or water
may give rise to significant liabilities on the part of the Company to the
government and third parties and may require the Company to incur substantial
costs of remediation. No assurance can be given that existing environmental laws
or regulations, as currently interpreted or reinterpreted in the future, or
future laws or regulations will not materially adversely affect the Company's
results of operations and financial condition. See "Item 1. Business --
Environmental Matters."

     Risk of Hedging Activities. In an attempt to reduce its sensitivity to
energy price volatility, the Company uses swap arrangements that generally
result in a fixed price over a period of six to eighteen months. If the
Company's reserves are not produced at rates equivalent to the hedged position,
the Company would be required to satisfy its obligations under hedging contracts
on potentially unfavorable terms without the ability to hedge that risk through
sales of comparable quantities of its own production. Further, the terms under
which the Company enters into hedging contracts are based on assumptions and
estimates of numerous factors such as cost of production and pipeline and other
transportation costs to delivery points. Substantial variations between the
assumptions and estimates used by the Company and actual results experienced
could materially adversely affect the Company's anticipated profit margins and
its ability to manage the risk associated with fluctuations in oil and natural
gas prices. Additionally, hedging contracts limit the benefits the Company will
realize if actual prices rise above the contract prices. In addition, hedging
contracts are subject to the risk that the other party may prove unable or
unwilling to perform its obligations

                                     - 36 -

<PAGE>   39


under such contracts. Any significant nonperformance could have a material
adverse financial effect on the Company. For the year ended December 31, 1998,
the Company realized an increase in revenues attributable to natural gas hedges
of $555,240. See "Item 7. Management's Discussion and Analysis of Financial
Condition and Results of Operations -- Other Matters -- Hedging Activities" and
"Item 7A. Quantitative and Qualitative Disclosures About Market Risk."

     Marketability of Production. The marketability of the Company's production
depends in part upon the availability, proximity and capacity of natural gas
gathering systems, pipelines and processing facilities. The Company generally
delivers natural gas through gas gathering systems and gas pipelines that it
does not own. Federal and state regulation of oil and natural gas production and
transportation, tax and energy policies, changes in supply and demand and
general economic conditions all could adversely affect the Company's ability to
produce and market its oil and natural gas. Any dramatic change in market
factors could have a material adverse effect on the Company.

     Dependence on Key Personnel. The Company has assembled a team of
geologists, geophysicists and engineers having considerable experience applying
3-D imaging technology. The Company is dependent upon the knowledge, skills and
experience of these experts to provide 3-D imaging and assist the Company in
reducing the risks associated with its participation in oil and natural gas
exploration projects. In addition, the success of the Company's business also
depends to a significant extent upon the abilities and continued efforts of its
management, particularly Ben M. Brigham, the Company's Chief Executive Officer,
President and Chairman of the Board. The Company has an employment agreement
with Ben M. Brigham, but does not have an employment agreement with any of its
other employees. The Company has key man life insurance on Mr. Brigham in the
amount of $2 million. The loss of services of key management personnel or the
Company's technical experts, or the inability to attract additional qualified
personnel, could have a material adverse effect on the Company's business,
financial condition, results of operations, development efforts and ability to
grow. There can be no assurance that the Company will be successful in
attracting and retaining such executives, geophysicists, geologists and
engineers. See "Item 1. Business -- Exploration Staff" and "Executive Officers
of the Registrant".

     Control by Existing Stockholders. As of March 26, 1999, directors,
executive officers and principal stockholders of the Company, and certain of
their affiliates, beneficially owned approximately 63% of the Company's
outstanding Common Stock. Accordingly, these stockholders, as a group, will be
able to control the outcome of stockholder votes, including votes concerning the
election of directors, the adoption or amendment of provisions in the Company's
Certificate of Incorporation or Bylaws and the approval of mergers and other
significant corporate transactions. The existence of these levels of ownership
concentrated in a few persons make it unlikely that any other holder of Common
Stock will be able to affect the management or direction of the Company. These
factors may also have the effect of delaying or preventing a change in the
management or voting control of the Company.

     Certain Antitakeover Considerations. The Company's Certificate of
Incorporation authorizes the Board of Directors of the Company to issue up to 10
million shares of preferred stock without stockholder approval and to set the
rights, preferences and other designations, including voting rights, of those
shares as the Board of Directors may determine. These provisions, alone or in
combination with the matters described in "Risk Factors -- Control by Existing
Stockholders," may discourage transactions involving actual or potential changes
of control of the Company, including transactions that otherwise could involve
payment of a premium over prevailing market prices to holders of Common Stock.
The Company also is subject to provisions of the Delaware General Corporation
Law that may make some business combinations more difficult.

     Year 2000 Compliance. Many computer software systems, as well as certain
hardware and equipment using date-sensitive data, were structured to use a
two-digit date field meaning that they may not be able to properly recognize
dates in the year 2000. The Company currently expects that any costs necessary
for the Company to become Year 2000 compliant will not have a material adverse
effect on the Company's financial condition, operations or liquidity. However,
the Company cannot reasonably estimate the potential impact on its financial
condition and operations if key third parties including, among others,
suppliers, contractors, joint venture partners, financial institutions,
customers and governments do not become Year 2000 compliant on a timely basis.
There can be no assurance that the Company will be able to complete any
necessary remediation or replacement of its critical systems, facilities and
equipment or establish alternative procedures in a timely manner; that those
with whom the Company

                                     - 37 -

<PAGE>   40


conduct business will be successful in implementing timely solutions; or that
Year 2000 issues will not have a material adverse effect on the Company's
business, financial position and results of operations. See "Item 7.
Management's Discussion and Analysis of Financial Conditions and Result of
Operations -- Other Matters -- Year 2000 Issues".

     Possible Stock Price Volatility. The trading price of the Common Stock and
the price at which the Company may sell securities in the future could be
subject to large fluctuations in response to limited trading volume in the
Company's stock and changes in government regulations, quarterly variations in
operating results, litigation, general market conditions, the prices of natural
gas and oil, announcements by the Company and its competitors, the liquidity of
the Company, the Company's ability to raise additional funds and other events.



                                     - 38 -

<PAGE>   41


ITEM 7A.     QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK

MANAGEMENT OPINION CONCERNING DERIVATIVE INSTRUMENTS

     The Company limits its use of derivative instruments principally to
commodity price hedging activities, whereby gains and losses are generally
offset by price changes in the underlying commodity. As a result, management
believes that its use of derivative instruments does not expose the Company to
material risk. The Company's use of derivative instruments for hedging
activities could materially affect the Company's results of operations in
particular quarterly or annual periods since such instruments can limit the
Company's ability to benefit from favorable oil and natural gas price movements.
However, management believes that use of these instruments will not have a
material adverse effect on the Company's financial position or liquidity.

COMMODITY PRICE RISK

     The Company's primary commodity market risk exposure is to changes in the
prices related to the sale of its oil and natural gas production. The market
prices for oil and natural gas have been volatile and are likely to continue to
be volatile in the future. As such, the Company employs established policies and
procedures to manage its exposure to fluctuations in the sales prices it
receives for its oil and natural gas production through hedging activities. See
"Item 7. Management's Discussion and Analysis of Financial Condition and Results
of Operations -- Other Matters -- Hedging Activities."

     The Company believes that hedging, although not free of risk, allows the
Company to reduce its exposure to oil and natural gas sales price fluctuations
and thereby to achieve more predictable cash flows. However, hedging
arrangements, when utilized, limit the benefit to the Company of increases in
the prices of the hedged commodity. Moreover, the Company's hedging arrangements
apply only to a portion of its production and provide only partial price
protection against declines in commodity prices. The Company expects that the
amount of its hedges will vary from time to time.

     Based on the Company's natural gas swap arrangements outstanding at
December 31, 1998, an adverse change (defined as a hypothetical 10% and 25%
increase in underlying commodity prices for open positions) would lower revenue
and income before taxes by approximately $902,000 and $2.3 million,
respectively, from currently projected levels. Additionally, as the Company
utilizes swap arrangements to hedge anticipated and firmly committed
transactions, a loss in fair value for those instruments is generally offset by
price changes in the underlying commodity. The impact of these price changes are
not reflected in this sensitivity analysis.

INTEREST RATE RISK

     The Company does not utilize derivative instruments to protect against
changes in interest rates on debt borrowings. See Note 11 of Notes to
Consolidated Financial Statements for a description of the Company's financial
instruments at December 31, 1998.


ITEM 8.      FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA

     The Company's Consolidated Financial Statements required by this item are
included on the pages immediately following the Index to Financial Statements
appearing on page F1-1.


ITEM 9.      CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
             FINANCIAL DISCLOSURE

     None.


                                     - 39 -

<PAGE>   42


                                    PART III

ITEM 10.     DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT

     The information required by this item is incorporated by reference to
information under the caption "Proposal 1 - Election of Directors" and to the
information under the caption "Compliance with Section 16(a) of the Securities
Exchange Act of 1934" in the Company's definitive Proxy Statement (the "1999
Proxy Statement") for its annual meeting of stockholders to be held on May 13,
1999. The 1999 Proxy Statement will be filed with the Securities and Exchange
Commission (the "Commission") not later than 120 days subsequent to December 31,
1998.

     Pursuant to Item 401(b) of Regulation S-K, the information required by this
item with respect to executive officers of the Company is set forth in Part I of
this report.


ITEM 11.     EXECUTIVE COMPENSATION

     The information required by this item is incorporated herein by reference
to the 1999 Proxy Statement, which will be filed with the Commission not later
than 120 days subsequent to December 31, 1998.


ITEM 12.     SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

     The information required by this item is incorporated herein by reference
to the 1999 Proxy Statement, which will be filed with the Commission not later
than 120 days subsequent to December 31, 1998.


ITEM 13.     CERTAIN RELATIONSHIPS AND RELATED PARTY TRANSACTIONS

     The information required by this item is incorporated herein by reference
to the 1999 Proxy Statement, which will be filed with the Commission not later
than 120 days subsequent to December 31, 1998.


                                     - 40 -

<PAGE>   43


                                     PART IV

ITEM 14.     EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K

(a)  1.      Consolidated Financial Statements:

             See Index to Consolidated Financial Statements on page F-1.

     2.      Financial Statement Schedules:

             See Index to Consolidated Financial Statements on page F-1.

     3.      Exhibits:  The following documents are filed as exhibits to this 
                        report:

<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
2.1      --       Exchange Agreement (filed as Exhibit 2.1 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
3.1      --       Certificate of Incorporation (filed as Exhibit 3.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
3.2      --       Bylaws (filed as Exhibit 3.2 to the Company's Registration 
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
4.1      --       Form of Common Stock Certificate (filed as Exhibit 4.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
4.2+     --       Indenture dated as of August 20, 1998 between Brigham 
                  Exploration Company and Chase Bank of Texas, National
                  Association, as Trustee.
4.2.1++  --       Supplemental Indenture dated as of March 26, 1999 between
                  Brigham Exploration Company and Chase Bank of Texas, National
                  Association, as Trustee.
4.3++    --       Form of Warrant Certificate.
4.4      --       Form of Senior Subordinated Secured Note due 2003 (filed as
                  Exhibit 4.4 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-53873), and incorporated herein by
                  reference).
10.1     --       Agreement of Limited Partnership, dated May 1, 1992, between
                  Brigham Exploration Company and General Atlantic Partners III,
                  L.P. as general partners, and Harold D. Carter and GAP-Brigham
                  Partners, L.P. as limited partners (filed as Exhibit 10.1 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.1.1   --       Amendment No. 1 to Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated May 1, 1992, by and among
                  Brigham Exploration Company, General Atlantic Partners III,
                  L.P., GAP-Brigham Partners, L.P. and Harold D. Carter (filed
                  as Exhibit 10.1.1 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.1.2   --       Amendment No. 2 to Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated September 30, 1994, by and
                  among Brigham Exploration Company, General Atlantic Partners
                  III, L.P., GAP-Brigham Partners, L.P., Harold D. Carter and
                  the additional signatories thereto (filed as Exhibit 10.1.2 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.1.3   --       Amendment No. 3 to Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated August 24, 1995, by and among
                  Brigham Exploration Company, General Atlantic Partners III,
                  L.P., GAP-Brigham Partners, L.P., Harold D.
</TABLE>

                                     - 41 -

<PAGE>   44



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
                  Carter, Craig M. Fleming, David T. Brigham and Jon L. Glass
                  (filed as Exhibit 10.1.3 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.1.4+  --       Amended and Restated Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated December 30, 1997 by and among
                  Brigham, Inc., Brigham Holdings I, L.L.C. and Brigham Holdings
                  II, L.L.C.
10.2     --       Agreement of Limited Partnership of Venture Acquisitions,
                  L.P., dated September 23, 1994, by and between Quest
                  Resources, L.L.C. and RIMCO Energy, Inc. as general partners,
                  and RIMCO Production Company, Inc., RIMCO Exploration
                  Partners, L.P. I and RIMCO Exploration Partners, L.P. II, as
                  limited partners (filed as Exhibit 10.2 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.3     --       Regulations of Quest Resources, L.L.C. (filed as Exhibit 10.3
                  to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.4     --       Management and Ownership Agreement, dated September 23, 1994,
                  by and among Brigham Oil & Gas, L.P., Brigham Exploration
                  Company, General Atlantic Partners III, L.P., Harold D.
                  Carter, Ben M. Brigham and GAP- Brigham Partners, L.P. (filed
                  as Exhibit 10.4 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.5*    --       Consulting Agreement, dated May 1, 1997, by and between 
                  Brigham Oil & Gas, L.P. and Harold D. Carter (filed as Exhibit
                  10.4 to the Company's Registration Statement on Form S-1
                  (Registration No. 33-53873), and incorporated herein by
                  reference).
10.6*    --       Employment Agreement, by and between Brigham Exploration
                  Company and Ben M. Brigham (filed as Exhibit 10.7 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.7*    --       Form of Confidentiality and Noncompete Agreement between the 
                  Registrant and each of its executive officers (filed as
                  Exhibit 10.8 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.8*    --       1997 Incentive Plan of Brigham Exploration Company (filed as
                  Exhibit 10.9 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333- 22491), and incorporated herein by
                  reference).
10.8.1*  --       Form of Option Agreement for certain executive officers (filed
                  as Exhibit 10.9.1 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333- 22491), and incorporated
                  herein by reference).
10.8.2*  --       Option Agreement dated as of March 4, 1997, by and between
                  Brigham Exploration Company and Jon L. Glass (filed as Exhibit
                  10.9.2 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.9*    --       Incentive Bonus Plan dated as of February 28, 1997 of Brigham,
                  Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit 10.10 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.10    --       Two Bridgepoint Lease Agreement, dated September 30, 1996,
                  by and between Investors Life Insurance Company of North
                  America and Brigham Oil & Gas, L.P. (filed as Exhibit 10.14 to
                  the Company's Registration Statement on Form S- 1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
</TABLE>

                                     - 42 -

<PAGE>   45



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
10.10.1  --       First Amendment to Two Bridge Point Lease Agreement dated
                  April 11, 1997 between Investors Life Insurance Company of
                  North America and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.9.1 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-53873), and incorporated herein by
                  reference).
10.10.2  --       Second Amendment to Two Bridge Point Lease Agreement dated
                  October 13, 1997 between Investors Life Insurance Company of
                  North America and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.9.2 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-53873), and incorporated herein by
                  reference).
10.10.3  --       Letter dated April 17, 1998 exercising Right of First Refusal
                  to Lease "3rd Option Space" (filed as Exhibit 10.9.3 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-53873), and incorporated herein by reference).
10.11    --       Anadarko Basin Seismic Operations Agreement, dated 
                  February 15, 1996, by and between Brigham Oil & Gas, L.P. and
                  Veritas Geophysical, Ltd. (filed as Exhibit 10.15 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.11.1  --       Letter Amendment to Anadarko Basin Seismic Operations 
                  Agreement, dated June 10, 1996, between Brigham Oil & Gas,
                  L.P. and Veritas Geophysical, Ltd. (filed as Exhibit 10.15.1
                  to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.12    --       Expense Allocation and Participation Agreement, dated April 1,
                  1996, between Brigham Oil & Gas, L.P. and Gasco Limited
                  Partnership. (filed as Exhibit 10.16 to the Company's
                  Registration Statement on Form S-1 (Registration No. 333-
                  22491), and incorporated herein by reference).
10.12.1  --       Amendment to Expense Allocation and Participation Agreement,
                  dated October 21, 1996, between Brigham Oil & Gas, L.P. and
                  Gasco Limited Partnership (filed as Exhibit 10.16.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.13    --       Expense Allocation and Participation Agreement, dated April 1,
                  1996, between Brigham Oil & Gas, L.P. and Middle Bay Oil
                  Company, Inc. (filed as Exhibit 10.17 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.13.1  --       Amendment to Expense Allocation and Participation Agreement,
                  dated September 26, 1996, between Brigham Oil & Gas, L.P. and
                  Middle Bay Oil Company, Inc. (filed as Exhibit 10.17.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.13.2  --       Letter Amendment to Expense Allocation and Participation
                  Agreement, dated May 20, 1996, between Brigham Oil & Gas, L.P.
                  and Middle Bay Oil Company, Inc. (filed as Exhibit 10.17.2 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.14    --       Anadarko Basin Joint Participation Agreement, dated May 1,
                  1996, by and among Stephens Production Company and Brigham Oil
                  & Gas, L.P. (filed as Exhibit 10.18 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.15    --       Anadarko Basin Joint Participation Agreement, dated May 1, 
                  1996, by and between Vintage Petroleum, Inc. and Brigham Oil &
                  Gas, L.P. (filed as Exhibit 10.19 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.16    --       Processing Alliance Agreement, dated July 20, 1993, between 
                  Veritas Seismic Ltd. and Brigham Oil & Gas, L.P. (filed as
                  Exhibit 10.20 to the Company's
</TABLE>

                                     - 43 -

<PAGE>   46



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
                  Registration Statement on Form S-1 (Registration 
                  No. 333-22491), and incorporated herein by reference).
10.16.1  --       Letter Amendment to Processing Alliance Agreement, dated
                  November 3, 1994, between Veritas Seismic Ltd. and Brigham Oil
                  & Gas, L.P. (filed as Exhibit 10.20.1 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.17    --       Agreement and Assignment of Interest, West Bradley Project,
                  dated September 1, 1995, by and between Aspect Resources
                  Limited Liability Company and Brigham Oil & Gas, L.P. (filed
                  as Exhibit 10.21 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.18    --       Agreement and Assignment of Interests in lands located in
                  Grady County, Oklahoma, West Bradley Project, dated December
                  1, 1995, by and between Aspect Resources Limited Liability
                  Company, Brigham Oil & Gas, L.P. and Venture Acquisitions,
                  L.P. (filed as Exhibit 10.22 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.19    --       Agreement and Assignment of Interests, West Bradley Project,
                  dated December 1, 1995, by and between Aspect Resources
                  Limited Liability Company and Brigham Oil & Gas, L.P. (filed
                  as Exhibit 10.23 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.20    --       Geophysical Exploration Agreement, Hardeman Project, Hardeman
                  and Wilbarger Counties, Texas and Jackson County, Oklahoma,
                  dated March 15, 1993 by and among General Atlantic Resources,
                  Inc., Maynard Oil Company, Ruja Muta Corporation, Tucker
                  Scully Interests Ltd., JHJ Exploration, Ltd., Cheyenne
                  Petroleum Company, Antrim Resources, Inc., and Brigham Oil &
                  Gas, L.P. (filed as Exhibit 10.24 to the Company's
                  Registration Statement on Form S- 1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.21    --       Agreement and Partial Assignment of Interests in OK13-P
                  Prospect Area, Jackson County, Oklahoma (Hardeman Project),
                  dated August 1, 1995, by and between Brigham Oil & Gas, L.P.
                  and Aspect Resources Limited Liability Company (filed as
                  Exhibit 10.25 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.22    --       Agreement and Partial Assignment of Interests in Q140-E
                  Prospect Area, Hardeman County, Texas (Hardeman Project),
                  dated August 1, 1995, by and between Brigham Oil & Gas, L.P.
                  and Aspect Resources Limited Liability Company (filed as
                  Exhibit 10.26 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.23    --       Agreement and Partial Assignment of Interests in Hankins #1
                  Chappel Prospect Agreement, Jackson County, Oklahoma (Hardeman
                  Project), dated March 21, 1996, by and between Brigham Oil &
                  Gas, L.P., NGR, Ltd. and Aspect Resources Limited Liability
                  Company (filed as Exhibit 10.27 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.24    --       Form of Indemnity Agreement between the Registrant and each
                  of its executive officers (filed as Exhibit 10.28 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.25    --       Registration Rights Agreement dated February 26, 1997 by and 
                  among Brigham Exploration Company, General Atlantic Partners
                  III L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P. II,
                  RIMCO Partners L.P. III, and RIMCO Partners, L.P. IV, Ben M.
                  Brigham, Anne L. Brigham, Harold D.
</TABLE>

                                     - 44 -

<PAGE>   47



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
                  Carter, Craig M. Fleming, David T. Brigham and Jon L. Glass
                  (filed as Exhibit 10.29 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.26    --       1997 Director Stock Option Plan (filed as Exhibit 10.30 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.27    --       Form of Employee Stock Ownership Agreement (filed as Exhibit
                  10.31 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.28    --       Agreement and Assignment of Interest in Geophysical 
                  Exploration Agreement, Esperson Dome Project, dated November
                  1, 1994, by and between Brigham Oil & Gas, L.P. and Vaquero
                  Gas Company (filed as Exhibit 10.33 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.29    --       Geophysical Exploration Agreement, Southwest Danbury Project,
                  Brazoria County, Texas, dated as of July 1, 1996, by and among
                  UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.34 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.30    --       Geophysical Exploration Agreement, Welder Project, Duval
                  County, Texas, dated as of October 1, 1996, by and among
                  UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.35 to the Company's Registration Statement on Form S- 1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.31    --       Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                  Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre Energy
                  Corporation and Resource Investors Management Company (filed
                  as Exhibit 10.36 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.31.1  --       Letter relating to Proposed Trade Structure, RIMCO/Tigre
                  Project, dated January 31, 1997, from Resource Investors
                  Management Company to Brigham Oil & Gas, L.P. (filed as
                  Exhibit 10.36 to the Company's Registration Statement on Form
                  S- 1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.32    --       Anadarko Basin Seismic Operations Agreement II, dated as of
                  April 1, 1997, by and between Brigham Oil & Gas, L.P. (filed
                  as Exhibit 10.37 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.32.1  --       Letter Amendment to Anadarko Basin Seismic Operations 
                  Agreement II, dated March 20, 1997, between Brigham Oil & Gas,
                  L.P. and Veritas DGC Land, Inc. (filed as Exhibit 10.37 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.33    --       Expense Allocation and Participation Agreement II, dated
                  April 1, 1997, between Brigham Oil & Gas, L.P., and Gasco
                  Limited Partnership (filed as Exhibit 10.31 to the Company's
                  Quarterly Report on Form 10-Q for the quarter ended June 30,
                  1997, and incorporated herein by reference).
10.36    --       Credit Agreement dated as of January 26, 1998 among Brigham
                  Oil & Gas, L.P., Bank of Montreal, as Agent, and the lenders
                  signatory thereto (filed as Exhibit 10.36 to the Company's
                  Annual Report on Form 10-K for the year ended December 31,
                  1997, and incorporated herein by reference).
10.36.1+ --       First Amendment to Credit Agreement dated as of August 20,
                  1998 among Brigham Oil & Gas, L.P., Bank of Montreal, as
                  Agent, and the lenders signatory thereto.
</TABLE>

                                     - 45 -

<PAGE>   48



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
10.36.2++  --     Second Amendment to Credit Agreement dated as of March 26,
                  1999 among Brigham Oil & Gas, L.P., Bank of Montreal, as
                  Agent, and the lenders signatory thereto.
10.37      --     Guaranty Agreement dated January 26, 1998 by Brigham
                  Exploration Company in favor of Bank of Montreal, as Agent,
                  and each of the Lenders party to the Credit Agreement (filed
                  as Exhibit 10.33.1 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-53873), and incorporated herein
                  by reference).
10.37.1    --     First Amendment to Guaranty Agreement dated as of March 30,
                  1998 between Brigham Exploration Company and Bank of Montreal,
                  as Agent for the Lenders party to the Credit Agreement (filed
                  as Exhibit 10.33.2 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-53873), and
                  incorporated herein by reference).
10.37.2+   --     Second Amendment to Guaranty Agreement dated as of August 20,
                  1998 between Brigham Exploration Company and Bank of Montreal,
                  as Agent for the Lenders party to the Credit Agreement.
10.37.3++  --     Third Amendment to Guaranty Agreement dated as of March 26,
                  1999 between Brigham Exploration Company and Bank of Montreal,
                  as Agent for the Lenders party to the Credit Agreement.
10.38+     --     Securities Purchase Agreement dated as of August 20, 1998
                  among Brigham Exploration Company, Enron Capital & Trade
                  Resources Corp. and Joint Energy Development Investments II
                  Limited Partnership.
10.39+     --     Registration Rights Agreement dated as of August 20, 1998, by
                  and among Brigham Exploration Company, Enron Capital & Trade
                  Resources Corp. and Joint Energy Development Investments II
                  Limited Partnership.
10.39.1++  --     Amendment to Registration Rights Agreement dated as of
                  March 26, 1999, by and among Brigham Exploration Company,
                  Enron Capital & Trade Resources Corp., ECT Merchant
                  Investments Corp. and Joint Energy Development Investments II
                  Limited Partnership.
10.40+     --     Form of Guaranty for subsidiaries.
10.41++    --     Exchange Agreement dated as of March 30, 1999 by and between
                  Brigham Exploration Company and Veritas DGC Land, Inc.
10.42++    --     Registration Rights Agreement dated as of March 30, 1999 by
                  and between Brigham Exploration Company and Veritas DGC Land,
                  Inc.
21+        --     Subsidiaries of the Registrant.
23.1+      --     Consent of Price Waterhouse LLP, independent public
                  accountants.
23.2+      --     Consent of Cawley, Gillespie & Associates, Inc., independent
                  petroleum engineers.
27+        --     Financial Data Schedule.
</TABLE>

- ---------------

*      Management contract or compensatory plan.
+      Filed herewith
++     Not filed herewith pursuant to Rule 12b-25 under the Act, and to be 
       filed by amendment.


(b) The following reports on Form 8-K were filed by the Company during the last
quarter of the period covered by this Annual Report on Form 10-K:

       None.

                                     - 46 -

<PAGE>   49




                          GLOSSARY OF OIL AND GAS TERMS


       The following are abbreviations and definitions of certain terms commonly
used in the oil and gas industry and in this report.

       Bbl. One stock tank barrel, or 42 U.S. gallons liquid volume, used herein
in reference to oil or other liquid hydrocarbons.

       Bcf. One billion cubic feet.

       Bcfe. One billion cubic feet of natural gas equivalent. In reference to
natural gas, natural gas equivalents are determined using the ratio of 6 Mcf of
natural gas to 1 Bbl of oil, condensate of natural gas liquids.

       CAEX. Computer-aided exploration.

       Completion. The installation of permanent equipment for the production of
oil or natural gas.

       Developed Acreage. The number of acres which are allocated or assignable
to producing wells or wells capable of production.

       Development Well. A well drilled within the proved area of an oil or
natural gas reservoir to the depth of a stratigraphic horizon known to be
productive.

       Drilling Costs. The costs associated with drilling and completing a well
(exclusive of seismic and land acquisition costs for that well and future
development costs associated with proved undeveloped reserves added by the well)
divided by total proved reserve additions.

       Dry Well. A well found to be incapable of producing either oil or natural
gas in sufficient quantities to justify completion of an oil or gas well.

       Exploratory Well. A well drilled to find and produce oil or natural gas
in an unproved area, to find a new reservoir in a field previously found to be
productive of oil or gas in another reservoir, or to extend a known reservoir.

       Finding and Development Costs. Capital costs incurred in the acquisition,
exploration and development of proved oil and natural gas reserves divided by
total proved reserve additions.

       Gross Acres or Gross Wells. The total acres or wells, as the case may be,
in which the Company has a working interest.

       MBbl. One thousand barrels of oil or other liquid hydrocarbons.

       Mcf. One thousand cubic feet of natural gas.

       Mcfe. One thousand cubic feet of natural gas equivalents.

       MMBbl. One million barrels of oil or other liquid hydrocarbons.

       MMBtu. One million Btu, or British Thermal Units. One British Thermal
Unit is the quantity of heat required to raise the temperature of one pound of
water by one degree Fahrenheit.

       MMcf. One million cubic feet of natural gas.

       MMcfe. One million cubic feet of natural gas equivalents.

                                     - 47 -

<PAGE>   50


       Net Acres or Net Wells. Gross acres or wells multiplied, in each case, by
the percentage working interest owned by the Company.

       Net Production. Production that is owned by the Company less royalties
and production due others.

       Oil. Crude oil, condensate or other liquid hydrocarbons.

       Operator. The individual or company responsible for the exploration,
development, and production of an oil or gas well or lease.

       Present Value of Future Net Revenues or PV10%. The pretax present value
of estimated future revenues to be generated from the production of proved
reserves calculated in accordance with SEC guidelines, net of estimated
production and future development costs, using prices and costs as of the date
of estimation without future escalation, without giving effect to non-property
related expenses such as general and administrative expenses, debt service and
depreciation, depletion and amortization, and discounted using an annual
discount rate of 10%.

       Proved Developed Reserves. Reserves that can be expected to be recovered
through existing wells with existing equipment and operating methods.

       Proved Reserves. The estimated quantities of crude oil, natural gas and
natural gas liquids which geological and engineering data demonstrate with
reasonable certainty to be recoverable in future years from known reservoirs
under existing economic and operating conditions.

       Proved Undeveloped Reserves. Reserves that are expected to be recovered
from new wells on undrilled acreage or from existing wells where a relatively
major expenditure is required for recompletion.

       Royalty. An interest in an oil and gas lease that gives the owner of the
interest the right to receive a portion of the production from the leased
acreage (or of the proceeds of the sale thereof), but generally does not require
the owner to pay any portion of the costs of drilling or operating the wells on
the leased acreage. Royalties may be either landowner's royalties, which are
reserved by the owner of the leased acreage at the time the lease is granted, or
overriding royalties, which are usually reserved by an owner of the leasehold in
connection with a transfer to a subsequent owner.

       Spud. Start drilling a new well (or restart).

       Standardized Measure. The aftertax present value of estimated future
revenues to be generated from the production of proved reserves calculated in
accordance with SEC guidelines, net of estimated production and future
development costs, using prices and costs as of the date of estimation without
future escalation, without giving effect to non-property related expenses such
as general and administrative expenses, debt service and depreciation, depletion
and amortization, and discounted using an annual discount rate of 10%.

       Success Rate. The number of wells on which production casing has been run
for a completion attempt as a percentage of the number of wells drilled.

       2-D Seismic. The method by which a cross-section of the earth's
subsurface is created through the interpretation of reflecting seismic data
collected along a single source profile.

       3-D Seismic. The method by which a three dimensional image of the earth's
subsurface is created through the interpretation of reflection seismic data
collected over surface grid. 3-D seismic surveys allow for a more detailed
understanding of the subsurface than do conventional surveys and contribute
significantly to field appraisal, development and production.

       Working Interest. An interest in an oil and gas lease that gives the
owner of the interest the right to drill for and produce oil and natural gas on
the leased acreage and requires the owner to pay a share of the costs of
drilling and production operations.

                                     - 48 -

<PAGE>   51




                                   SIGNATURES

       Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this report to be signed on
its behalf by the undersigned, hereunder duly authorized, as of March 31, 1999.

                                      BRIGHAM EXPLORATION COMPANY


                                      By:         /s/ Ben M. Brigham
                                         --------------------------------------
                                         Ben M. Brigham
                                         Chief Executive Officer and President

       Pursuant to the requirements of the Securities Exchange Act of 1934, this
report has been signed below as of March 31, 1999, by the following persons on
behalf of the Registrant and in the capacity indicated.


             /s/ Ben M. Brigham                          
- -------------------------------------------------------
Ben M. Brigham
Chief Executive Officer, President and Chairman of the Board


             /s/ Jon L. Glass                            
- -------------------------------------------------------
Jon L. Glass
Vice President - Exploration and Director


             /s/ Craig M. Fleming                        
- -------------------------------------------------------
Craig M. Fleming
Chief Financial Officer
(principal financial and accounting officer)


             /s/ Anne L. Brigham                         
- -------------------------------------------------------
Anne L. Brigham
Director


             /s/ Harold D. Carter                        
- -------------------------------------------------------
Harold D. Carter
Director


             /s/ W. Craig Childers                       
- -------------------------------------------------------
W. Craig Childers
Director


             /s/ Alexis M. Cranberg                      
- -------------------------------------------------------
Alexis M. Cranberg
Director


             /s/ Stephen P. Reynolds                     
- -------------------------------------------------------
Stephen P. Reynolds
Director

                                     - 49 -

<PAGE>   52




                          INDEX TO FINANCIAL STATEMENTS


<TABLE>
<CAPTION>
                                                                                                        PAGE
                                                                                                        -----
<S>                                                                                                     <C>
Financial Statements of Brigham Exploration Company
     Report of Independent Accountants.............................................................     F1-2
     Consolidated Balance Sheets as of December 31, 1998 and 1997..................................     F1-3
     Consolidated Statements of Operations for the Years Ended
        December 31, 1998, 1997, and 1996..........................................................     F1-4
     Consolidated Statements of Stockholders' Equity for the Years Ended
        December 31, 1998, 1997, and 1996..........................................................     F1-5
     Consolidated Statements of Cash Flows for the Years Ended
        December 31, 1998, 1997, and 1996..........................................................     F1-6
     Notes to the Consolidated Financial Statements................................................     F1-7
Financial Statements of Brigham Exploration Company Guarantor Subsidiaries*
     Report of Independent Accountants.............................................................     F2-1
     Combined Balance Sheets as of December 31, 1998...............................................     F2-2
     Combined Balance Sheets as of December 31, 1997...............................................     F2-3
     Combined Statements of Operations for the Year Ended December 31, 1998........................     F2-4
     Combined Statements of Operations for the Year Ended December 31, 1997........................     F2-5
     Combined Statements of Equity for the Year Ended December 31, 1998............................     F2-6
     Combined Statements of Equity for the Year Ended December 31, 1997............................     F2-7
     Combined Statements of Cash Flows for the Year Ended December 31, 1998........................     F2-8
     Combined Statements of Cash Flows for the Year Ended December 31, 1997........................     F2-9
     Notes to the Combined Financial Statements....................................................     F2-10
</TABLE>


As all Brigham Exploration Company subsidiaries fully and unconditionally
guarantee the Senior Subordinated Secured Notes and the Company has no
significant assets other than its investments in its subsidiaries, the
consolidated financial statements are substantially the same as the financial
statements of the subsidiary guarantors and separate financial statements have
been omitted as they would not be meaningful to investors.

Financial statements for the wholly owned subsidiaries whose securities are
pledged as collateral for the Senior Subordinated Notes are included in the
combined financial statements.*




- --------------

     *These items are omitted from this Form 10-K pursuant to Rule 12b-25 under
the Act and will be filed by amendment to this Form 10-K.


                                      F1-1

<PAGE>   53



                        REPORT OF INDEPENDENT ACCOUNTANTS


To the Board of Directors
and Stockholders of Brigham Exploration Company

In our opinion, the accompanying consolidated balance sheets and the related
consolidated statements of operations and changes in stockholders' equity and of
cash flows, after the restatement discussed in Note 12, present fairly, in all
material respects, the financial position of Brigham Exploration Company and its
subsidiaries at December 31, 1998 and 1997, and the results of their operations
and their cash flows for each of the three years in the period ended December
31, 1998, in conformity with generally accepted accounting principles. These
financial statements are the responsibility of the Company's management; our
responsibility is to express an opinion on these financial statements based on
our audits. We conducted our audits of these statements in accordance with
generally accepted auditing standards which require that we plan and perform the
audit to obtain reasonable assurance about whether the financial statements are
free of material misstatement. An audit includes examining, on a test basis,
evidence supporting the amounts and disclosures in the financial statements,
assessing the accounting principles used and significant estimates made by
management, and evaluating the overall financial statement presentation. We
believe that our audits provide a reasonable basis for the opinion expressed
above.



PricewaterhouseCoopers LLP

Houston, Texas
March 30, 1999



                                      F1-2


<PAGE>   54

                           BRIGHAM EXPLORATION COMPANY

                           CONSOLIDATED BALANCE SHEETS
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                                        December 31,
                                                                                     --------------------
                                                                                       1998        1997
                                                                                     --------    --------
<S>                                                                                  <C>         <C>     
                                                       ASSETS
Current assets:
     Cash and cash equivalents                                                       $  2,569    $  1,701
     Accounts receivable                                                                7,938       4,909
     Prepaid expenses                                                                     290         280
                                                                                     --------    --------
        Total current assets                                                           10,797       6,890
                                                                                     --------    --------

Natural gas and oil properties, at cost, net                                          134,317      84,294
Other property and equipment, at cost, net                                              2,014       1,239
Drilling advances paid                                                                    230          78
Other noncurrent assets                                                                 3,158          18
                                                                                     --------    --------
                                                                                     $150,516    $ 92,519
                                                                                     ========    ========

                                        LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Accounts payable                                                                $ 19,883    $ 11,892
     Accrued drilling costs                                                             1,219       2,406
     Participant advances received                                                        764         489
     Other current liabilities                                                          1,647         726
                                                                                     --------    --------
        Total current liabilities                                                      23,513      15,513
                                                                                     --------    --------

Notes payable                                                                          59,000      32,000
Senior subordinated notes, net                                                         35,786          --
Other noncurrent liabilities                                                            7,536         507
Deferred income tax liability                                                              --       1,186

Stockholders' equity:
     Preferred stock, $.01 par value, 10 million shares
        authorized, none issued and outstanding                                            --          --
     Common stock, $.01 par value, 30 million shares
        authorized, 13,306,206 and 12,253,574 issued and outstanding at
        December 31, 1998 and 1997, respectively                                          133         123
     Additional paid-in capital                                                        58,838      44,919
     Unearned stock compensation                                                         (890)     (1,674)
     Accumulated deficit                                                              (33,400)        (55)
                                                                                     --------    --------
        Total stockholders' equity                                                     24,681      43,313
                                                                                     --------    --------
                                                                                     $150,516    $ 92,519
                                                                                     ========    ========
</TABLE>

  The Company uses the full cost method to account for its natural gas and oil
properties.



        See accompanying notes to the consolidated financial statements.

                                      F1-3

<PAGE>   55

                           BRIGHAM EXPLORATION COMPANY

                      CONSOLIDATED STATEMENTS OF OPERATIONS
                      (in thousands, except per share data)

<TABLE>
<CAPTION>
                                                                 Year Ended December 31,
                                                          ----------------------------------
                                                             1998        1997         1996
                                                          ----------   --------     --------
<S>                                                       <C>          <C>          <C>     
Revenues:
     Natural gas and oil sales                            $   13,799   $  9,184     $  6,141
     Workstation revenue                                         390        637          627
                                                          ----------   --------     --------
                                                              14,189      9,821        6,768
                                                          ----------   --------     --------
Costs and expenses:
     Lease operating                                           2,172      1,151          726
     Production taxes                                            850        549          362
     General and administrative                                4,672      3,570        2,199
     Depletion of natural gas and oil properties               8,410      2,743        2,323
     Depreciation and amortization                               413        306          487
     Capitalized ceiling impairment                           24,847         --           --
     Amortization of stock compensation                          372        388           --
                                                          ----------   --------     --------
                                                              41,736      8,707        6,097
                                                          ----------   --------     --------
       Operating income (loss)                               (27,547)     1,114          671
                                                          ----------   --------     --------

Other income (expense):
     Interest income                                             136        145           52
     Interest expense                                         (7,120)    (1,017)        (373)
     Interest expense - related party                             --       (173)        (800)
                                                          ----------   --------     --------
                                                             (6,984)    (1,045)       (1,121)
                                                          ----------   --------     --------

Net income (loss) before income taxes                        (34,531)        69         (450)

Income tax benefit (expense)                                   1,186     (1,186)          --
                                                          ----------   --------     --------
     Net loss                                             $  (33,345)    (1,117)    $   (450)
                                                          ==========   ========     ========

Net loss per share:
     Basic/Diluted                                        $    (2.64)  $  (0.10)    $  (0.05)

Common shares outstanding:
     Basic/Diluted                                            12,626     11,081        8,929

Unaudited pro forma information (Notes 1 and 2)
     Net loss                                                                       $   (450)
     Pro forma Exchange adjustments                                                      275
                                                                                    --------
     Pro forma net loss before income taxes                                             (175)
     Pro forma income tax benefit                                                        147
                                                                                    --------
     Pro forma net loss                                                             $    (28)
                                                                                    ========

     Pro forma net loss per basic/diluted common share                              $  (0.00)
     Pro forma weighted average number of common
        basic/diluted shares outstanding                                               9,170
</TABLE>



        See accompanying notes to the consolidated financial statements.

                                      F1-4


<PAGE>   56

                          BRIGHAM EXPLORATION COMPANY

           CONSOLIDATED STATEMENT OF CHANGES IN STOCKHOLDERS' EQUITY
                                 (in thousands)


<TABLE>
<CAPTION>
                            Common Stock        Additional    Unearned
                       ----------------------    Paid-in        Stock        Accumulated      Predecessor
                         Shares      Amounts     Capital     Compensation       Deficit         Capital       Total
                       ----------   ---------   ----------   ------------  --------------    -------------   -------
<S>                    <C>          <C>         <C>          <C>           <C>               <C>             <C>    
Balance,
  December 31, 1995            --   $      --   $       --   $         --    $         --    $       3,694   $ 3,694

Net loss                       --          --           --             --              --             (450)     (450)
                       ----------   ---------   ----------   ------------    ------------    -------------   -------

Balance,
  December 31, 1996            --          --           --             --              --            3,244     3,244

Consummation of
  the Exchange          8,928,574          90       19,580             --              --           (3,244)   16,426
Issuance of stock
  options                      --          --        2,576         (2,576)             --               --        --
Forfeiture of stock
  options                      --          --          (69)            69              --               --        --
Issuance of common
  stock                 3,325,000          33       23,894             --              --               --    23,927
Net loss for
  period ended 
  February 27, 1997            --          --       (4,869)            --              --               --    (4,869)
Net income for
  period from
  February 27, 1997
  to Dec. 31, 1997             --          --        3,807             --             (55)              --     3,752
Amortization of
  unearned stock
  compensation                 --          --           --            833              --               --       833
                       ----------   ---------   ----------    -----------    ------------    -------------   -------

Balance,
December 31, 1997      12,253,574         123       44,919         (1,674)            (55)              --    43,313

Net loss                       --          --           --             --         (33,345)              --   (33,345)
Issuance of
  common stock          1,052,632          10        9,419             --              --               --     9,429
Issuance of warrants           --          --        4,500             --              --               --     4,500
Amortization of
  unearned stock
  compensation                 --          --           --            784              --               --       784
                      -----------   ----------  ----------    -----------    ------------    -------------   -------

Balance,
  December 31, 1998    13,306,206   $     133   $   58,838    $      (890)   $    (33,400)   $          --   $24,681
                      ===========   =========   ==========    ===========    ============    =============   =======
</TABLE>


        See accompanying notes to the consolidated financial statements.
                                      F1-5

<PAGE>   57

                          BRIGHAM EXPLORATION COMPANY

                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                                Year ended December 31,
                                                                         -----------------------------------
                                                                            1998        1997         1996
                                                                         ---------    ---------    ---------
<S>                                                                      <C>          <C>          <C>          
Cash flows from operating activities:
     Net loss                                                            $ (33,345)   $  (1,117)   $    (450)   
     Adjustments to reconcile net loss to cash
     provided by operating activities:
         Depletion of natural gas and oil properties                         8,410        2,743        2,323
         Depreciation and amortization                                         413          306          487
         Capitalized ceiling impairment                                     24,847           --           --
         Amortization of stock compensation                                    372          388           --
         Amortization of deferred loan fees and debt issuance costs            726           --           --
         Amortization of discount on senior subordinated notes                 286           --           --
         Changes in working capital and other items:
            Increase in accounts receivable                                 (3,029)      (2,213)      (1,440)
            (Increase) decrease in prepaid expenses                            (10)        (128)          25
            Increase in accounts payable                                     7,991        8,955        1,619
            Increase (decrease) in participant advances received               275         (648)         804
            Increase in interest payable on senior subordinated notes          507           --           --
            Increase in other current liabilities                              355           50           60
            Increase in deferred interest payable - related party               --           53          320
            Increase (decrease) in deferred income tax liability            (1,186)       1,186           --
            Other noncurrent assets                                              6          281         (224)
            Other noncurrent liabilities                                     7,004          (50)         186
                                                                         ---------    ---------    ---------
              Net cash provided by operating activities                     13,622        9,806        3,710
                                                                         ---------    ---------    ---------
Cash flows from investing activities:
     Additions to natural gas and oil properties                           (84,055)     (57,170)     (13,612)
     Proceeds from the sale of natural gas and oil properties                   --           74        2,149
     Additions to other property and equipment                                (868)        (545)         (41)
     (Increase) decrease in drilling advances paid                            (152)         341         (292)
                                                                         ---------    ---------    ---------
              Net cash used by investing activities                        (85,075)     (57,300)     (11,796)
                                                                         ---------    ---------    ---------
Cash flows from financing activities:
     Proceeds from issuance of common stock                                  9,429       23,927           --
     Proceeds from issuance of senior subordinated notes
         payable and warrants                                               40,000           --           --
     Increase in notes payable                                             105,800       37,250        8,000
     Repayment of notes payable                                            (78,800)     (13,250)          --
     Principal payments on capital lease obligations                          (236)        (179)        (269)
     Deferred loan fees and debt issuance costs                             (3,872)          --           --
                                                                         ---------    ---------    ---------
              Net cash provided by financing activities                     72,321       47,748        7,731
                                                                         ---------    ---------    ---------

Net increase (decrease) in cash and cash equivalents                           868          254         (355)

Cash and cash equivalents, beginning of year                                 1,701        1,447        1,802
                                                                         ---------    ---------    ---------
Cash and cash equivalents, end of year                                   $   2,569    $   1,701    $   1,447    
                                                                         =========    =========    =========

Supplemental disclosure of cash flow information:
     Cash paid during the year for interest                              $   5,490    $   1,679    $     762
                                                                         =========    =========    =========

Supplemental disclosure of noncash investing and financing activities:
     Capital lease asset additions                                       $     320    $     403    $     101
                                                                         =========    =========    =========
</TABLE>

        See accompanying notes to the consolidated financial statements.

                                      F1-6
<PAGE>   58





                           BRIGHAM EXPLORATION COMPANY

                 NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS


1.   ORGANIZATION AND NATURE OF OPERATIONS

       Brigham Exploration Company is a Delaware corporation formed on February
25, 1997 for the purpose of exchanging its common stock for the common stock of
Brigham, Inc. and the partnership interests of Brigham Oil & Gas, L.P. (the
"Partnership"). Hereinafter, Brigham Exploration Company and the Partnership are
collectively referred to as "the Company." Brigham, Inc. is a Nevada corporation
whose only asset is its ownership interest in the Partnership. The Partnership
was formed in May 1992 to explore and develop onshore domestic natural gas and
oil properties using 3-D seismic imaging and other advanced technologies. Since
its inception, the Partnership has focused its exploration and development of
natural gas and oil properties primarily in West Texas, the Anadarko Basin and
the onshore Gulf Coast.

       Pursuant to an exchange agreement dated February 26, 1997 (the "Exchange
Agreement") and upon the initial filing on February 27, 1997 of a registration
statement with the Securities and Exchange Commission (the "SEC") for the public
offering of common stock (the "Offering"), the shareholders of Brigham, Inc.
transferred all of the outstanding stock of Brigham, Inc. to the Company in
exchange for 3,859,821 shares of common stock of the Company. Pursuant to the
Exchange Agreement, the Partnership's other general partner and the limited
partners also transferred all of their partnership interests to the Company in
exchange for 3,314,286 shares of common stock of the Company. Furthermore, the
holders of the Partnership's subordinated convertible notes transferred these
notes to the Company in exchange for 1,754,464 shares of common stock. These
transactions are referred to as "the Exchange." In completing the Exchange, the
Company issued 8,928,571 shares of common stock to the stockholders of Brigham,
Inc., the partners of the Partnership and the holder of the Partnership's
subordinated notes payable. As a result of the Exchange, the Company now owns
all the partnership interests in the Partnership. In May 1997, the Company sold
3,325,000 shares of its common stock in the Offering at a price of $8.00 per
share.

2.   SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

Basis of Accounting

       The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results may differ from those estimates.

     The Exchange has been reflected in the consolidated financial statements of
the Company as a reorganization.

Principles of Consolidation

       The accompanying financial statements include the accounts of the Company
and its wholly-owned subsidiaries, and its proportionate share of assets,
liabilities and income and expenses of the limited partnerships in which the
Company, or any of its subsidiaries has a participating interest. All
significant intercompany accounts and transactions have been eliminated.


                                      F1-7

<PAGE>   59



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Cash and Cash Equivalents

       The Company considers all highly liquid financial instruments with an
original maturity of three months or less to be cash equivalents.

Property and Equipment

       The Company uses the full cost method of accounting for its investment in
natural gas and oil properties. Under this method, all acquisition, exploration
and development costs, including certain payroll and other internal costs,
incurred for the purpose of finding natural gas and oil reserves are
capitalized. Internal costs capitalized are directly attributable to
acquisition, exploration and development activities and do not include costs
related to production, general corporate overhead or similar activities. Costs
associated with production and general corporate activities are expensed in the
period incurred.

       The capitalized costs of the Company's natural gas and oil properties
plus future development, dismantlement, restoration and abandonment costs (the
"Amortizable Base"), net of estimated of salvage values, are amortized using the
unit-of-production method based upon estimates of total proved reserve
quantities. The Company's capitalized costs of its natural gas and oil
properties, net of accumulated amortization, are limited to the total of
estimated future net cash flows from proved natural gas and oil reserves,
discounted at ten percent, plus the cost of unevaluated properties. There are
many factors, including global events, that may influence the production,
processing, marketing and valuation of natural gas and oil. A reduction in the
valuation of natural gas and oil properties resulting from declining prices or
production could adversely impact depletion rates and capitalized cost
limitations.

       All costs directly associated with the acquisition and evaluation of
unproved properties are initially excluded from the Amortizable Base. Upon the
interpretation by the Company of the 3-D seismic data associated with unproved
properties, the geological and geophysical costs related to acreage that is not
specifically identified as prospective are added to the Amortizable Base.
Geological and geophysical costs associated with prospective acreage, as well as
leasehold costs, are added to the Amortizable Base when the prospects are
drilled. Costs of prospective acreage are reviewed annually for impairment on a
property-by-property basis.

     At December 31, 1998, a capitalized ceiling impairment of $24.8 million was
recognized. The write down was calculated based on the estimated discounted
present value of future net cash flows from proved natural gas and oil reserves
using prices in effect at December 31, 1998.

     Other property and equipment, which primarily consists of 3-D seismic
interpretation workstations, are depreciated on a straight-line basis over the
estimated useful lives of the assets after considering salvage value. Estimated
useful lives are as follows:

<TABLE>
<S>                                                                  <C>     
       Furniture and fixtures..................................      10 years
       Machinery and equipment.................................       5 years
       3-D seismic interpretation workstations and software....       3 years
</TABLE>


                                      F1-8

<PAGE>   60



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


       Betterments and major improvements that extend the useful lives are
capitalized, while expenditures for repairs and maintenance of a minor nature
are expensed as incurred.

Revenue Recognition

     The Company recognizes natural gas and oil sales from its interests in
producing wells under the sales method of accounting. Under the sales method,
the Company recognizes revenues based on the amount of natural gas or oil sold
to purchasers, which may differ from the amounts to which the Company is
entitled based on its interest in the properties. Gas balancing obligations as
of December 31, 1996, 1997 and 1998 were not significant.

       Industry participants in the Company's seismic programs are charged on an
hourly basis for the work performed by the Company on its 3-D seismic
interpretation workstations. The Company recognizes workstation revenue as
service is provided.

Derivative Instruments

     Net realized gains or losses and related cash flows arising from the
Company's commodity price swaps (see Note 11) are recognized in the period
incurred as a component of natural gas and oil sales. If subsequent to being
hedged, underlying transactions are determined not to be likely to occur, the
related derivatives gains and losses are recognized in that period as "Other
income."

Stock Based Compensation

     The Company measures compensation expense for its stock based incentive
plan using the intrinsic value method and has provided in Note 12 the pro forma
disclosure of the effect on net loss and net loss per common share as if the
fair value based method prescribed by Statement of Financial Accounting
Standards ("SFAS") No. 123, "Accounting for Stock Based Compensation," had been
applied in measuring compensation expense.

Federal and State Income Taxes

       Prior to the consummation of the Exchange, there was no income tax
provision included in the financial statements as the Partnership was not a
taxpaying entity. Income and losses were passed through to its partners on the
basis of the allocation provisions established by the partnership agreement.
Upon consummation of the Exchange, the Partnership became subject to federal
income taxes through its ownership by the Company.

       In conjunction with the Exchange, the Company recorded a deferred income
tax liability of $5 million to recognize the temporary differences between the
financial statement and tax bases of the assets and liabilities of the
Partnership at the Exchange date, February 27, 1997, given the provisions of
enacted tax laws. Subsequent to this date, the Company elected to record a
step-up in basis of its assets for tax purposes as a result of the Exchange.
Related to this election, the Company recorded a $3.8 million deferred income
tax benefit, resulting in a net $1.2 million deferred income tax charge for the
year ended December 31, 1997.


                                      F1-9

<PAGE>   61



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Unaudited Pro Forma Information

     Pro forma net loss for the year ended December 31, 1996 reflects the
Exchange, including income taxes that would have been recorded had the
Partnership been a taxable entity. Pro forma exchange adjustments primarily
represent the amortization of the compensation expense related to employee stock
options granted upon the formation of the Company (see Note 12), and the
reduction of interest expense related to the elimination of debt as part of the
Exchange. Pro forma income taxes have been included in the Statement of
Operations pursuant to the rules and regulations of the SEC for instances when a
partnership becomes subject to federal income taxes.

Comprehensive Income

     In June 1997, the FASB issued SFAS No. 130, "Reporting Comprehensive
Income." The standard, which was effective for financial statements issued for
periods ending after December 15, 1997, established standards for reporting, in
addition to net income, comprehensive income and its components including, as
applicable, foreign currency items, minimum pension liability adjustments and
unrealized gains and losses on certain investments in debt and equity
securities. Adoption of this Standard has no impact on the Company's financial
statements.

Recent Pronouncements

       In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities." SFAS No. 133 requires that all derivative
instruments be recorded on the balance sheet at fair value. Changes in the fair
value of derivatives are recorded each period in current earnings or other
comprehensive income, depending on whether a derivative is designated as part of
a hedge transaction and, if it is, depending on the type of hedge transaction.
For fair value hedge transactions in which the Company is hedging changes in an
asset's, liability's, or firm commitment's fair value, changes in the fair value
of the derivative instrument will generally be offset in the income statement by
changes in the hedged item's fair value. For cash flow hedge transactions in
which the Company is hedging the variability of cash flows related to a
variable-rate asset, liability, or a forecasted transaction, changes in the fair
value of the derivative instrument will be reported in other comprehensive
income. The gains and losses on the derivative instrument that are reported in
other comprehensive income will be reclassified as earnings in the periods in
which earnings are impacted by the variability of the cash flows of the hedged
item. The ineffective portion of all hedges will be recognized in current period
earnings. The Company must adopt SFAS No. 133 effective January 1, 2000. The
Company is in the process of analyzing the potential impact of this standard on
its financial statements presentation.

3.   ACQUISITION

       On November 12, 1997, the Company acquired a 50% interest in certain
producing properties in Grady County, Oklahoma (the "Acquisition"). These
properties were formerly owned by Mobil and were acquired by Ward Petroleum. The
acquisition was accounted for as a purchase and the results of operations of the
properties acquired were included in the Company's results of operations
effective September 1, 1997. The purchase price of $13.4 million was financed
primarily through the Company's existing revolving credit facility and was based
on the Company's determination of the fair value of the assets acquired.

                                      F1-10

<PAGE>   62



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Pro Forma Information

       The following unaudited pro forma statement of operations information has
been prepared to give effect to the Acquisition as if the transaction had
occurred at the beginning of 1996 and 1997. The historical results of operations
have been adjusted to reflect (i) the difference between the acquired
properties' historical depletion and such expense calculated based on the value
allocated to the acquired assets, (ii) the increase in interest expense
associated with the debt issued in the transaction, and (iii) the increase in
federal income taxes related to historical net income attributable to the
properties acquired. The pro forma amounts do not purport to be indicative of
the results of operations that would have been reported had the Acquisition
occurred as of the dates indicated, or that may be reported in the future (in
thousands).


<TABLE>
<CAPTION>
                                                                                       PRO FORMA
                                                                                      YEAR ENDED
                                                                                      DECEMBER 31,
                                                                                   -------------------
                                                                                     1997       1996
                                                                                   --------    -------
<S>                                                                                <C>         <C>    
Revenues.......................................................................... $ 11,194    $ 8,516
Costs and expenses:

      Lease operating and production taxes .......................................    1,864      1,300
      General and administrative .................................................    3,570      2,199
      Depletion of natural gas and oil properties ................................    3,307      2,791
      Depreciation and amortization ..............................................      593        487
      Interest expense, net ......................................................    2,235      2,355
                                                                                   --------    -------
      Total costs and expenses ...................................................   11,569      9,132
                                                                                   --------    -------
Net loss before income taxes .....................................................     (375)      (616)
      Income tax expense .........................................................    1,035         --
                                                                                   --------    -------
Net loss.........................................................................  $ (1,410)   $  (616)
                                                                                   ========    =======
Net loss per share:
      Basic/Diluted..............................................................  $  (0.13)   $ (0.07)
                                                                                   ========    =======
Common shares outstanding:
      Basic/Diluted ..............................................................   11,081      8,929
                                                                                   ========    =======
</TABLE>

4.   PROPERTY AND EQUIPMENT

       Property and equipment, at cost, are summarized as follows (in
thousands):

<TABLE>
<CAPTION>
                                                                            DECEMBER 31,
                                                                    ----------------------------
                                                                        1998            1997
                                                                    ------------    ------------
<S>                                                                 <C>             <C>         
Natural gas and oil properties....................................  $    179,867    $     96,587
Accumulated depletion.............................................      (45,550)        (12,293)
                                                                    ------------    ------------
                                                                         134,317          84,294
                                                                    ------------    ------------
Other property and equipment:
    3-D seismic interpretation workstations and software..........         2,186           1,693
    Office furniture and equipment................................         1,774           1,095
    Accumulated depreciation......................................        (1,946)         (1,549)
                                                                    ------------    ------------
                                                                           2,014           1,239
                                                                    ------------    ------------
                                                                    $    136,331    $     85,533
                                                                    ============    ============
</TABLE>


                                     F1-11
<PAGE>   63
                          BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)

       The accumulated depletion balance for natural gas and oil properties at
December 31, 1998, includes the effect of a capitalized ceiling impairment of
$24.8 million described at Note 2, "Property and Equipment."

     The Company sold its interest in certain producing properties for $74,000
during 1997. No gain or loss was recognized on this transaction because the
Company applies the full cost method of accounting for its investment in natural
gas and oil properties.

     The Company capitalizes certain payroll and other internal costs directly
attributable to acquisition, exploration and development activities as part of
its investment in natural gas and oil properties over the periods benefited by
these activities. Capitalized costs do not include any costs related to
production, general corporate overhead, or similar activities. During the years
ended December 31, 1996, 1997 and 1998, these capitalized costs amounted to $1.8
million, $3.5 million and $4.6 million, respectively.

5.   NOTES PAYABLE AND SENIOR SUBORDINATED NOTES PAYABLE

       In April 1996, the Company entered into a revolving credit facility which
provided for borrowings up to $25 million. On November 10, 1997, this facility
was amended and the amount available under the agreement was increased to $75
million. The Company's borrowings under this facility were limited to a
borrowing base determined periodically by the lender. This determination was
based upon the proved reserves of the Company's natural gas and oil properties.

       The amounts outstanding under this facility, excluding a $5.4 million
special advance made November 12, 1997, bore interest, at the borrower's option,
at the Base Rate or (i) LIBOR plus 1.75% if the principal outstanding was less
than or equal to 50% of the borrowing base, (ii) LIBOR plus 2.0% if the
principal outstanding was less than or equal to 75% but more than 50% of the
borrowing base, and (iii) LIBOR plus 2.25% if the principal outstanding was
greater than 75% of the borrowing base. The Base Rate is the fluctuating rate of
interest per annum established from time to time by the lender. Interest accrued
on the $5.4 million special advance at 11.50% per annum. The Company also paid a
quarterly commitment fee of 0.5% per annum for the unused portion of the
borrowing base.

       In January 1998, the Company entered into a new reserve-based revolving
credit facility (the "Credit Facility"). The Credit Facility originally provided
for borrowings up to $75 million, all of which was immediately available for
borrowing to fund capital expenditures. A portion of the funds available under
the Credit Facility were used to repay in full the debt outstanding under the
Company's previous revolving credit facility. Principal outstanding under the
Credit Facility is due at maturity on January 26, 2001 with interest due monthly
for base rate tranches or periodically as LIBOR tranches mature. Amounts
outstanding under the Credit Facility bore interest at either the lender's Base
Rate or LIBOR plus 2.25%, at the Company's option. The Credit Facility contains
covenants restricting the Company's ability to declare or pay dividends on its
stock. In connection with the origination of the Credit Facility, certain bank
fees and other expenses totaling approximately $1.9 million were recorded as
deferred costs and are amortized over the life of the loan. The Credit
Facility's borrowing base was reduced to $65 million upon issuance of the senior
subordinated notes in August 1998.


                                      F1-12

<PAGE>   64



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


     In March 1999, the Company and its lenders entered into an amendment to the
Credit Facility. Pursuant to this amendment, the borrowing availability under
the Credit Facility remains at $65 million and the initial borrowing
availability redetermination date was extended from January 31, 1999 to June 1,
1999, when the borrowing availability will be redetermined by the lenders based
on the Company's then proved reserve value and cash flows. To the extent that
the amounts outstanding under the Credit Facility exceed the borrowing
availability at the redetermination date, the Company may be required to repay
such excess under provision of the amendment. In addition, certain financial
covenants have been amended, additional covenants have been included that place
significant restrictions on the Company's ability to make certain capital
expenditures, and the annual interest rate for borrowings under the Credit
Facility is revised to the lender's base rate or LIBOR plus 3.0% and the Company
will pay the lender a $500,000 transaction fee over a ten month period. The
Company's obligations under the Credit Facility are secured by substantially all
of the natural gas and oil properties and other tangible assets of the Company.

     In August 1998, upon the filing of a registration statement with the SEC,
the Company issued $50 million of debt and equity securities to two affiliated
institutional investors. The financing transaction consisted of the issuance of
$40 million of senior subordinated secured notes (the "Notes") with warrants
(the "Warrants") to purchase the Company's common stock and the sale of $10
million of the Company's common stock, or 1,052,632 shares at a price of $9.50
per share. The combined sale of the Notes and common stock of the Company
generated proceeds, net of offering costs, of approximately $47.5 million that
was used to repay a portion of the then outstanding borrowings under the
Company's Credit Facility.

     The Notes mature in August 2003, with no principal payments required until
maturity and quarterly interest payments payable either in cash at an annual
rate of 12% or, in limited circumstances, the issuance of additional notes at an
annual interest rate of 13% for the first three years. The Company may repay the
Notes in full without premium at any time prior to maturity. The indenture
governing the Notes contains certain covenants including, but not limited to,
limitations or restrictions on indebtedness, distributions, affiliate
transactions, liens and sale and leaseback transactions. The indenture prohibits
all dividends on the Company's stock. Warrants to purchase 1 million shares of
the Company's common stock exercisable during a period of seven years at a price
of $10.45 per share were issued in connection with the Notes.

     The Notes are fully and unconditionally guaranteed, on a joint and several
basis, by each of the Company's subsidiaries (the "Subsidiary Guarantors"), all
of which are directly or indirectly wholly-owned by the Company. The obligations
of the Subsidiary Guarantors under the subsidiary guaranty agreements are
subordinated to the senior indebtedness of the Subsidiary Guarantors. The assets
of the parent, Brigham Exploration Company, consist solely of investments in its
subsidiaries.

     Concurrent with the issuance of the Notes, the Company recorded a discount
on the Notes of $4.5 million to reflect the estimated value of the Warrants.
Also in connection with the issuance of the Notes, certain fees and expenses
totaling approximately $1.8 million were recorded as deferred costs. The Note
discount and deferred fees are amortized over the five year term of the Notes.

     In March 1999, the indenture governing the Notes was amended to provide the
Company with the option to pay interest due on the Notes in kind, for any
reason, through the second quarter of 2000. In addition, certain financial and
other covenants were amended. The amendment also provides for a reduction in the
exercise price per share of the Warrants from $10.45 per share to $3.50 per
share.

                                      F1-13

<PAGE>   65


                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


6.   CAPITAL LEASE OBLIGATIONS

       Property under capital leases consists of the following (in thousands):

<TABLE>
<CAPTION>
                                                                                DECEMBER 31,
                                                                            --------------------
                                                                              1998        1997
                                                                            --------    --------
<S>                                                                         <C>         <C>     
3-D seismic interpretation workstations and software....................... $    620    $    497
Office furniture and equipment.............................................      167         204
                                                                            --------    --------
                                                                                 787         701
Accumulated depreciation and amortization..................................     (276)       (241)
                                                                            --------    --------
                                                                            $    511    $    460
                                                                            ========    ========
</TABLE>

       The obligations under capital leases are at fixed interest rates ranging
from 8.7% to 17.9% and are collateralized by property, plant and equipment. The
future minimum lease payments under the capital leases and the present value of
the net minimum lease payments at December 31, 1998 are as follows (in
thousands):


<TABLE>
<S>                                                                                               <C>   
1999............................................................................................. $  323
2000.............................................................................................    237
2001.............................................................................................     95
2002.............................................................................................     24
                                                                                                  ------
Total minimum lease payments.....................................................................    679
    Estimated executory costs included in capital leases.........................................   (50)
                                                                                                  ------
Net minimum lease payments.......................................................................    629
    Amounts representing interest................................................................   (90)
                                                                                                  ------
Present value of net minimum lease payments......................................................    539
Less:  current portion...........................................................................  (240)
                                                                                                  ------
Noncurrent portion............................................................................... $  299
                                                                                                  ======
</TABLE>

7.   INCOME TAXES

       The provision for income taxes consists of the following (in thousands):


<TABLE>
<CAPTION>
                                                                                           YEAR ENDED
                                                                                          DECEMBER 31,
                                                                                  ----------------------------
                                                                                      1998            1997
                                                                                  ------------    ------------
<S>                                                                               <C>             <C>         
Current income taxes:
    Federal...................................................................... $         --    $         --
    State........................................................................           --              --
Deferred income taxes:
    Federal .....................................................................       (1,186)          1,186
    State........................................................................           --              --
                                                                                  ------------    ------------
                                                                                  $     (1,186)   $      1,186
                                                                                  ============    ============
</TABLE>

       The difference in income taxes provided and the amounts determined by
applying the federal statutory tax rate to income before income taxes result
from the following (in thousands):

                                      F1-14

<PAGE>   66



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



<TABLE>
<CAPTION>
                                                                                           YEAR ENDED
                                                                                          DECEMBER 31,
                                                                                  ----------------------------
                                                                                      1998            1997
                                                                                  ------------    ------------
<S>                                                                               <C>             <C>         
Tax at statutory rate............................................................ $    (11,740)   $         23
Add (deduct) the effect of:
    January and February 1997 income, not taxable................................           --            (44)
    Tax effect of Exchange.......................................................           --           1,193
    Nondeductible expenses ......................................................           10              14
    Valuation reserve............................................................       10,544              --
                                                                                 -------------    ------------
                                                                                 $      (1,186)   $      1,186
                                                                                 =============    ============
</TABLE>

       The components of deferred income tax assets and liabilities are as
follows (in thousands):


<TABLE>
<CAPTION>
                                                                                          DECEMBER 31,
                                                                                   ---------------------------
                                                                                      1998            1997
                                                                                   -----------    ------------
<S>                                                                                <C>            <C>         
Deferred tax assets:
    Net operating loss carryforwards.............................................. $    11,219    $      5,563
    Amortization of stock compensation............................................         258             132
    Other.........................................................................           3               3
                                                                                   -----------    ------------
                                                                                        11,480           5,698
Deferred tax liability:
    Depreciable and depletable property...........................................        (936)         (6,884)
    Valuation reserve.............................................................     (10,544)             --
                                                                                   -----------    ------------
                                                                                   $        --    $     (1,186)
                                                                                   ===========    ============
</TABLE>

       At December 31, 1998, the Company had regular and alternative minimum tax
net operating loss carryforwards of approximately $32.9 million and $23.7
million, respectively, each including separate return limitation year carryovers
of approximately $1.2 million, which expire by December 31, 2018.

8.   NET INCOME (LOSS) PER SHARE

       Net income (loss) per share is presented in the consolidated financial
statements based on a basic EPS calculation as well as a diluted EPS
calculation. Basic EPS is computed by dividing net income (loss) applicable to
common shareholders by the weighted average number of common shares outstanding
during each period. Diluted EPS is computed by dividing net income (loss)
applicable to common shareholders by the weighted average number of common
shares and common share equivalents outstanding (if dilutive), during each
period. The number of common share equivalents outstanding is computed using the
treasury stock method.

       Historical net loss per common share for 1996 is based on shares issued
upon consummation of the Exchange, assuming such shares has been outstanding for
all periods presented. Net loss per share for 1997 is presented giving effect to
the shares issued pursuant to the Exchange as well as shares issued in the
initial public offering. At December 31, 1997 and 1998, options and warrants to
purchase 628,737 and 1,194,654, respectively, shares of common stock were
outstanding but were not included in the computation of diluted EPS due to the
anti-dilutive effect they would have on EPS if converted.

                                      F1-15

<PAGE>   67



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


9.   CONTINGENCIES, COMMITMENTS AND FACTORS WHICH MAY AFFECT FUTURE OPERATIONS

Litigation

       The Company is, from time to time, party to certain lawsuits and claims
arising in the ordinary course of business. While the outcome of lawsuits and
claims cannot be predicted with certainty, management does not expect these
matters to have a materially adverse effect on the financial condition, results
of operations or cash flows of the Company.

       As of December 31, 1998, there were no known environmental or other
regulatory matters related to the Company's operations which are reasonably
expected to result in a material liability to the Company. Compliance with
environmental laws and regulations has not had, and is not expected to have, a
material adverse effect on the Company's capital expenditures, earnings or
competitive position.

Lease Commitments

       The Company leases office equipment and space under operating leases
expiring at various dates through 2002. The future minimum annual rental
payments under the noncancelable terms of these leases at December 31, 1998, are
as follows (in thousands):


<TABLE>
<S>                                                                <C>         
     1999........................................................  $        868
     2000........................................................           790
     2001........................................................           789
     2002........................................................           395
                                                                   ------------
                                                                   $      2,842
                                                                   ============
</TABLE>

       Rental expense for the years ended December 31, 1996, 1997 and 1998 was
$253,112, $606,173 and $875,150, respectively.

Factors Which May Affect Future Operations

       Since the Company's major products are commodities, significant changes
in the prices of natural gas and oil could have a significant impact on the
Company's results of operations for any particular year.

     Due to an expectation for continuing difficult industry and capital markets
conditions, the Company has substantially reduced its planned capital budget for
1999 and has undertaken a number of strategic initiatives in an effort to
improve and preserve its capital liquidity in the current environment. The
Company has adapted its business strategy in the near-term through the
implementation of the following principal strategic initiatives: (i) focusing
all of the Company's planned exploration efforts in 1999 towards the drilling of
its highest grade 3-D prospects, (ii) eliminating substantially all planned
seismic and land expenditures for new projects until its capital resources can
support such additional activity, (iii) seeking to divest certain producing
natural gas and oil properties in an effort to raise capital to reduce debt
borrowings and to redirect capital to drilling projects that have the potential
to generate higher investment returns, (iv) restructuring its outstanding senior
and subordinated debt agreements to provide the Company with flexibility needed
to preserve cash flow to fund its expected near-term exploration activities, (v)
implementing an overhead

                                      F1-16

<PAGE>   68



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


reduction plan to reduce annual general and administrative expenses, and (vi)
evaluating opportunities to raise additional equity capital either through the
sales of interests in certain of its seismic projects or the issuance of equity
securities. The Company believes that the successful execution of these
strategic initiatives will provide it with sufficient capital resources to
execute its planned 1999 exploration program and position it to realize the
significant value it believes it has captured in its inventory of 3-D seismic
projects and delineated drilling locations. While the Company has initiated each
of these strategic directives in late 1998 and early 1999, and has effected
certain of them to date, the successful completion of any or all of these
efforts to improve the Company's capital availability within the expected time
frame is uncertain and will likely have a material impact on the Company's
near-term capital expenditure levels and growth profile.

10.  SEGMENT INFORMATION

     In June 1997, the FASB issued SFAS No. 131, "Disclosures about Segments of
an Enterprise and Related Information," which the Company adopted in the first
quarter of 1998. The statement supersedes SFAS No. 14, "Financial Reporting for
Segments of a Business Enterprise," replacing the "industry segment" approach
with the "management" approach. The management approach designates the internal
organization that is used by management for making operating decisions and
assessing performance as the source of the Company's reportable segments. It
also requires disclosures about products and services, geographic areas and
major customers.

     All of the Company's natural gas and oil properties and related operations
are located in the United States and management has determined that the Company
has one reportable segment.

       During 1998, approximately 25%, 15%, 11% and 11% of the Company's natural
gas and oil production was sold to four separate customers. During 1997,
approximately 14% and 12% of the Company's natural gas and oil production was
sold to two separate customers. During 1996, approximately 16%, 12% and 10% of
the Company's natural gas and oil production was sold to three separate
customers. However, due to the availability of other markets, the Company does
not believe that the loss of any one of these individual customers would
adversely affect the Company's result of operations.

11.  FINANCIAL INSTRUMENTS

       The Company periodically enters into commodity price swap agreements
which require payments to (or receipts from) counterparties based on the
differential between a fixed price and a variable price for a fixed quantity of
natural gas or crude oil without the exchange of the underlying volumes. The
notional amounts of these derivative financial instruments are based on planned
production from existing wells. The Company uses these derivative financial
instruments to manage market risks resulting from fluctuations in commodity
prices. Commodity price swaps are effective in minimizing these risks by
creating essentially equal and offsetting market exposures. The derivative
financial instruments held by the Company are not leveraged and are held for
purposes other than trading.

       In 1996 and 1997, the Company was a party to a crude oil swap arrangement
resulting in a fixed price over a period of time for a specified volume of crude
oil. Adjustment to the price received for oil under these

                                      F1-17

<PAGE>   69



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


swap arrangements resulted in a decrease in oil revenues of $301,280 and $6,191
in 1996 and 1997, respectively.

     In February 1998, the Company entered into a hedging contract whereby
10,000 MMBtu per day of natural gas is purchased and sold subject to a fixed
price swap agreement for monthly periods from April 1998 through October 1999.
Pursuant to these arrangements the Company exchanges a floating market price for
a contract month and payments are received when the fixed price exceeds the
floating price. Total natural gas subject to this hedging contract is 2,750,000
MMBtu in 1998 and 3,040,000 MMBtu in 1999. As a result of this natural gas
hedging contract, the Company realized an increase in revenues of $555,240
during 1998.

     In August 1998, the Company entered into a hedging contract whereby 5,000
MMBtu per day of natural gas is purchased and sold subject to a fixed price swap
agreement for monthly periods from April 1999 through October 1999. Pursuant to
these arrangements the Company exchanges a floating market price for a fixed
contract price of $2.015 per MMBtu. Payments are made by the Company when the
floating price exceeds the fixed price for a contract month and payments are
received when the fixed price exceeds the floating price. Total natural gas
subject to this hedging contract is 1,070,000 MMBtu in 1999.

     In January 1999, the Company entered into a swap agreement with terms
similar to existing agreements which relates to production for monthly periods
from November 1999 through April 2001. Pursuant to these arrangements, 15,000
MMBtu per day of natural gas is purchased and sold subject to a fixed price swap
agreement, and the Company exchanges a floating market price for a fixed
contract price of $2.065 per MMBtu. Total natural gas volumes subject to this
agreement are 915,000 MMBtu, 5,490,000 MMBtu and 1,800,000 MMBtu in 1999, 2000
and 2001, respectively.

       The Company's non-derivative financial instruments include cash and cash
equivalents, accounts receivable, accounts payable and long-term debt. The
carrying amount of cash and cash equivalents, accounts receivable and accounts
payable approximate fair value because of their immediate or short maturities.
The carrying value of the Company's revolving credit facility (see Note 5)
approximates its fair market value since it bears interest at floating market
interest rates.

       The Company's accounts receivable relate to natural gas and oil sales to
various industry companies, amounts due from industry participants for
expenditures made by the Company on their behalf and workstation revenues.
Credit terms, typical of industry standards, are of a short-term nature and the
Company does not require collateral. The Company's accounts receivable at
December 31, 1998 do not represent significant credit risks as they are
dispersed across many counterparties. Counterparties to the natural gas and
crude oil price swaps are investment grade financial institutions.

12.  EMPLOYEE BENEFIT PLANS

Retirement Savings Plan

       During 1996 the Company adopted a defined contribution 401(k) plan for
substantially all of its employees. Eligible employees may contribute up to 15%
of their compensation to this plan. The 401(k) plan provides that the Company
may, at its discretion, match employee contributions. The Company has not
matched employee contributions in any plan year.

                                      F1-18

<PAGE>   70

                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Stock Compensation

       In 1994 three employees were granted restricted interests in the Company
which vest in increments through July 1999. At the date of grant, the value of
these interests was immaterial. On February 26, 1997, in connection with the
Exchange (see Note 1), the three employees transferred these company interests
to the Company in exchange for 156,250 shares of restricted common stock of the
Company. The terms of the restricted stock and the restricted company interests
are substantially the same. The shares vest over a three-year period ending in
1999. No compensation expense will result from this exchange.

       The Company adopted an incentive plan, effective upon completion of the
Exchange (see Note 1), which provides for the issuance of stock options, stock
appreciation rights, stock, restricted stock, cash or any combination of the
foregoing. The objective of this plan is to reward key employees whose
performance may have a significant effect on the success of the Company. An
aggregate of 1,588,170 shares of the Company's common stock was reserved for
issuance pursuant to this plan. The Compensation Committee of the Board of
Directors will determine the type of awards made to each participant and the
terms, conditions and limitations applicable to each award. Options granted
subsequent to March 4, 1997 have an exercise price equal to the fair market
value of the Company's common stock on the date of grant and generally vest, in
increments, over five to six years.

     The Company also maintains a plan under which it offers stock compensation
to non-employee directors. Pursuant to the terms of the plan, non-employee
directors are entitled to annual grants. Options granted under this plan have an
exercise price equal to the fair value of the Company's common stock on the date
of grant and generally vest over five years.

     The following table summarizes activity under the incentive plan for each
of the two years ended December 31, 1998:


<TABLE>
<CAPTION>
                                                                                                   WEIGHTED
                                                                                                    AVERAGE
                                                                                                    EXERCISE
                                                                                     SHARES          PRICE
                                                                                  ------------    ------------
<S>                                                                               <C>             <C>
Options outstanding December 31, 1996...........................................            --    $         --
      Options granted ..........................................................       646,097            5.03
      Options forfeited or cancelled............................................      (17,360)            5.00
      Options exercised.........................................................            --              --
                                                                                  ------------    ------------
Options outstanding December 31, 1997...........................................       628,737            5.03
      Options granted...........................................................       873,500            8.62
      Options forfeited or cancelled............................................     (307,583)         (12.88)
      Options exercised.........................................................            --              --
                                                                                  ------------    ------------
Options outstanding December 31, 1998...........................................     1,194,654    $       5.63
                                                                                  ============    ============
</TABLE>

     On December 14, 1998, the Board of Directors approved a proposal to cancel
and reissue outstanding employee stock options which were granted in January
1998 with an exercise price of $12.88. A total of 305,250 options with an
exercise price of $12.88 per share were cancelled and reissued with an exercise
price

                                      F1-19

<PAGE>   71



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


of $6.31 per share, the fair market value of the Company's stock at the date of
reissuance. Vesting schedules remained unchanged by the reissuance.

     Exercise prices for options outstanding at December 31, 1997 range from
$5.00 to $14.375 and remaining contractual lives range from 5.5 years to 6
years. Exercise prices for options outstanding at December 31, 1998 range from
$5.00 to $14.375 and remaining contractual lives range from 5.5 years to 7
years. No options were exercisable at December 31, 1997 and 145,740 were
exercisable at December 31, 1998.

     The weighted average fair value per share of stock compensation issued
during 1997 and 1998 was $6.24 and $5.40, respectively. The fair value for these
options was estimated using the Black-Scholes model with the following weighted
average assumptions for grants made in 1997 and 1998: risk free interest rate of
6.24% and 4.70%; volatility of the expected market prices of the Company's
common stock of 38% and 77%; expected dividend yield of zero and weighted
average expected option lives of 7.3 and 5.0 years, respectively.

     The Black-Scholes valuation model was developed for use in estimating the
fair value of traded options which have no vesting restrictions and are
transferable. Additionally, the assumptions required by the valuation model are
highly subjective. Because the Company's stock options have significantly
different characteristics from those of traded options, and because changes in
the subjective input assumptions can materially affect the fair value estimate,
in management's opinion the model does not necessarily provide a reliable single
measure of the fair value of the Company's stock options.

     Had compensation cost for the Company's stock options been determined based
on the fair market value at the grant dates of the awards consistent with the
methodology prescribed by SFAS No. 123 the Company's net loss and net loss per
share for 1998, 1997 and 1996 would have been the pro forma amounts indicated
below:


<TABLE>
<CAPTION>
                                                                                                 1998           1997
                                                                                              -----------    -----------
<S>                                                                                           <C>            <C>        
Net loss:
    As reported.............................................................................. $   (33,345)   $   (1,117)
    Pro forma       .........................................................................     (33,591)       (1,314)
Net loss per share:
    As reported..............................................................................       (2.64)        (0.10)
    Pro forma................................................................................       (2.66)        (0.12)
</TABLE>

     The Company granted 644,097 stock options as of March 4, 1997. These
options have an exercise price of $5.00 compared to an originally determined
estimated fair market value of the Company's common stock at date of grant of
$8.00. This grant resulted in noncash compensation expense which is being
recognized over the related vesting period of the options. During 1999, the
Company revised the fair market value of its common stock at the date these
options were granted from $8.00 to $9.00. As a result, the Company restated its
financial statements to reflect the impact of this change in estimate.

     The impact of the restatement on the 1997 financial statements is presented
below:


                                      F1-20

<PAGE>   72



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



<TABLE>
<CAPTION>
                                                                                     AS
                                                                                 PREVIOUSLY          AS
                                                                                  REPORTED        RESTATED
                                                                               --------------   -------------
<S>                                                                            <C>              <C>          
For the year ended December 31, 1997
      Net loss ..............................................................  $      (1,036)   $     (1,117)
      Net loss per share:
         Basic/Diluted.......................................................          (0.09)          (0.10)
As of December 31, 1997
      Retained earnings/(accumulated deficit)................................              26            (55)
          Total stockholders' equity.........................................          43,153          43,313
</TABLE>


13.  RELATED PARTY TRANSACTIONS

       During the years ended December 31, 1996, 1997 and 1998, the Company paid
approximately $596,000, $837,000 and $851,000 respectively, in fees for land
acquisition services performed by a company owned by a brother of the Company's
President and Chief Executive Officer. Other participants in the Company's 3-D
seismic projects reimbursed the Company for a portion of these amounts.

       In 1996 and 1997, the Company paid $110,000 and $18,000 for working
interests in natural gas and oil properties owned by affiliates of a member of
the Company's board of directors/management committee. The Company billed the
affiliates $68,000 in 1996 for their proportionate share of the costs related to
this project.

       A Director of the Company served as a consultant to the Company on
various aspects of the Company's business and strategic issues. Fees paid for
these services by the Company were $79,200, $86,580 and $100,539 for the twelve
month periods ended December 31, 1996, 1997 and 1998, respectively. Additional
disbursements totaling approximately $13,000 and $12,000 were made during 1997
and 1998, respectively, for the reimbursement of certain expenses.

14.  SUBSEQUENT EVENT

     In February 1999, the Company entered into a project financing arrangement
with Duke Energy Financial Services, Inc. ("Duke") to fund the continued
exploration of five projects covered by approximately 200 square miles of 3-D
seismic data acquired in 1998. In this transaction, the Company conveyed 100% of
its working interest in land and seismic in these project areas to a newly
formed limited liability company (the "Duke LLC") for a total consideration of
$10 million. The Company is the managing member of the Duke LLC with a 1%
interest, and Duke is the sole remaining member with a 99% interest. Pursuant to
the terms of the Duke LLC agreement, the Company pays 100% of the drilling and
completion costs for all wells drilled by the Duke LLC in exchange for a 70%
working interest in the wells and their associated drilling and spacing units
and allocable seismic data. Upon 100% project payout, the Company has certain
rights to back-in for up to a 94% effective working interest in the Duke LLC
properties.



                                     F1-21

<PAGE>   73



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


15.  NATURAL GAS AND OIL EXPLORATION AND PRODUCTION ACTIVITIES

       The tables presented below provide supplemental information about natural
gas and oil exploration and production activities as defined by SFAS No. 69,
"Disclosures about Oil and Gas Producing Activities."

Results of Operations for Natural Gas and Oil Producing Activities (in
thousands)


<TABLE>
<CAPTION>
                                                                               YEAR ENDED DECEMBER 31,
                                                                          ----------------------------------
                                                                             1998        1997        1996
                                                                          ----------   ---------   ---------
<S>                                                                       <C>          <C>         <C>      
Natural gas and oil sales...............................................  $   13,799   $   9,184   $   6,141
Costs and expenses:
    Lease operating.....................................................       2,172       1,151         726
    Production taxes....................................................         850         549         362
    Depletion of natural gas and oil properties.........................       8,410       2,743       2,323
    Capitalized ceiling impairment......................................      24,847          --          --
    Income tax expense (benefit) (a)....................................     (7,868)       1,318          --
                                                                          ----------   ---------   ---------
Total costs and expenses................................................      28,411       5,761       3,411
                                                                          ----------   ---------   ---------
                                                                          $ (14,612)   $   3,423   $   2,730
                                                                          ==========   =========   =========
Depletion per physical unit of production (equivalent Mcf of gas).......  $     1.27   $    0.88   $    1.13
                                                                          ==========   =========   =========
</TABLE>

- ------------
       (a) The income tax expense (benefit) for 1997 and 1998 is calculated at
           the statutory rate and determined without regard to the Company's
           deduction for general and administrative expenses, interest costs and
           other income tax deductions and credits.

       Natural gas and oil sales reflect the market prices of net production
sold or transferred, with appropriate adjustments for royalties, net profits
interest and other contractual provisions. Lease operating expenses include
lifting costs incurred to operate and maintain productive wells and related
equipment, including such costs as operating labor, repairs and maintenance,
materials, supplies and fuel consumed. Production taxes include production and
severance taxes. No provision was made for income taxes for 1996 since these
taxes are the responsibility of the partners (see Note 2). Depletion of natural
gas and oil properties relates to capitalized costs incurred in acquisition,
exploration and development activities. Results of operations do not include
interest expense and general corporate amounts.

Costs Incurred and Capitalized Costs

       The costs incurred in natural gas and oil acquisition, exploration and
development activities follow (in thousands):

<TABLE>
<CAPTION>
                                                                                   DECEMBER 31,
                                                                     ---------------------------------------
                                                                        1998          1997          1996
                                                                     -----------   -----------   -----------
<S>                                                                  <C>           <C>           <C>        
Costs incurred for the year:
    Exploration....................................................  $    67,110   $    29,516   $    10,527
    Property acquisition...........................................       16,245        26,956         6,195
    Development....................................................       10,427         2,953         1,328
    Proceeds from participants.....................................     (10,502)         (319)       (4,111)
                                                                     -----------   -----------   -----------
                                                                     $    83,280   $    59,106   $    13,939
                                                                     ===========   ===========   ===========
</TABLE>

                                     F1-22
<PAGE>   74


                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


       Costs incurred represent amounts incurred by the Company for exploration,
property acquisition and development activities. Periodically, the Company will
receive proceeds from participants subsequent to project initiation for an
assignment of an interest in the project. These payments are represented by
"Proceeds from participants" in the table above.

       Capitalized costs related to natural gas and oil acquisition, exploration
and development activities follow (in thousands):

<TABLE>
<CAPTION>
                                                                                         DECEMBER 31,
                                                                                 ----------------------------
                                                                                     1998            1997
                                                                                 ------------    ------------
<S>                                                                              <C>             <C>         
Cost of natural gas and oil properties at year-end:
    Proved.....................................................................  $    127,491    $     67,744
    Unproved...................................................................        52,376          28,843
                                                                                 ------------    ------------
    Total capitalized costs....................................................       179,867          96,587
    Accumulated depletion......................................................      (45,550)        (12,293)
                                                                                 ------------    ------------
                                                                                 $    134,317    $     84,294
                                                                                 ============    ============
</TABLE>

       Following is a summary of costs (in thousands) excluded from depletion at
December 31, 1998, by year incurred. At this time, the Company is unable to
predict either the timing of the inclusion of these costs and the related
natural gas and oil reserves in its depletion computation or their potential
future impact on depletion rates.


<TABLE>
<CAPTION>
                                                           DECEMBER 31,                 
                                                -----------------------------------     PRIOR
                                                   1998         1997        1996        YEARS       TOTAL
                                                ----------   ----------   ---------   ---------   ----------
<S>                                             <C>          <C>          <C>         <C>         <C>       
Property acquisition..........................  $    9,659   $   13,161   $   1,176   $   1,278   $   25,274
Exploration...................................      21,577        5,072         320         133       27,102
                                                ----------   ----------   ---------   ---------   ----------
Total.........................................  $   31,236   $   18,233   $   1,496   $   1,411   $   52,376
                                                ==========   ==========   =========   =========   ==========
</TABLE>

16.  NATURAL GAS AND OIL RESERVES AND RELATED FINANCIAL DATA (UNAUDITED)

       Information with respect to the Company's natural gas and oil producing
activities is presented in the following tables. Reserve quantities as well as
certain information regarding future production and discounted cash flows were
determined by the Company's independent petroleum consultants and internal
petroleum reservoir engineer.

Natural Gas and Oil Reserve Data

       The following tables present the Company's estimates of its proved
natural gas and oil reserves. The Company emphasizes that reserve estimates are
approximates and are expected to change as additional information becomes
available. Reservoir engineering is a subjective process of estimating
underground accumulations of natural gas and oil that cannot be measured in an
exact way, and the accuracy of any reserve estimate is a function of the quality
of available data and of engineering and geological interpretation and judgment.
Accordingly, there can be no assurance that the reserves set forth herein will
ultimately be produced nor can there be assurance that the proved undeveloped
reserves will be developed within the periods anticipated. A substantial portion
of the reserve balances were estimated utilizing the volumetric method, as
opposed to the production performance method.

                                      F1-23

<PAGE>   75


                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



<TABLE>
<CAPTION>
                                                                                   NATURAL    
                                                                                     GAS             OIL
                                                                                    (MMCF)         (MBBLS)
                                                                                 ------------    ------------
<S>                                                                              <C>             <C>  
Proved reserves at December 31, 1995...........................................         4,257           1,672
    Revisions to previous estimates............................................       (1,005)           (232)
    Extensions, discoveries and other additions................................         7,742             996
    Purchase of minerals-in-place..............................................           260               3
    Sales of minerals-in-place.................................................         (299)           (272)
    Production.................................................................         (698)           (227)
                                                                                 ------------    ------------
Proved reserves at December 31, 1996...........................................        10,257           1,940
    Revisions to previous estimates............................................       (3,044)           (447)
    Extensions, discoveries and other additions................................        33,721             735
    Purchase of minerals-in-place..............................................        13,718           1,244
    Sales of minerals-in-place.................................................          (40)              --
    Production.................................................................       (1,382)           (291)
                                                                                 ------------    ------------
Proved reserves at December 31, 1997...........................................        53,230           3,181
    Revisions of previous estimates............................................      (26,696)           (115)
    Extensions, discoveries and other additions................................        48,050           1,752
    Purchase of minerals-in-place..............................................           851              11
    Production.................................................................       (4,269)           (396)
                                                                                 ------------    ------------
Proved reserves at December 31, 1998...........................................        71,166           4,433
                                                                                 ============    ============

Proved developed reserves at December 31:
    1996.......................................................................         6,034           1,453
    1997.......................................................................        30,677           2,665
    1998.......................................................................        38,571           2,935
</TABLE>

       Proved reserves are estimated quantities of crude natural gas and oil
which geological and engineering data indicate with reasonable certainty to be
recoverable in future years from known reservoirs under existing economic and
operating conditions. Proved developed reserves are proved reserves which can be
expected to be recovered through existing wells with existing equipment and
operating methods.

Standardized Measure of Discounted Future Net Cash Inflows and Changes Therein

       The following table presents a standardized measure of discounted future
net cash inflows (in thousands) relating to proved natural gas and oil reserves.
Future cash flows were computed by applying year end prices of natural gas and
oil relating to the Company's proved reserves to the estimated year-end
quantities of those reserves. Future price changes were considered only to the
extent provided by contractual agreements in existence at year-end. Future
production and development costs were computed by estimating those expenditures
expected to occur in developing and producing the proved natural gas and oil
reserves at the end of the year, based on year-end costs. Actual future cash
inflows may vary considerably and the standardized measure does not necessarily
represent the fair value of the Company's natural gas and oil reserves.


                                      F1-24

<PAGE>   76
                          BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



<TABLE>
<CAPTION>
                                                                                   DECEMBER 31,
                                                                     ---------------------------------------
                                                                        1998          1997          1996
                                                                     -----------   -----------   -----------
<S>                                                                  <C>           <C>           <C>        
Future cash inflows................................................  $   198,082   $   165,156   $    84,987
Future development and production costs............................     (61,064)      (40,923)      (20,998)
Future income taxes................................................      (6,972)      (22,919)            --
                                                                     -----------   -----------   -----------
Future net cash inflows............................................  $   130,046   $   101,314   $    63,989
                                                                     ===========   ===========   ===========

Future net cash inflow before income taxes, discounted
    at 10% per annum...............................................  $    81,741   $    69,249   $    44,506
                                                                     ===========   ===========   ===========

Standardized measure of future net cash inflows discounted
    at 10% per annum...............................................  $    81,649   $    64,274   $    44,506
                                                                     ===========   ===========   ===========
</TABLE>

       The base sales prices for the Company's reserves were $3.71 per Mcf for
natural gas and $25.37 per Bbl for oil as of December 31, 1996, $2.27 per Mcf
for natural gas and $15.50 per Bbl for oil as of December 31, 1997, and $2.12
per Mcf for natural gas and $9.50 per Bbl for oil as of December 31, 1998. These
base prices were adjusted to reflect applicable transportation and quality
differentials on a well-by-well basis to arrive at realized sales prices used to
estimate the Company's reserves at these dates.

       Changes in the future net cash inflows discounted at 10% per annum
follow:


<TABLE>
<CAPTION>
                                                                                   DECEMBER 31,
                                                                     ---------------------------------------
                                                                        1998          1997          1996
                                                                     -----------   -----------   -----------
<S>                                                                  <C>           <C>           <C>        
Beginning of period................................................  $    64,274   $    44,506   $    18,222
    Sales of natural gas and oil produced, net of production
         costs.....................................................     (10,776)       (7,484)       (5,053)
    Development costs incurred.....................................        5,423         1,955           246
    Extensions and discoveries.....................................       52,389        38,016        29,457
    Purchases of minerals-in-place.................................          687        16,965           384
    Sales of minerals-in-place.....................................           --          (94)       (2,380)
    Net change of prices and production costs......................     (11,921)      (20,466)         7,023
    Change in future development costs.............................        (656)           319           303
    Changes in production rates and other..........................      (6,109)       (1,954)         (342)
    Revisions of quantity estimates................................     (23,470)       (6,964)       (5,176)
    Accretion of discount..........................................        6,925         4,450         1,822
    Change in income taxes ........................................        4,883       (4,975)            --
                                                                     -----------   -----------   -----------
End of period......................................................  $    81,649   $    64,274   $    44,506
                                                                     ===========   ===========   ===========
</TABLE>

                                     F1-25
<PAGE>   77
                                 EXHIBIT INDEX


<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
2.1      --       Exchange Agreement (filed as Exhibit 2.1 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
3.1      --       Certificate of Incorporation (filed as Exhibit 3.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
3.2      --       Bylaws (filed as Exhibit 3.2 to the Company's Registration 
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
4.1      --       Form of Common Stock Certificate (filed as Exhibit 4.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
4.2+     --       Indenture dated as of August 20, 1998 between Brigham 
                  Exploration Company and Chase Bank of Texas, National
                  Association, as Trustee.
4.2.1++  --       Supplemental Indenture dated as of March 26, 1999 between
                  Brigham Exploration Company and Chase Bank of Texas, National
                  Association, as Trustee.
4.3++    --       Form of Warrant Certificate.
4.4      --       Form of Senior Subordinated Secured Note due 2003 (filed as
                  Exhibit 4.4 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-53873), and incorporated herein by
                  reference).
10.1     --       Agreement of Limited Partnership, dated May 1, 1992, between
                  Brigham Exploration Company and General Atlantic Partners III,
                  L.P. as general partners, and Harold D. Carter and GAP-Brigham
                  Partners, L.P. as limited partners (filed as Exhibit 10.1 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.1.1   --       Amendment No. 1 to Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated May 1, 1992, by and among
                  Brigham Exploration Company, General Atlantic Partners III,
                  L.P., GAP-Brigham Partners, L.P. and Harold D. Carter (filed
                  as Exhibit 10.1.1 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.1.2   --       Amendment No. 2 to Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated September 30, 1994, by and
                  among Brigham Exploration Company, General Atlantic Partners
                  III, L.P., GAP-Brigham Partners, L.P., Harold D. Carter and
                  the additional signatories thereto (filed as Exhibit 10.1.2 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.1.3   --       Amendment No. 3 to Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated August 24, 1995, by and among
                  Brigham Exploration Company, General Atlantic Partners III,
                  L.P., GAP-Brigham Partners, L.P., Harold D.
</TABLE>



<PAGE>   78



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
                  Carter, Craig M. Fleming, David T. Brigham and Jon L. Glass
                  (filed as Exhibit 10.1.3 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.1.4+  --       Amended and Restated Agreement of Limited Partnership of
                  Brigham Oil & Gas, L.P., dated December 30, 1997 by and among
                  Brigham, Inc., Brigham Holdings I, L.L.C. and Brigham Holdings
                  II, L.L.C.
10.2     --       Agreement of Limited Partnership of Venture Acquisitions,
                  L.P., dated September 23, 1994, by and between Quest
                  Resources, L.L.C. and RIMCO Energy, Inc. as general partners,
                  and RIMCO Production Company, Inc., RIMCO Exploration
                  Partners, L.P. I and RIMCO Exploration Partners, L.P. II, as
                  limited partners (filed as Exhibit 10.2 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.3     --       Regulations of Quest Resources, L.L.C. (filed as Exhibit 10.3
                  to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.4     --       Management and Ownership Agreement, dated September 23, 1994,
                  by and among Brigham Oil & Gas, L.P., Brigham Exploration
                  Company, General Atlantic Partners III, L.P., Harold D.
                  Carter, Ben M. Brigham and GAP- Brigham Partners, L.P. (filed
                  as Exhibit 10.4 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.5*    --       Consulting Agreement, dated May 1, 1997, by and between 
                  Brigham Oil & Gas, L.P. and Harold D. Carter (filed as Exhibit
                  10.4 to the Company's Registration Statement on Form S-1
                  (Registration No. 33-53873), and incorporated herein by
                  reference).
10.6*    --       Employment Agreement, by and between Brigham Exploration
                  Company and Ben M. Brigham (filed as Exhibit 10.7 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.7*    --       Form of Confidentiality and Noncompete Agreement between the 
                  Registrant and each of its executive officers (filed as
                  Exhibit 10.8 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.8*    --       1997 Incentive Plan of Brigham Exploration Company (filed as
                  Exhibit 10.9 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333- 22491), and incorporated herein by
                  reference).
10.8.1*  --       Form of Option Agreement for certain executive officers (filed
                  as Exhibit 10.9.1 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333- 22491), and incorporated
                  herein by reference).
10.8.2*  --       Option Agreement dated as of March 4, 1997, by and between
                  Brigham Exploration Company and Jon L. Glass (filed as Exhibit
                  10.9.2 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.9*    --       Incentive Bonus Plan dated as of February 28, 1997 of Brigham,
                  Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit 10.10 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.10    --       Two Bridgepoint Lease Agreement, dated September 30, 1996,
                  by and between Investors Life Insurance Company of North
                  America and Brigham Oil & Gas, L.P. (filed as Exhibit 10.14 to
                  the Company's Registration Statement on Form S- 1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
</TABLE>



<PAGE>   79



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
10.10.1  --       First Amendment to Two Bridge Point Lease Agreement dated
                  April 11, 1997 between Investors Life Insurance Company of
                  North America and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.9.1 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-53873), and incorporated herein by
                  reference).
10.10.2  --       Second Amendment to Two Bridge Point Lease Agreement dated
                  October 13, 1997 between Investors Life Insurance Company of
                  North America and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.9.2 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-53873), and incorporated herein by
                  reference).
10.10.3  --       Letter dated April 17, 1998 exercising Right of First Refusal
                  to Lease "3rd Option Space" (filed as Exhibit 10.9.3 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-53873), and incorporated herein by reference).
10.11    --       Anadarko Basin Seismic Operations Agreement, dated 
                  February 15, 1996, by and between Brigham Oil & Gas, L.P. and
                  Veritas Geophysical, Ltd. (filed as Exhibit 10.15 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.11.1  --       Letter Amendment to Anadarko Basin Seismic Operations 
                  Agreement, dated June 10, 1996, between Brigham Oil & Gas,
                  L.P. and Veritas Geophysical, Ltd. (filed as Exhibit 10.15.1
                  to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.12    --       Expense Allocation and Participation Agreement, dated April 1,
                  1996, between Brigham Oil & Gas, L.P. and Gasco Limited
                  Partnership. (filed as Exhibit 10.16 to the Company's
                  Registration Statement on Form S-1 (Registration No. 333-
                  22491), and incorporated herein by reference).
10.12.1  --       Amendment to Expense Allocation and Participation Agreement,
                  dated October 21, 1996, between Brigham Oil & Gas, L.P. and
                  Gasco Limited Partnership (filed as Exhibit 10.16.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.13    --       Expense Allocation and Participation Agreement, dated April 1,
                  1996, between Brigham Oil & Gas, L.P. and Middle Bay Oil
                  Company, Inc. (filed as Exhibit 10.17 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.13.1  --       Amendment to Expense Allocation and Participation Agreement,
                  dated September 26, 1996, between Brigham Oil & Gas, L.P. and
                  Middle Bay Oil Company, Inc. (filed as Exhibit 10.17.1 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.13.2  --       Letter Amendment to Expense Allocation and Participation
                  Agreement, dated May 20, 1996, between Brigham Oil & Gas, L.P.
                  and Middle Bay Oil Company, Inc. (filed as Exhibit 10.17.2 to
                  the Company's Registration Statement on Form S-1 (Registration
                  No. 333-22491), and incorporated herein by reference).
10.14    --       Anadarko Basin Joint Participation Agreement, dated May 1,
                  1996, by and among Stephens Production Company and Brigham Oil
                  & Gas, L.P. (filed as Exhibit 10.18 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.15    --       Anadarko Basin Joint Participation Agreement, dated May 1, 
                  1996, by and between Vintage Petroleum, Inc. and Brigham Oil &
                  Gas, L.P. (filed as Exhibit 10.19 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.16    --       Processing Alliance Agreement, dated July 20, 1993, between 
                  Veritas Seismic Ltd. and Brigham Oil & Gas, L.P. (filed as
                  Exhibit 10.20 to the Company's
</TABLE>



<PAGE>   80



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
                  Registration Statement on Form S-1 (Registration 
                  No. 333-22491), and incorporated herein by reference).
10.16.1  --       Letter Amendment to Processing Alliance Agreement, dated
                  November 3, 1994, between Veritas Seismic Ltd. and Brigham Oil
                  & Gas, L.P. (filed as Exhibit 10.20.1 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.17    --       Agreement and Assignment of Interest, West Bradley Project,
                  dated September 1, 1995, by and between Aspect Resources
                  Limited Liability Company and Brigham Oil & Gas, L.P. (filed
                  as Exhibit 10.21 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.18    --       Agreement and Assignment of Interests in lands located in
                  Grady County, Oklahoma, West Bradley Project, dated December
                  1, 1995, by and between Aspect Resources Limited Liability
                  Company, Brigham Oil & Gas, L.P. and Venture Acquisitions,
                  L.P. (filed as Exhibit 10.22 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.19    --       Agreement and Assignment of Interests, West Bradley Project,
                  dated December 1, 1995, by and between Aspect Resources
                  Limited Liability Company and Brigham Oil & Gas, L.P. (filed
                  as Exhibit 10.23 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.20    --       Geophysical Exploration Agreement, Hardeman Project, Hardeman
                  and Wilbarger Counties, Texas and Jackson County, Oklahoma,
                  dated March 15, 1993 by and among General Atlantic Resources,
                  Inc., Maynard Oil Company, Ruja Muta Corporation, Tucker
                  Scully Interests Ltd., JHJ Exploration, Ltd., Cheyenne
                  Petroleum Company, Antrim Resources, Inc., and Brigham Oil &
                  Gas, L.P. (filed as Exhibit 10.24 to the Company's
                  Registration Statement on Form S- 1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.21    --       Agreement and Partial Assignment of Interests in OK13-P
                  Prospect Area, Jackson County, Oklahoma (Hardeman Project),
                  dated August 1, 1995, by and between Brigham Oil & Gas, L.P.
                  and Aspect Resources Limited Liability Company (filed as
                  Exhibit 10.25 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.22    --       Agreement and Partial Assignment of Interests in Q140-E
                  Prospect Area, Hardeman County, Texas (Hardeman Project),
                  dated August 1, 1995, by and between Brigham Oil & Gas, L.P.
                  and Aspect Resources Limited Liability Company (filed as
                  Exhibit 10.26 to the Company's Registration Statement on Form
                  S-1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.23    --       Agreement and Partial Assignment of Interests in Hankins #1
                  Chappel Prospect Agreement, Jackson County, Oklahoma (Hardeman
                  Project), dated March 21, 1996, by and between Brigham Oil &
                  Gas, L.P., NGR, Ltd. and Aspect Resources Limited Liability
                  Company (filed as Exhibit 10.27 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.24    --       Form of Indemnity Agreement between the Registrant and each
                  of its executive officers (filed as Exhibit 10.28 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.25    --       Registration Rights Agreement dated February 26, 1997 by and 
                  among Brigham Exploration Company, General Atlantic Partners
                  III L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P. II,
                  RIMCO Partners L.P. III, and RIMCO Partners, L.P. IV, Ben M.
                  Brigham, Anne L. Brigham, Harold D.
</TABLE>



<PAGE>   81



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
                  Carter, Craig M. Fleming, David T. Brigham and Jon L. Glass
                  (filed as Exhibit 10.29 to the Company's Registration
                  Statement on Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.26    --       1997 Director Stock Option Plan (filed as Exhibit 10.30 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.27    --       Form of Employee Stock Ownership Agreement (filed as Exhibit
                  10.31 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.28    --       Agreement and Assignment of Interest in Geophysical 
                  Exploration Agreement, Esperson Dome Project, dated November
                  1, 1994, by and between Brigham Oil & Gas, L.P. and Vaquero
                  Gas Company (filed as Exhibit 10.33 to the Company's
                  Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.29    --       Geophysical Exploration Agreement, Southwest Danbury Project,
                  Brazoria County, Texas, dated as of July 1, 1996, by and among
                  UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.34 to the Company's Registration Statement on Form S-1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.30    --       Geophysical Exploration Agreement, Welder Project, Duval
                  County, Texas, dated as of October 1, 1996, by and among
                  UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit
                  10.35 to the Company's Registration Statement on Form S- 1
                  (Registration No. 333-22491), and incorporated herein by
                  reference).
10.31    --       Proposed Trade Structure, RIMCO/Tigre Project, Vermillion
                  Parish, Louisiana, among Brigham Oil & Gas, L.P., Tigre Energy
                  Corporation and Resource Investors Management Company (filed
                  as Exhibit 10.36 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and incorporated herein
                  by reference).
10.31.1  --       Letter relating to Proposed Trade Structure, RIMCO/Tigre
                  Project, dated January 31, 1997, from Resource Investors
                  Management Company to Brigham Oil & Gas, L.P. (filed as
                  Exhibit 10.36 to the Company's Registration Statement on Form
                  S- 1 (Registration No. 333-22491), and incorporated herein by
                  reference).
10.32    --       Anadarko Basin Seismic Operations Agreement II, dated as of
                  April 1, 1997, by and between Brigham Oil & Gas, L.P. (filed
                  as Exhibit 10.37 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-22491), and
                  incorporated herein by reference).
10.32.1  --       Letter Amendment to Anadarko Basin Seismic Operations 
                  Agreement II, dated March 20, 1997, between Brigham Oil & Gas,
                  L.P. and Veritas DGC Land, Inc. (filed as Exhibit 10.37 to the
                  Company's Registration Statement on Form S-1 (Registration No.
                  333-22491), and incorporated herein by reference).
10.33    --       Expense Allocation and Participation Agreement II, dated
                  April 1, 1997, between Brigham Oil & Gas, L.P., and Gasco
                  Limited Partnership (filed as Exhibit 10.31 to the Company's
                  Quarterly Report on Form 10-Q for the quarter ended June 30,
                  1997, and incorporated herein by reference).
10.36    --       Credit Agreement dated as of January 26, 1998 among Brigham
                  Oil & Gas, L.P., Bank of Montreal, as Agent, and the lenders
                  signatory thereto (filed as Exhibit 10.36 to the Company's
                  Annual Report on Form 10-K for the year ended December 31,
                  1997, and incorporated herein by reference).
10.36.1+ --       First Amendment to Credit Agreement dated as of August 20,
                  1998 among Brigham Oil & Gas, L.P., Bank of Montreal, as
                  Agent, and the lenders signatory thereto.
</TABLE>



<PAGE>   82



<TABLE>
<CAPTION>
Number                                      Description
- ------                                      -----------
<S>      <C>      <C>
10.36.2++  --     Second Amendment to Credit Agreement dated as of March 26,
                  1999 among Brigham Oil & Gas, L.P., Bank of Montreal, as
                  Agent, and the lenders signatory thereto.
10.37      --     Guaranty Agreement dated January 26, 1998 by Brigham
                  Exploration Company in favor of Bank of Montreal, as Agent,
                  and each of the Lenders party to the Credit Agreement (filed
                  as Exhibit 10.33.1 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-53873), and incorporated herein
                  by reference).
10.37.1    --     First Amendment to Guaranty Agreement dated as of March 30,
                  1998 between Brigham Exploration Company and Bank of Montreal,
                  as Agent for the Lenders party to the Credit Agreement (filed
                  as Exhibit 10.33.2 to the Company's Registration Statement on
                  Form S-1 (Registration No. 333-53873), and
                  incorporated herein by reference).
10.37.2+   --     Second Amendment to Guaranty Agreement dated as of August 20,
                  1998 between Brigham Exploration Company and Bank of Montreal,
                  as Agent for the Lenders party to the Credit Agreement.
10.37.3++  --     Third Amendment to Guaranty Agreement dated as of March 26,
                  1999 between Brigham Exploration Company and Bank of Montreal,
                  as Agent for the Lenders party to the Credit Agreement.
10.38+     --     Securities Purchase Agreement dated as of August 20, 1998
                  among Brigham Exploration Company, Enron Capital & Trade
                  Resources Corp. and Joint Energy Development Investments II
                  Limited Partnership.
10.39+     --     Registration Rights Agreement dated as of August 20, 1998, by
                  and among Brigham Exploration Company, Enron Capital & Trade
                  Resources Corp. and Joint Energy Development Investments II
                  Limited Partnership.
10.39.1++  --     Amendment to Registration Rights Agreement dated as of
                  March 26, 1999, by and among Brigham Exploration Company,
                  Enron Capital & Trade Resources Corp., ECT Merchant
                  Investments Corp. and Joint Energy Development Investments II
                  Limited Partnership.
10.40+     --     Form of Guaranty for subsidiaries.
10.41++    --     Exchange Agreement dated as of March 30, 1999 by and between
                  Brigham Exploration Company and Veritas DGC Land, Inc.
10.42++    --     Registration Rights Agreement dated as of March 30, 1999 by
                  and between Brigham Exploration Company and Veritas DGC Land, Inc.
21+        --     Subsidiaries of the Registrant.
23.1+      --     Consent of Price Waterhouse LLP, independent public
                  accountants.
23.2+      --     Consent of Cawley, Gillespie & Associates, Inc., independent
                  petroleum engineers.
27+        --     Financial Data Schedule.
</TABLE>

- ---------------

*      Management contract or compensatory plan.
+      Filed herewith
++     Not filed herewith pursuant to Rule 12b-25 under the Act, and to be 
       filed by amendment.



<PAGE>   1
                                                                     EXHIBIT 4.2

- -------------------------------------------------------------------------------


                          BRIGHAM EXPLORATION COMPANY

                                   Borrower

                                      AND

                   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION

                                    Trustee



                                _______________



                               I N D E N T U R E

                          Dated as of August 20, 1998



                                _______________



                                  $50,000,000
                  Senior Subordinated Secured Notes due 2003
<PAGE>   2
 
                               TABLE OF CONTENTS
<TABLE>
<S>                                                                           <C>
PRELIMINARY STATEMENT......................................................... 1
 
ARTICLE I
     DEFINITIONS.............................................................. 1
     Section 1.01  Definitions................................................ 1
     Section 1.02  Accounting Procedures and Interpretation...................16
 
ARTICLE II
     ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION 
     OF TRANSFER AND EXCHANGE OF NOTES........................................17
     Section 2.01  Form and Dating............................................17
     Section 2.02  Execution and Authentication...............................17
     Section 2.03  Denomination of Notes and Record Date......................17
     Section 2.04  Manual Execution...........................................18
     Section 2.05  Transfer and Exchange......................................18
     Section 2.06  Replacement Notes..........................................19
     Section 2.07  Cancellation of Notes......................................20
     Section 2.08  No Third Party Benefit.....................................20
 
ARTICLE III
     SUBORDINATION............................................................20
 
ARTICLE IV
     SECURITY FOR THE OBLIGATIONS.............................................20
     Section 4.01  Security...................................................20
 
ARTICLE V
     [RESERVED]...............................................................22
 
ARTICLE VI
     [RESERVED]...............................................................22
 
ARTICLE VII
     AFFIRMATIVE COVENANTS....................................................22
     Section 7.01  Financial Statements and Reports...........................22
     Section 7.02  Litigation.................................................24
     Section 7.03  Maintenance, Etc...........................................24
     Section 7.04  Environmental Matters......................................25
     Section 7.05  Further Assurances.........................................25
     Section 7.06  Performance of Obligations.................................26
     Section 7.07  Engineering Reports........................................26
     Section 7.08  Intentionally Omitted......................................27
</TABLE>

                                      -i-
<PAGE>   3

<TABLE>
<S>                                                                           <C>
     Section 7.09  Additional Collateral......................................27
     Section 7.10  ERISA Information and Compliance...........................28
     Section 7.11  Subsidiary Security........................................28
 
ARTICLE VIII
     NEGATIVE COVENANTS.......................................................29
     Section 8.01  Debt.......................................................29
     Section 8.02  Liens......................................................30
     Section 8.03  Investments, Loans and Advances............................30
     Section 8.04  Dividends, Distributions and Redemptions...................31
     Section 8.05  Sales and Leasebacks.......................................32
     Section 8.06  Nature of Business.........................................32
     Section 8.07  Mergers, Etc...............................................32
     Section 8.08  Proceeds of Notes..........................................32
     Section 8.09  ERISA Compliance...........................................32
     Section 8.10  Sale of Oil and Gas Properties.............................33
     Section 8.11  Environmental Matters......................................34
     Section 8.12  Transactions with Affiliates...............................34
     Section 8.13  Negative Pledge Agreements.................................34
     Section 8.14  Gas Imbalances, Take-or-Pay Prepayments....................34
     Section 8.15  Borrower as Operator.......................................34
     Section 8.16  Consolidated Interest Coverage Ratio.......................35
     Section 8.17  Current Ratio..............................................35
 
ARTICLE IX
     PAYMENT OF THE NOTES.....................................................35
     Section 9.01  Repayment..................................................35
     Section 9.02  Interest...................................................35
     Section 9.03  Payments and Computations..................................38
 
ARTICLE X
     DEFAULT AND REMEDIES.....................................................39
     Section 10.01  Events of Default.........................................39
     Section 10.02  Remedies..................................................41
     Section 10.03  Production and Proceeds...................................42
     Section 10.04  Set-Off...................................................42
 
ARTICLE XI
     THE AGENT................................................................42
     Section 11.01  Authorization and Action..................................42
     Section 11.02  Agent's Reliance, Etc.....................................43
     Section 11.03  The Agent and Its Affiliates..............................43
     Section 11.04  Noteholders Loan Decision.................................43
     Section 11.05  Indemnification...........................................44
     Section 11.06  Successor Agent...........................................44
</TABLE>


                                      -ii-
<PAGE>   4

<TABLE>
<S>                                                                           <C>
ARTICLE XII
     TRUSTEE..................................................................45
     Section 12.01  Duties of Trustee.........................................45
     Section 12.02  Rights of Trustee.........................................46
     Section 12.03  Individual Rights of Trustee..............................47
     Section 12.04  Trustee's Disclaimer......................................47
     Section 12.05  Notice of Defaults........................................47
     Section 12.06  Reports by Trustee to Noteholders.........................47
     Section 12.07  Compensation and Indemnity................................48
     Section 12.08  Replacement of Trustee....................................49
     Section 12.09  Successor Trustee by Merger, etc..........................50
     Section 12.10  Eligibility, Disqualification.............................50
     Section 12.11  Preferential Collection of Claims Against Borrower........50
     Section 12.12  Appointment of Co-Trustee.................................50
     Section 12.13  No Conflict...............................................51
 
ARTICLE XIII
     MISCELLANEOUS............................................................51
     Section 13.01  Interpretation and Survival of Provisions.................51
     Section 13.02  Costs, Expenses and Taxes.................................52
     Section 13.03  No Waiver; Modifications in Writing.......................54
     Section 13.04  Binding Effect; Assignment................................54
     Section 13.05  Communications............................................55
     Section 13.06  Governing Law.............................................56
     Section 13.07  Arbitration...............................................56
     Section 13.08  Confidentiality...........................................57
     Section 13.09  Execution in Counterparts.................................58
     Section 13.10  Trust Indenture Act Controls..............................58
     Section 13.11  Communication by Noteholders with Other Noteholders.......58
     Section 13.12  Certificate and Opinion as to Conditions Precedent........58
     Section 13.13  Statements Required in Certificate or Opinion.............59
     Section 13.14  Rules by Trustee and Agents...............................59
     Section 13.15  Legal Holidays............................................59

EXHIBITS

     Exhibit A  Form of Note
     Exhibit B  Form of Guaranty Agreement
     Exhibit C  Form of Subordination Agreement
     Exhibit D  Form of Security Agreement
     Exhibit E  Form of Security Agreement
     Exhibit F  Form of Mortgage, Deed of Trust, Assignment of Production,
                    Security Agreement and Financing Statement
     Exhibit G  Acceptance of Appointment
</TABLE>

                                     -iii-
<PAGE>   5
 
     INDENTURE, dated as of August 20, 1998, between BRIGHAM EXPLORATION
COMPANY, a corporation duly organized and existing under the laws of the State
of Delaware (hereinafter sometimes referred to as the "Borrower"), and CHASE
BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association existing
under the laws of the United States (hereinafter sometimes referred to as the
"Trustee").

                             PRELIMINARY STATEMENT

     All covenants and agreements made by the Borrower herein are for the
benefit and security of the holders of the Borrower's Senior Subordinated
Secured Notes due 2003.


                                   ARTICLE I
                                  DEFINITIONS

     Section 1.01  Definitions.

     "Acquired Shares" means 1,052,632 shares of Common Stock acquired by the
Noteholders on the Funding Date in accordance with Section 2.01 of the
Securities Purchase Agreement and any additional shares of Common Stock of the
Borrower issued to the Noteholders after the Funding Date in accordance with
Section 2.01(ii) of the Securities Purchase Agreement.

     "Adjusted Consolidated Net Tangible Assets" or "ACNTA" means (without
duplication), as of the date of determination, (a) the sum of (i) the discounted
future net revenue from proved crude oil and natural gas reserves of the
Borrower and its Consolidated Subsidiaries calculated in accordance with
Commission guidelines before any state or federal income taxes, as estimated in
the most current Reserve Report, as increased by, as of the date of
determination, the discounted future net revenue of (A) estimated proved crude
oil and natural gas reserves of the Borrower and its Consolidated Subsidiaries
attributable to acquisitions consummated since the date of such Reserve Report,
and (B) estimated proved crude oil and natural gas reserves of the Borrower and
its Consolidated Subsidiaries attributable to extensions, discoveries and other
additions and upward determinations of estimates of proved crude oil and natural
gas reserves due to exploration, development or exploitation, production or
other activities which reserves were not reflected in the most current Reserve
Report which would, in the case of determination made pursuant to clauses (A)
and (B), in accordance with standard industry practice, result in such
determinations, in each case calculated in accordance with Commission guidelines
(utilizing the Commission guideline prices utilized in the most current Reserve
Report), and decreased by, as of the date of determination, the discounted
future net revenue attributable to (C) estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in the
most current Reserve Report produced or disposed of since the date of such
Reserve Report and (D) reductions in the estimated proved crude oil and natural
gas reserves of the Borrower and its Consolidated Subsidiaries reflected in such
Reserve Report since the date of such Reserve Report attributable to downward
determinations of estimates of proved crude oil and natural gas reserves due to
exploration, development or exploitation, production

                                      -1-
<PAGE>   6

or other activities conducted or otherwise occurring since the date of the most
current Reserve Report which would, in the case of determinations made pursuant
to clauses (C) and (D), in accordance with standard industry practice, result in
such determinations, in each case calculated in accordance with Commission
guidelines (utilizing the Commission guideline prices utilized in the most
current Reserve Report); provided, however, that, in the case of each of the
determinations made pursuant to clauses (A) through (D), such increases and
decreases shall be as estimated by the Borrower's engineers, except that if as a
result of such acquisitions, dispositions, discoveries, extensions or revisions,
there is a net increase in the ACNTA which exceeds $10,000,000, the Agent shall
have the right to require that such increases and decreases in the discounted
future net revenue be confirmed in writing by an independent petroleum engineer,
at the Borrower's expense, (ii) the capitalized costs that are attributable to
seismic and undeveloped oil and gas leases of the Borrower and its Consolidated
Subsidiaries to which no proved crude oil and natural gas reserves are
attributed, based on the Borrower's books and records as of a date no earlier
than the date of the Borrower's latest annual or quarterly financial statements,
(iii) the Net Working Capital on a date no earlier than the date of the
Borrower's latest annual or quarterly financial statements and (iv) the greater
of (I) the net book value on a date no earlier than the date of the Borrower's
latest annual or quarterly financial statements and (II) the appraised value, as
estimated by independent appraisers reasonably acceptable to the Agent, of other
tangible assets of the Borrower and its Consolidated Subsidiaries as of a date
no earlier than the date of the Borrower's latest audited financial statements,
minus (b) to the extent not otherwise taken into account in the immediately
preceding clause (a), the sum of (i) minority interests, (ii) any natural gas
balancing liabilities and credits of the Borrower and its Consolidated
Subsidiaries reflected in the Borrower's latest audited financial statements,
(iii) the discounted future net revenue, calculated in accordance with
Commission guidelines (utilizing the Commission guideline prices utilized in the
Borrower's most current Reserve Report), attributable to reserves subject to
participation interests, overriding royalty interests or other interests of
third parties, pursuant to participation, partnership, vendor financing or other
agreements then in effect, or which otherwise are required to be delivered to
third parties, (iv) the discounted future net revenue, calculated in accordance
with Commission guidelines (utilizing the Commission guideline prices utilized
in the Borrower's most current Reserve Report), attributable to reserves that
are required to be delivered to third parties to fully satisfy the obligations
of the Borrower and its Consolidated Subsidiaries with respect to volumetric
production payments and (v) the discounted future net revenue, calculated in
accordance with Commission guidelines, attributable to reserves subject to
dollar-denominated production payments that, based on the estimates of
production included in determining the discounted future net revenue specified
in the immediately preceding clause (a) (i) (utilizing the Commission guideline
prices utilized in the Borrower's most current Reserve Report), would be
necessary to satisfy fully the obligations of the Borrower and its Consolidated
Subsidiaries with respect to dollar-denominated production payments.

     "Affiliate" of any Person shall mean (i) any Person directly or indirectly
controlled by, controlling or under common control with such first Person, (ii)
any director or officer of such first Person or of any Person referred to in
clause (i) above and (iii) if any Person in clause (i) above is an individual,
any member of the immediate family (including parents, spouse and children) of
such individual and any trust whose principal beneficiary is such individual or
one 

                                      -2-
<PAGE>   7
 
or more members of such immediate family and any Person who is controlled by any
such member or trust. For purposes of this definition, any Person which owns
directly or indirectly 20% or more of the securities having ordinary voting
power for the election of directors or other governing body of a corporation or
20% or more of the partnership or other ownership interests of any other Person
(other than as a limited partner of such other Person) will be deemed to
"control" (including, with its correlative meanings, "controlled by" and "under
common control with") such corporation or other Person.

     "Agent" means JEDI-II in its capacity as agent pursuant to Article XI and
includes any successor agent pursuant to Section 11.06.

     "Agent's Account" shall have the meaning specified in Section 9.03.

     "Average Share Price" means $9.50.

     "Basic Documents" means, collectively, this Indenture, the Securities
Purchase Agreement and the other Loan Documents.

     "Board of Directors" means the Board of Directors of the Borrower.

     "BOG" means Brigham Oil & Gas, L.P., a Delaware limited partnership.

     "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.

     "Business Opportunities Agreement" means the Corporate Shareholders'
Agreement dated as of even date herewith between the Purchasers and the
Borrower.

     "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.

     "Change in Control" means (i) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the shareholders of
the Borrower immediately prior to such transaction (treating the holders of the
Warrants as holders of voting shares) do not own at least fifty-one percent
(51.0%) of the voting shares of stock of the Borrower (or the surviving 
entity in the case of a merger or consolidation) immediately following the
consummation of such transaction, or (ii) a transaction, including any merger or
consolidation of Borrower with any other Person, in which the members of the
Board of Directors immediately prior to such transaction do not comprise at
least a majority of the board of directors of the Borrower (or the surviving
entity in the case of a merger or consolidation) for a period of twelve (12)
months immediately following the consummation of such transaction, or (iii) an
event, including any merger or consolidation of Borrower with any other Person,
such that Mr. Ben Brigham no longer manages the Borrower (or the surviving

                                      -3-
<PAGE>   8
 
entity in the case of a merger or consolidation), other than as a result of his
death or disability.

     "Closing" has the meaning provided therefor in Section 2.02 of the
Securities Purchase Agreement.

     "Closing Date" means the date upon which the Closing occurs as provided in
Section 2.02 of the Securities Purchase Agreement.

     "Code" means the Internal Revenue Code of 1986, as amended from time to
time, and any successor statute.

     "Collateral" means the properties, property interests and rights described
in Section 4.01 hereof, or otherwise covered by the Collateral Documents, as
security for the Obligations.

     "Collateral Documents" means collectively the documents required by the
Agent or the Noteholders to obtain the security interests in the Collateral, as
described in Section 4.01 hereof, and all other agreements, documents and
instruments required in Section 4.01, as the same may from time to time be
amended or supplemented.

     "Commission" means the United States Securities and Exchange Commission.

     "Common Stock" means the common stock, par value $0.01 per share, of the
Borrower or such other class of securities as shall, after the date of this
Indenture, constitute the common equity of the Borrower.

     "Consolidated Indebtedness" means all Debt of the Borrower and its
Consolidated Subsidiaries.

     "Consolidated Interest Coverage Ratio" means, as of the date of
determination, the ratio of (i) EBITDA for the preceding four calendar quarters
to (ii) Interest Expense for the same four calendar quarters.

     "Consolidated Net Income" means with respect to the Borrower and its
Consolidated Subsidiaries, for any period, the aggregate of the net income (or
loss) of the Borrower and its Consolidated Subsidiaries after allowance for
taxes for such period, determined on a consolidated basis in accordance with
GAAP; provided that there shall be excluded from the calculation of such net
income (to the extent otherwise included therein) the following: (i) the net
income of any Person in which Borrower or any Consolidated Subsidiary has an
interest (which interest does not cause the net income of such other Person to
be consolidated with the net income of Borrower and its Consolidated
Subsidiaries in accordance with GAAP), except to the extent of the amount of
dividends or distributions actually paid in such period by such other Person to
the Borrower or to a Consolidated Subsidiary, as the case may be; (ii) the net
income (but not loss) of any Consolidated Subsidiary to the extent that 

                                      -4-
<PAGE>   9
 
the declaration or payment of dividends or similar distributions or transfers or
loans by that Consolidated Subsidiary is not at the time permitted by operation
of the terms of its charter or any agreement, instrument or Governmental
Requirement applicable to such Consolidated Subsidiary, or is otherwise
restricted or prohibited, in each case determined in accordance with GAAP; (iii)
the net income (or loss) of any Person acquired in a pooling-of-interests
transaction for any period prior to the date of such transaction; (iv) any
extraordinary gains or losses, including gains or losses attributable to
Property sales not in the ordinary course of business; and (v) the cumulative
effect of a change in accounting principles and any gains or losses attributable
to writeups or writedowns of assets.

     "Consolidated Subsidiaries" shall mean each Subsidiary of the Borrower
(whether now existing or hereafter created or acquired) the financial statements
of which shall be (or should have been) consolidated with the financial
statements of the Borrower in accordance with GAAP.

     "corporate trust office" of the Trustee means the office of the Trustee at
the address set out in Section 13.05 or at any other office or agency so
designated by the Trustee.

     "Debt" means, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or evidenced
by bonds, debentures, notes or other similar instruments (including principal
and earned but unpaid issuance fees); (ii) all obligations of such Person
(whether contingent or otherwise) in respect of bankers' acceptances, letters of
credit, surety or other bonds and similar instruments; (iii) all obligations of
such Person to pay the deferred purchase price of Property or services (other
than for borrowed money) excluding Trade Payables but including Schedule 8.02
Payables; (iv) all obligations under leases which shall have been, or should
have been, in accordance with GAAP, recorded as capital leases in respect of
which such Person is liable (whether contingent or otherwise); (v) all
obligations under leases (other than capital leases and oil and gas leases)
which require such Person or its Affiliate to make payments exceeding $100,000
(or $500,000 in the aggregate) over the term of such lease, including payments
at termination, which are substantially equal to at least eighty percent (80%)
of the purchase price of the Property subject to such lease plus interest at an
imputed rate of interest; (vi) all Debt (as described in the other clauses of
this definition) of others secured by a Lien on any asset of such Person,
whether or not such Debt is assumed by such Person; (vii) all Debt (as described
in the other clauses of this definition) of others guaranteed by such Person or
in which such Person otherwise assures a creditor against loss of the Debt of
others; (viii) all obligations or undertakings of such Person to maintain or
cause to be maintained the financial position or covenants of others including
without limitation agreements expressed as an agreement to purchase the Debt or
Property of others or otherwise; (ix) obligations to deliver Hydrocarbons in
consideration of advance payments; (x) obligations to pay for goods or services
whether or not such goods or services are actually received or utilized by such
Person; (xi) any capital stock of such Person in which such Person has a
mandatory obligation to redeem such stock; (xii) any Debt of a Special Entity
for which such Person is liable either by agreement or because of a Governmental
Requirement; (xiii) the undischarged balance of any production payment created
by such Person or for the creation 

                                      -5-
<PAGE>   10
 
of which such Person directly or indirectly received payment; and (xiv) all
obligations of such Person under Hedging Agreements, provided that "Debt" shall
not include (a) interest or fees (other than earned but unpaid issuance fees) on
any of the foregoing, (b) obligations associated with bid, performance, surety
or appeal bonds (including those required by Governmental Requirements in
connection with Oil and Gas Properties), (c) gas balancing obligations (whether
volumetric or dollar denominated), (d) intercompany obligations among the
Borrower and its Consolidated Subsidiaries, (e) indemnity obligations which have
not matured into fixed liabilities, and (f) purchase price adjustments and
similar post-closing obligations (but excluding the deferred payment of any
purchase price) incurred in connection with the permitted purchase and sale of
Property or stock, and which is to be determined and payable no later than 180
days following the closing of such purchase and sale.

     "Default" shall mean an Event of Default or an  event which with notice or
lapse of time, or both, would become, an Event of Default.

     "Default Rate" means, for any applicable period, an interest rate equal to
the then applicable rate of interest on the Notes (for cash payments of
interest) plus 4.00% per annum, but in no event shall the Default Rate exceed
the Maximum Rate.

     "EBITDA" shall mean, for any period, the sum of Consolidated Net Income for
such period plus the following expenses or charges to the extent deducted from
Consolidated Net Income in such period: interest, taxes, depreciation, depletion
and amortization, and other non-cash charges, minus all non-cash income added to
Consolidated Net Income in such period.

     "ECT" means Enron Capital & Trade Resources Corp., a Delaware corporation.

     "Effective Date" means the date this Indenture is executed by all the
parties hereto.

     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Borrower or any ERISA Affiliate may have any liability or
any obligation to contribute, other than a Plan or a Multiemployer Plan.

     "Environmental Laws" means any and all Governmental Requirements pertaining
to the environment in effect in any and all jurisdictions in which the Borrower
or any Subsidiary is conducting or at any time has conducted business, or where
any Property of the Borrower or any Subsidiary is located, including, without
limitation, the Oil Pollution Act of 1990 ("OPA"), as amended, the Clean Air
Act, as amended, the Comprehensive Environmental, Response, Compensation, and
Liability Act of 1980 ("CERCLA"), as amended, the Federal Water Pollution
Control Act, as amended, the Occupational Safety and Health Act of 1970, as
amended, the Resource Conservation and Recovery Act of 1976 ("RCRA"), as
amended, the Safe Drinking Water Act, as amended, the Toxic Substances Control
Act, as amended, the Superfund Amendments and Reauthorization Act of 1986, as
amended, the Hazardous Materials Transportation Act, as amended, and other
environmental conservation or protection laws.  As used in the provisions hereof
relating to Environmental 

                                      -6-
<PAGE>   11
 
Laws, the term "oil" has the meaning specified in OPA; the terms "hazardous
substance" and "release" (or "threatened release") have the meanings specified
in CERCLA, and the terms "solid waste" and "disposal" (or "disposed") have the
meanings specified in RCRA; provided, however, that (i) in the event either OPA,
CERCLA or RCRA is amended so as to broaden the meaning of any term defined
thereby, such broader meaning shall apply subsequent to the effective date of
such amendment, and (ii) to the extent the laws of the state in which any
Property of the Borrower or any Subsidiary is located establish a meaning for
"oil," "hazardous substance," "release," "solid waste" or "disposal" which is
broader than that specified in either OPA, CERCLA or RCRA, such broader meaning
shall apply.

     "Equity Documents" means the Warrants, the stock certificates representing
the Acquired Shares, the Registration Rights Agreement and the Business
Opportunities Agreement.

     "ERISA" means the Employee Retirement Income Security Act of 1974, as
amended from time to time and any successor statute.

     "ERISA Affiliate" shall mean each trade or business (whether or not
incorporated) which together with the Borrower or any Subsidiary of the Borrower
would be deemed to be a "single employer" within the meaning of Section
4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section 414 of the
Code.

     "Event of Default" shall have the meaning assigned such term in Section
10.01.

     "Excepted Liens" means (i) Liens for taxes, assessments or other
governmental charges or levies not yet due or which are being contested in good
faith by appropriate action and for which adequate reserves have been maintained
in accordance with GAAP; (ii) Liens in connection with workman's compensation,
unemployment insurance or other social security, old age pension or public
liability obligations not yet due or which are being contested in good faith by
appropriate action and for which adequate reserves have been maintained in
accordance with GAAP; (iii) operators', vendors', carriers', warehousemen's,
repairmen's, mechanics', workmen's, materialmen's, construction or other like
Liens arising by operation of law in the ordinary course of business or incident
to the exploration, development, operation and maintenance of Oil and Gas
Properties or customary landlord's liens, each of which is in respect of
obligations that have not been outstanding more than 90 days or which are being
contested in good faith by appropriate proceedings and for which adequate
reserves have been maintained in accordance with GAAP; (iv) any Liens reserved
in leases or farmout agreements for rent or royalties and for compliance with
the terms of the farmout agreements or leases in the case of leasehold estates,
to the extent that any such Lien referred to in this clause does not materially
impair the use of the Property covered by such Lien for the purposes for which
such Property is held or materially impair the value of the Property subject
thereto; (v) encumbrances (other than to secure the payment of borrowed money or
the deferred purchase price of Property or services), easements, restrictions,
servitudes, permits, conditions, covenants, exceptions or reservations in any
rights of way or other Property for the purpose of roads, pipelines,
transmission lines, transportation lines, 

                                      -7-
<PAGE>   12
 
distribution lines for the removal of gas, oil, coal or other minerals or
timber, and other like purposes, or for the joint or common use of real estate,
rights of way, facilities and equipment, and defects, irregularities, zoning
restrictions and deficiencies in title of any rights of way or other Property
which in the aggregate do not materially impair the use of such rights of way or
other Property for the purposes for which such rights of way and other Property
are held or materially impair the value of such Property subject thereto; (vi)
deposits of cash or securities to secure the performance of bids, trade,
contracts, leases, statutory obligations and other obligations of a like nature
incurred in the ordinary course of business; and (vii) Liens permitted by the
Loan Documents.

     "Federal Funds Rate" means, for any day, a fluctuating interest rate per
annum (rounded upwards, if necessary, to the nearest 1/100 of 1%) equal to the
weighted average of the rates on overnight federal funds transactions with
members of the Federal Reserve System arranged by federal funds brokers on such
day, as published for such day (or, if such day is not a Business Day, for the
next preceding Business Day) by the Federal Reserve Bank of New York, or, if
such rate is not so published for any day which is a Business Day, the average
of the quotations for any such day on such transactions received by the Agent
from three federal funds brokers of recognized standing selected by it.

     "Financial Statements" means the financial statement or statements
described or referred to in Section 4.02 of the Securities Purchase Agreement.

     "First Reserve Report" shall have the meaning set out in Section 7.07(a).

     "Funding Date" means the first Business Day following the date all of the
conditions precedent to funding in Article VI of the Securities Purchase
Agreement have been satisfied.

     "GAAP" means generally accepted accounting principles in the United States
of America in effect from time to time.

     "Governmental Authority" shall include the country, the state, county, city
and political subdivisions in which any Person or such Person's Property is
located or which exercises valid jurisdiction over any such Person or such
Person's Property, and any court, agency, department, commission, board, bureau
or instrumentality of any of them including monetary authorities which exercises
valid jurisdiction over any such Person or such Person's Property.  Unless
otherwise specified, all references to Governmental Authority herein shall mean
a Governmental Authority having jurisdiction over, where applicable, the
Borrower, the Subsidiaries or any of their Property or the Agent or any
Noteholder.

     "Guarantors" means Brigham, Inc., Brigham Holdings I, LLC, Brigham Holdings
II, LLC, BOG and any other Person who becomes party to a Guaranty Agreement
pursuant to the terms of Section 7.11.

                                      -8-
<PAGE>   13
 
     "Guaranty Agreements" means the agreements executed by the Guarantors
substantially in the form of Exhibit B guarantying, unconditionally, payment of
the Obligations, as the same may be amended, modified or supplemented from time
to time.

     "Hedging Agreements" means any commodity, interest rate or currency swap,
cap, floor, collar, forward agreement or other exchange or protection agreements
or any option with respect to any such transaction.

     "Hydrocarbon Interests" means all rights, titles, interests and estates now
or hereafter acquired in and to oil and gas leases, oil, gas and mineral leases,
or other liquid or gaseous hydrocarbon leases, mineral fee interests, overriding
royalty and royalty interests, net profit interests and production payment
interests, including any reserved or residual interests of whatever nature.

     "Hydrocarbons" means oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.

     "Indenture" means this instrument as originally executed, or, if amended or
supplemented as herein provided, as so amended or supplemented.

     "Initial Reserve Report" means the report of Cawley, Gillespie & Associates
with respect to the Oil and Gas Properties of BOG as of November 30, 1997, a
copy of which has been delivered to Agent.

     "Interest Expense" means, for each applicable period for which EBITDA is to
be calculated, the sum of all required cash payments of interest during such
period on borrowed money. Interest on the Notes, for purposes of this
definition, shall be deemed cash payments, calculated at the cash interest rate,
whether paid in cash or in kind, except that if a payment of interest is made in
kind on any Interest Payment Date, an amount equal to the cash payment of
interest that would have been due on such Interest Payment Date if payment in
kind had not been made shall be deemed subtracted from Interest Expense for the
four quarter period ending on the last day of the fiscal quarter preceding such
Interest Payment Date (but not for any other four quarter period for which
Interest Expense is calculated).

     "Interest Payment Date" means each November 20, February 20, May 20, and
August 20 following the Funding Date until and including the Maturity Date.

     "JEDI-II" means Joint Energy Development Investments II Limited
Partnership, a Delaware limited partnership.

     "Lien" means any interest in Property securing an obligation owed to, or a
claim by, a Person other than the owner of the Property, whether such interest
is based on the common law, statute or contract, and whether such obligation or
claim is fixed or contingent,

                                      -9-
<PAGE>   14
 
and including but not limited to (i) the lien or security interest arising from
a mortgage, encumbrance, pledge, security agreement, conditional sale or trust
receipt or a lease, consignment or bailment for security purposes or (ii)
production payments and the like payable out of Oil and Gas Properties. The term
"Lien" shall include reservations, exceptions, encroachments, easements, rights
of way, covenants, conditions, restrictions, leases and other title exceptions
and encumbrances affecting Property. For the purpose of this Indenture, a Person
shall be deemed to be the owner of any Property which it has acquired or holds
subject to a conditional sale agreement, or leases under a financing lease or
other arrangement pursuant to which title to the Property has been retained by
or vested in some other Person in a transaction intended to create a financing.

     "Loan Documents" means this Indenture, the Notes, the Structuring Fee
Agreement, the Collateral Documents, and any and all other agreements or
instruments now or hereafter executed and delivered by the Borrower or any
Subsidiary or Affiliate of the Borrower (other than the Equity Documents and any
assignments, participation or similar agreements between any Noteholder and any
other lender or creditor with respect to any Obligations pursuant to this
Indenture) in connection with, or as security for the payment or performance of,
the Notes or this Indenture, as such agreements may be amended, supplemented or
restated from time to time.

     "Majority Noteholders" means, at any time, the Noteholders holding more
than 50% of the outstanding principal balance of the Notes.

     "Material Adverse Effect" means any material and adverse effect on (i) the
assets, liabilities, financial condition, business, operations or affairs of the
Borrower and its Subsidiaries taken as a whole, from those reflected in the
Financial Statements, or from the facts represented or warranted in any Loan
Document at the time made, or (ii) the ability of the Borrower and its
Subsidiaries taken as a whole to carry out their business as of the Closing Date
or as proposed as of the Closing Date to be conducted or to meet their
obligations under the Loan Documents on a timely basis.

     "Maturity Date" means August 20, 2003, or in the event of an acceleration
of the Obligations, such earlier date as the Obligations become due and payable
in full.

     "Maximum Rate" means at any particular time in question, the maximum
nonusurious rate of interest, if any, which under applicable law may then be
charged on the Notes. If such maximum rate changes after the date hereof, the
Maximum Rate shall be automatically increased or decreased, as the case may be,
without notice to the Borrower from time to time as the effective date of each
change in such maximum rate.

     "Mortgage" means the "Mortgage" referred to in Section 4.01(c) or
4.01(f)(ii) and any other mortgages executed pursuant to Section 7.09 hereof.

     "Mortgaged Property" means the Property owned by the Borrower and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.

                                      -10-
<PAGE>   15
 
     "Multiemployer Plan" means a Plan defined as such in Section 3(37) or
4001(a)(3) of ERISA.

     "NASDAQ" means  the National Association of Securities Dealers Automated
Quotation System.

     "Net Working Capital" means, for any Person or group of Persons and as of
any date of its determination, the difference (shown on the balance sheets of
such Person or group as of the end of the most recent fiscal quarter of such
Person or group for which internal financial statements are available) between
(i) all current assets of such Person or group and (ii) all current liabilities
of such Person or group, except the current portion of long-term Debt.

     "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of the Securities Purchase Agreement, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Borrower and payable to
the order of the Noteholders in their respective Participations.

     "Noteholders" means ECT and JEDI-II and/or, to the extent then applicable,
each assignee of ECT or JEDI-II or their respective successors or assigns in
whose name a Note may be registered in the Note Register kept for that purpose.

     "Noteholder's Account" means for any Noteholder, the account specified by
such Noteholder as its Noteholder's Account by notice in writing to the Agent.

     "Note Register" and "Note Registrar" have the respective meanings specified
in Section 2.05.

     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Borrower to the Agent or the Noteholders, pursuant to any
of the Basic Documents and all renewals, extensions and/or rearrangements
thereof, whether such amounts, liabilities or obligations be liquidated or
unliquidated, now existing or hereafter arising, absolute or contingent.

     "Officers' Certificate" means a certificate signed by the Chairman of the
Board, the President or any Vice President and by the Treasurer or any Assistant
Treasurer or the Secretary or any Assistant Secretary of the Borrower. Each such
certificate shall include the statements provided for in Section 13.13, if and
to the extent required by the provisions thereof.

     "Oil and Gas Properties" means Hydrocarbon Interests; the Properties now or
hereafter pooled or unitized with Hydrocarbon Interests; all presently existing
or future unitization, pooling agreements and declarations of pooled units and
the units created thereby (including without limitation all units created under
orders, regulations and rules of any Governmental Authority) which may affect
all or any portion of the Hydrocarbon Interests; 

                                      -11-
<PAGE>   16
 
all operating agreements, contracts and other agreements which relate to any of
the Hydrocarbon Interests or the production, sale, purchase, exchange or
processing of Hydrocarbons from or attributable to such Hydrocarbon Interests;
all Hydrocarbons in and under and which may be produced and saved or
attributable to the Hydrocarbon Interests, including all oil in tanks, the lands
covered thereby and all rents, issues, profits, proceeds, products, revenues and
other incomes from or attributable to the Hydrocarbon Interests; all tenements,
hereditaments, appurtenances and Properties in any manner appertaining,
belonging, affixed or incidental to the Hydrocarbon Interests; and all
Properties, rights, titles, interests and estates described or referred to
above, including any and all Property, real or personal, now owned or hereafter
acquired and situated upon, used, held for use or useful in connection with the
operating, working or development of any of such Hydrocarbon Interests or
Property (excluding drilling rights, automotive equipment or other personal
property which may be on such premises for the purpose of drilling a well or
other similar temporary use) and including any and all oil wells, gas wells,
injection wells or other wells, buildings, structures, fuel separators, liquid
extraction plants, plant compressors, pumps, pumping units, field gathering
systems, tanks and tank batteries, fixtures, valves, fittings, machinery and
parts, engines, boilers, meters, apparatus, appliances, tools, implements,
cables, wires, towers, casing, tubing and rods, similar equipment, surface
leases, rights-of-way, easements and servitudes together with all additions,
substitutions, replacements, accessions and attachments to any and all of the
foregoing.

     "Opinion of Counsel" means an opinion in writing signed by legal counsel
who shall be reasonably satisfactory to the Trustee and may be counsel to the
Borrower. Each such opinion shall include the statements provided for in Section
13.13, if and to the extent required by the provisions thereof.

     "outstanding", when used with reference to Notes, means, as of any
particular time, all Notes authenticated and delivered by the Trustee under this
Indenture, except

          (a) Notes that have been canceled by the Trustee or delivered to the
     Trustee for cancellation;

          (b) Notes for which monies in the necessary amount for payment or
     redemption shall have been deposited in trust with the Trustee or with any
     paying agent (other than the Borrower), provided that, if such Notes are to
     be redeemed, notice of such redemption shall have been given as provided in
     Article IV or provision satisfactory to the Trustee shall have been made
     for giving such notice; and

          (c) Notes in lieu of or in substitution for which other Notes shall
     have been authenticated and delivered pursuant to the terms of Section
     2.06.

     "Participation" means, for each Noteholder, such Noteholder's proportionate
share of the Obligations and the Warrants.  As of the Effective Date, ECT's
Participation shall be 25% and JEDI-II's Participation shall be 75%.

                                      -12-
<PAGE>   17
 
     "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.

     "Permitted Debt" means:

          (a) The Senior Loan, up to the lesser of $75,000,000 or the "Borrowing
     Base" under the Senior Credit Agreement;

          (b) The Notes or other Obligations arising under the Loan Documents or
     any guaranty of or suretyship arrangement for the Notes or other
     Obligations arising under the Loan Documents;

          (c) Debt of the Borrower which is existing on the Closing Date and is
     reflected in the Financial Statements or which constitutes Schedule 8.02
     Payables, and any renewals or extensions (but not increases) thereof;

          (d) Accounts payable for the deferred purchase price of Property or
     services (other than Trade Payables) from time to time incurred in the
     ordinary course of business which, if greater than 60 days past the invoice
     or billing date, are being contested in good faith by appropriate
     proceedings if reserves adequate under GAAP shall have been established
     therefor;

          (e) Debt of the Borrower under capital leases (as required to be
     reported on the financial statements of the Borrower pursuant to GAAP) not
     to exceed $2,000,000;

          (f) Debt of the Borrower under Hedging Agreements with a Senior Lender
     or another investment grade counterparty the notional amounts on which do
     not exceed 75% of Borrower's anticipated oil and/or gas production to be
     produced during the term of such Hedging Agreements entered into as a part
     of its normal business operations as a risk management strategy and/or
     hedge against changes resulting from market conditions related to the
     Borrower's and its Subsidiaries' operations; and

          (g) Debt of the Borrower not described in clauses (a) through (f)
     which, in the aggregate, does not exceed $1,000,000 at any one time
     outstanding.

     "Person" means any individual, corporation, company, voluntary association,
partnership, joint venture, trust, limited liability company, unincorporated
organization or government or any agency, instrumentality or political
subdivision thereof, or any other form of entity.

     "Plan" means any employee pension benefit plan, as defined in Section 3(2)
of ERISA, which (i) is currently or hereafter sponsored, maintained or
contributed to by the Borrower, any Subsidiary or an ERISA Affiliate or (ii) was
at any time during the preceding 

                                      -13-
<PAGE>   18
 
six calendar years sponsored, maintained or contributed to, by the Borrower, any
Subsidiary or an ERISA Affiliate.

     "Property" means any interest in any kind of property or asset, whether
real, personal or mixed, or tangible or intangible.

     "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Borrower relating to the Warrants, the
Warrant Shares and the Acquired Shares.

     "Reportable Event" means an event described in Section 4043(c) of ERISA
with respect to a Plan, other than an event described in paragraphs (1) through
(8) as to which the 30 day notice requirement has been waived by the PBGC.

     "Reserve Report" means a report, in form satisfactory to the Senior Loan
Agent (or if there is no Senior Loan or requirement for a Reserve Report under
the Senior Loan, the Agent), setting forth, as of the dates set forth in
Sections 7.07(a) and (b) (or such other date in the event of an unscheduled
redetermination); (i) the proved oil and gas reserves attributable to the
Borrower's and its Subsidiaries' Hydrocarbon Interests together with a
projection of the rate of production and future net income, taxes, operating
expenses and capital expenditures with respect thereto as of such date, based
upon the pricing assumptions consistent with Commission reporting requirements
at the time and (ii) such other information as the Senior Loan Agent (or, if
there is no Senior Loan, or requirement for a Reserve Report under the Senior
Loan, the Agent) may reasonably request.  The term "Reserve Report" shall also
include the Initial Reserve Report, the First Reserve Report, the supplemental
Reserve Reports described in Section 7.07(b), and the information to be provided
by the Borrower each year pursuant to Section 7.07(d).

     "Responsible Officer" means, as to any Person, the Chief Executive Officer,
the President, any Vice President or the Chief Financial Officer of such Person.
Unless otherwise specified, all references to a Responsible Officer herein shall
mean a Responsible Officer of the Borrower.  "Responsible Officer" when used
with respect to the Trustee means the chairman or the vice-chairman of the board
of directors, the chairman of the executive committee of the board of directors,
the president, any vice president, any second or assistant vice president, the
cashier, any assistant cashier, the secretary, any assistant secretary, the
treasurer, any assistant treasurer, any senior trust officer or trust officer,
or any other officer or assistant officer of the Trustee customarily performing
functions similar to those performed by the persons who at the time shall be
such officers, respectively, or to whom any corporate trust matter is referred
because of his knowledge of and familiarity with the particular subject.

     "Schedule 8.02 Payables" means payables owing under the agreements listed
on Schedule 8.02 which are outstanding more than 75 days after they become fixed
and owing, provided that the aggregate amounts of such payables under each such
agreement do not exceed the amount set forth for each such agreement on such
schedule.

                                      -14-
<PAGE>   19
 
     "Scheduled Redetermination Date"  means the last Business Day of each
September and  March during the term of the Notes, commencing September 1999.

     "Securities" means the Notes, the Warrants and the Acquired Shares.

     "Securities Act" means the Securities Act of 1933, as amended from time to
time, and the rules and regulations of the Commission promulgated thereunder.

     "Securities Purchase Agreement" means the Securities Purchase Agreement
dated of even date herewith between the Noteholders and the Borrower.

     "Senior Credit Agreement" means the Credit Agreement dated as of January
26, 1998, among BOG, the Senior Loan Agent, and the Senior Lenders, as it may
from time to time be amended, modified or supplemented from time to time, and
any Credit Agreement or similar agreement executed with banks or other financial
institutions in connection with any refinancing of the Senior Loan permitted
hereunder and under the Subordination Agreement.

     "Senior Loan Agent" means the agent or agents designated under the Senior
Credit Agreement.  Bank of Montreal is the Senior Loan Agent as of the date
hereof.

     "Senior Lenders" means each of the lenders from time to time under the
Senior Credit Agreement.

     "Senior Loan" shall mean, collectively, any advance or advances of
principal made by the Senior Lenders to BOG or the Borrower under the Senior
Credit Agreement and the other Senior Loan Documents.

     "Senior Loan Documents" means the Senior Credit Agreement and all
promissory notes, collateral documents and other agreements, documents and
instruments executed or delivered in connection therewith, as such agreements
may be amended, modified or supplemented from time to time.

     "Special Entity" means any joint venture, limited liability company or
partnership, general or limited partnership or any other type of partnership or
company other than a corporation, in which a Person or one or more of its other
Subsidiaries is a member, owner, partner or joint venturer and owns, directly or
indirectly, at least a majority of the equity of such entity or controls such
entity, but excluding any tax partnerships that are not classified as
partnerships under state law.  For purposes of this definition, any Person which
owns directly or indirectly an equity investment in another Person which allows
the first Person to manage or elect managers who manage the normal activities of
such second Person will be deemed to "control" such second Person (e.g.,a sole
general partner controls a limited partnership).

     "Structuring Fee Agreement" means the agreement between the Borrower and
ECT Securities Corp. dated as of the date hereof.

                                      -15-
<PAGE>   20
 
     "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Trustee, the Senior
Loan Agent, the Senior Lenders, the Agent, the Noteholders, the Borrower and
certain Subsidiaries, substantially in the form of Exhibit C as the same may be
supplemented or amended from time to time.

     "Subsidiary" means (i) any corporation of which at least a majority of the
outstanding shares of stock having by the terms thereof ordinary voting power to
elect a majority of the board of directors of such corporation (irrespective of
whether or not at the time stock of any other class or classes of such
corporation shall have or might have voting power by reason of the happening of
any contingency) is at the time directly or indirectly owned or controlled by a
Person or one or more of its Subsidiaries or by a Person and one or more of its
Subsidiaries and (ii) any Special Entity.  Unless otherwise indicated herein,
each reference to the term "Subsidiary" shall mean a Subsidiary of the Borrower.
Quest Resources L.L.C. and Venture Acquisitions L.P. shall not be considered
Subsidiaries of Borrower.

     "TIA" (except as herein otherwise expressly provided or unless the context
otherwise requires) means the Trust Indenture Act of 1939, as amended, as in
force at the date of this Indenture as originally executed.

     "Trade Payables" means customary trade payables incurred in the ordinary
course of business.

     "Trustee" means Chase Bank of Texas, National Association, and, subject to
the provisions of Article XII, shall also include its successors and assigns.

     "Warrants" means the Warrants issued by the Borrower to ECT and JEDI-II in
their respective Participations pursuant to Section 2.03 of the Securities
Purchase Agreement, for the purchase of an aggregate of 1,000,000 shares of
Common Stock, and any Warrants issued upon the transfer thereof or in
substitution therefore, pursuant to the Warrant Certificate to be issued to ECT
and JEDI-II, forms of which are attached to the Securities Purchase Agreement as
Exhibit A.

     "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.


     Section 1.02  Accounting Procedures and Interpretation .  Unless otherwise
specified herein, all accounting terms used herein shall be interpreted, all
determinations with respect to accounting matters hereunder shall be made, and
all financial statements and certificates and reports as to financial matters
required to be furnished to the Agent or the Noteholders (including ACNTA
calculations) hereunder shall be prepared, in accordance with GAAP, applied on a
basis consistent with the Financial Statements (except for changes concurred
with by the Borrower's independent public accountants).

                                      -16-
<PAGE>   21
 
                                  ARTICLE II
               ISSUE, DESCRIPTION, FORM, EXECUTION, REGISTRATION
                       OF TRANSFER AND EXCHANGE OF NOTES

     Section 2.01  Form and Dating.  The Notes and the Trustee's certificate of
authentication are to be substantially in the form of Exhibit A, with such
appropriate insertions, omissions, substitutions, amendments, changes and other
variations as are required or permitted by this Indenture, and may have such
letters, numbers or other marks of identification and such legends or
endorsements placed thereon as may be required to comply with the rules of any
securities exchange on which the Notes may be listed or as may, consistently
herewith, be determined by the officers executing such Notes as evidenced by
their execution of the Notes.

     The terms and provisions contained in the Notes and each Guaranty Agreement
shall constitute, and are hereby expressly made, a part of this Indenture and,
to the extent applicable, the Borrower and the Guarantors, by their execution
and delivery of this Indenture and each Guaranty Agreement, expressly agree to
such terms and provisions and to be bound thereby.

     The definitive Notes shall be printed or produced in any manner as may be
determined by the officers executing such Notes, as evidenced by their execution
of such Notes.

     Section 2.02  Execution and Authentication.  The Notes and each Guaranty
Agreement shall be executed by the Borrower and Guarantors, respectively, and be
delivered to the Trustee for authentication, and the Trustee shall thereupon, or
from time to time thereafter, authenticate and deliver said Notes and each
Guaranty Agreement to and upon the written order of the Borrower, signed by its
President or a Vice President and by its Treasurer, Assistant Treasurer,
Secretary or Assistant Secretary, without any further action by the Borrower.

     Section 2.03  Denomination of Notes and Record Date.  The Notes shall be
issuable as registered Notes without coupons in denominations of $1,000 and any
integral multiple thereof.  Each Note shall be dated the date of its
authentication.

     The person in whose name any Note is registered at the close of business on
any record date (as hereinafter defined) with respect to any interest payment
date shall be entitled to receive the interest payable on such interest payment
date. The term "record date" as used with respect to any Interest Payment Date
shall mean the day of the calendar month preceding the day on which such
Interest Payment Date falls.  The principal of, and premium, if any, and
interest on, the Notes shall be payable at the principal office of the Borrower
and any other office or agency of the Borrower designated for that purpose;
provided, however, that principal and interest may be payable at the option of
the Noteholders to the Agent's Account.

                                      -17-
<PAGE>   22
 
     Section 2.04  Manual Execution.  The Notes and Guaranty Agreements shall be
signed manually or by facsimile signature on behalf of the Borrower by its
President or a Vice President attested by the manual or facsimile signature of
its Secretary or an Assistant Secretary.

     Only such Notes as shall bear thereon a certificate of authentication
substantially in the form recited in Exhibit A, manually executed by the
Trustee, shall be entitled to the benefits of this Indenture or be valid or
obligatory for any purpose. Such certificate by the Trustee upon any Note
executed by the Borrower shall be conclusive evidence that the Note so
authenticated has been duly authenticated and delivered hereunder.

     In case any officer of the Borrower who shall have signed any of the Notes
shall cease to be such officer before the Notes so signed shall have been
authenticated and delivered by the Trustee, or disposed of by the Borrower, such
Notes nevertheless may be authenticated and delivered or disposed of as though
the person who signed such Notes had not ceased to be such officer of the
Borrower; and any Note may be signed on behalf of the Borrower by such persons
as, at the actual date of the execution of such Note, shall be the proper
officers of the Borrower, although at the date of the execution of this
Indenture any such person was not an officer.

     Section 2.05  Transfer and Exchange.  The Notes may be exchanged for a like
aggregate principal amount of Notes of other authorized denominations.  Notes to
be exchanged shall be surrendered at the Borrower's principal office, and the
Borrower shall execute and the Trustee shall authenticate and deliver in
exchange therefor the Note or Notes which the Noteholder making the exchange
shall be entitled to receive.

     The Borrower shall keep or cause to be maintained at said office or agency
a register (herein sometimes referred to as the "Note Register") in which,
subject to such reasonable regulations as it may prescribe, the Borrower shall
register Notes and shall register the transfer of Notes as in this Article II
provided. For the purposes of registration, exchange, registration of transfer,
redemption or conversion of Notes, the Trustee is hereby appointed Note
Registrar. Upon surrender for registration of transfer of any Note at said
office or agency, the Borrower shall execute and the Trustee shall authenticate
and deliver in the name of the transferee or transferees a new Note or Notes in
a like aggregate principal amount. At all reasonable times the Note Register
shall be open for inspection by the Trustee. No transfer of any Note shall be
valid unless made at said office or agency.

     All Notes presented or surrendered for registration of transfer, exchange,
conversion or payment shall (if so required by the Borrower or the Trustee) be
accompanied by a written instrument or instruments of transfer, in form
satisfactory to the Borrower and the Trustee, duly executed by the registered
Noteholder or his attorney duly authorized in writing.

     No service charge shall be made for any exchange or registration of
transfer of Notes, or issue of new Notes in case of partial prepayment or
conversion, but the Borrower may 

                                      -18-
<PAGE>   23
 
require payment of a sum sufficient to cover any tax or other governmental
charge that may be imposed in relation thereto.

     The Borrower shall not be required (i) to issue, register the transfer of,
or exchange any Note during a period beginning at the opening of business 15
days before the mailing of a notice of redemption of the Notes selected for
redemption and ending on the day of such mailing, or (ii) to register the
transfer of or exchange any Note so selected for redemption in whole or in part,
except the unredeemed portions of Notes being redeemed in part.

     Section 2.06  Replacement Notes.  In case any Note shall become mutilated
or be destroyed, lost or stolen, the Borrower shall execute, and the Trustee
shall authenticate and deliver, a new Note, in exchange and substitution for the
mutilated Note or in lieu of and substitution for the Note destroyed, lost or
stolen. In every case, the applicant for a substituted Note shall furnish to the
Borrower and the Trustee such security or indemnity as may be required by them
to hold each of them harmless, and, in every case of destruction, loss or theft,
the applicant shall also furnish to the Borrower and to the Trustee evidence to
their satisfaction of the destruction, loss or theft of such Note and of the
ownership thereof. The Trustee may authenticate any such substituted Note and
deliver the same upon the request or authorization of the Borrower.  Upon the
issuance of any substituted Note, the Borrower may require the payment of a sum
sufficient to cover any tax or other governmental charge that may be imposed in
relation thereto and any other expenses connected therewith, including fees and
expenses of the Trustee. In case any Note which has matured or is about to
mature or has been called for prepayment or has been presented for conversion
shall become mutilated or be destroyed, lost or stolen, the Borrower may,
instead of issuing a substitute Note, pay or authorize the payment of the same
(without surrender thereof except in the case of a mutilated Note) if the
applicant for such payment shall furnish the Borrower and the Trustee with such
security or indemnity as may be required by them to hold each of them harmless,
and, in case of destruction, loss or theft, evidence to the satisfaction of the
Borrower and the Trustee of the destruction, loss or theft of such Note and of
the ownership thereof.

     If, after the delivery of such replacement Note, a bona fide purchaser of
the original Note in lieu of which such replacement Note was issued presents for
payment or registration such original Note, the Trustee shall be entitled to
recover such replacement Note from the person to whom it was delivered or any
person taking therefrom, except a bona fide purchaser, and shall be entitled to
recover upon the security or indemnity provided therefor to the extent of any
loss, damage, cost or expense incurred by the borrower or Trustee in connection
therewith.

     Every substituted Note issued pursuant to the provisions of this Section
2.06 upon evidence that any Note is destroyed, lost or stolen shall, with
respect to such Note, constitute an additional contractual obligation of the
Borrower, whether or not the destroyed, lost or stolen Note shall be found at
any time, and shall be entitled to all the benefits of this Indenture equally
and proportionately with any and all other Notes duly issued hereunder. 

                                      -19-
<PAGE>   24
 
All Notes shall be held and owned upon the express condition that the foregoing
provisions are exclusive with respect to the replacement or payment of
mutilated, destroyed, lost or stolen Notes, and shall preclude any and all other
rights or remedies, notwithstanding any law or statute existing or hereafter
enacted to the contrary with respect to the replacement or payment of negotiable
instruments or other securities without their surrender.

     Section 2.07  Cancellation of Notes.  All Notes surrendered for payment,
conversion, registration of transfer or exchange shall, if surrendered to the
Borrower or any paying agent, be delivered to the Trustee for cancellation, or,
if surrendered to the Trustee, shall be canceled by it, and no Notes shall be
issued in lieu thereof except as expressly permitted by any of the provisions of
this Indenture. On request of the Borrower, the Trustee shall deliver to the
Borrower canceled Notes held by the Trustee; provided, however, that the Trustee
may at any time destroy any canceled Notes and deliver to the Borrower a
certificate of such destruction.  If the Borrower shall acquire any of the
Notes, however, such acquisition shall not operate as a redemption or
satisfaction of the indebtedness represented by such Notes unless and until the
same are delivered to the Trustee or surrendered to the Trustee for
cancellation.

     Section 2.08  No Third Party Benefit.  Subject to the terms of the
Subordination Agreement, nothing in this Indenture or in the Notes, expressed or
implied, shall give or be construed to give to any person, firm or corporation,
other than the parties hereto and the Noteholders, any legal or equitable right,
remedy or claim under or in respect of this Indenture, or under any covenant,
condition or provision herein contained; all its covenants, conditions and
provisions being for the sole benefit of the parties hereto and of the
Noteholders.


                                  ARTICLE III
                                 SUBORDINATION

     The Notes shall be subject to the Subordination Agreement.


                                  ARTICLE IV
                         SECURITY FOR THE OBLIGATIONS

     Section 4.01  Security.  The Obligations shall be secured by the following
which, in each case shall be subordinate in priority only to those liens,
security interests or rights granted in the same collateral to secure the
performance of Borrower under the Senior Loan Documents, in accordance with, but
subject to, the terms of the Subordination Agreement:

          (a) (i)  A Security Agreement substantially in the form of Exhibit D
duly executed by the Borrower in favor of the Trustee for the ratable benefit of
the Noteholders granting a security interest in all of the Borrower's right,
title and interest in and to the Capital Stock of Brigham, Inc. and Brigham
Holdings I, LLC, together with proper UCC-1 

                                      -20-
<PAGE>   25
 
Financing Statements duly filed in Texas, (ii) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham, Inc. in favor
of the Trustee for the ratable benefit of the Noteholders granting a security
interest in all of Brigham, Inc.'s right, title and interest in and to the
Capital Stock of Brigham Holdings II, LLC and BOG, together with proper UCC-1
Financing Statements duly filed in Texas, (iii) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham Holdings II, LLC
in favor of the Trustee for the ratable benefit of the Noteholders granting a
security interest in all of Brigham Holdings II, LLC's, right, title and
interest in and to the Capital Stock of BOG, together with proper UCC-1
Financing Statements duly filed in Texas and (iv) a Security Agreement
substantially in the form of Exhibit D duly executed by Brigham Holdings I, LLC
in favor of the Trustee for the ratable benefit of the Noteholders granting a
security interest in all of Brigham Holdings I, LLC's right, title and interest
in and to the Capital Stock of BOG, together with proper UCC-1 Financing
Statements duly filed in Texas.

          (b) A Security Agreement, substantially in the form of Exhibit E duly
executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders granting a security interest in all of BOG's right,
title and interest in and to all accounts, general intangibles, equipment and
inventory of BOG subject to Liens under the Senior Loan Documents.

          (c) A Mortgage, Deed of Trust, Assignment of Production, Security
Agreement and Financing Statement substantially in the form of Exhibit F
executed by BOG in favor of the Trustee, as collateral agent for the ratable
benefit of the Noteholders covering all of the Property of BOG subject to Liens
under the Senior Loan Documents.

          (d) A Guaranty Agreement duly executed by each of BOG, Brigham, Inc.,
Brigham Holdings I, LLC and Brigham Holdings II, LLC in favor of the Trustee for
the ratable benefit of the Noteholders guarantying the payment and performance
of the Obligations.

          (e)  Stock Powers executed by the Borrower and related stock
certificates of Brigham, Inc.

          (f) (i) Guaranty Agreements from each and every Person now or
hereafter guaranteeing all or any portion of the Senior Loan, (ii) Mortgages
covering any and all real property (including Oil and Gas Property) now or
hereafter pledged as collateral for all or any portion of the Senior Loan, (iii)
security agreements covering any and all Property (other than real property
subject to a Mortgage) now or hereafter pledged as collateral for all or any
portion of the Senior Loan, and (iv) financing statements, stock pledges or
other agreements necessary or appropriate to perfect the liens and/or security
interests granted pursuant to any of the foregoing.  Each of the foregoing
instruments shall be in substantially the same form and substance as those
executed of even date herewith or otherwise.

                                      -21-
<PAGE>   26
 
                                   ARTICLE V
                                  [RESERVED]


                                  ARTICLE VI
                                  [RESERVED]


                                  ARTICLE VII
                             AFFIRMATIVE COVENANTS

     Unless the Agent's prior written consent to the contrary is obtained, the
Borrower will, for the benefit of each of the Noteholders, at all times comply
with the covenants contained in this Article VII (or cause each Subsidiary's
compliance with the applicable covenants), from the date hereof and for so long
as any part of the Obligations is outstanding.

     Section 7.01  Financial Statements and Reports. The Borrower shall
deliver, or shall cause to be delivered, to the Agent with sufficient copies for
each of the Noteholders:

          (a) Annual Financial Statements.  As soon as available and in any
event within 90 days after the end of each fiscal year of the Borrower, the
audited consolidated statements of income, stockholders' equity, changes in
financial position and cash flow of the Borrower and its Consolidated
Subsidiaries for such fiscal year, and the related consolidated and unaudited
consolidating balance sheets of the Borrower and its Consolidated Subsidiaries
as at the end of such fiscal year, and setting forth in each case in comparative
form the corresponding figures for the preceding fiscal year, and accompanied by
the related opinion of independent public accountants of recognized national
standing acceptable to the Senior Loan Agent (or in the absence of a Senior
Loan, the Agent) which opinion shall state that said financial statements fairly
present the consolidated financial condition and results of operations of the
Borrower and its Consolidated Subsidiaries as at the end of, and for, such
fiscal year and that such financial statements have been prepared in accordance
with GAAP except for such changes in such principles with which the independent
public accountants shall have concurred and such opinion shall not contain a
"going concern" or like qualification or exception.

          (b) Quarterly Financial Statements.  As soon as available and in any
event within 60 days after the end of each of the first three fiscal quarterly
periods of each fiscal year of the Borrower, consolidated statements of income,
stockholders' equity, changes in financial position and cash flow of the
Borrower and its Consolidated Subsidiaries for such period and for the period
from the beginning of the respective fiscal year to the end of such period, and
the related consolidated and consolidating balance sheets as at the end of such
period, setting forth in each case in comparative form the corresponding figures
for the corresponding period in the preceding fiscal year, accompanied by the
certificate of a Responsible Officer, which certificate shall state that said
financial statements fairly present 

                                      -22-
<PAGE>   27
 
the consolidated financial condition and results of operations of the Borrower
and its Consolidated Subsidiaries in accordance with GAAP, as at the end of, and
for, such period (subject to normal year-end audit adjustments).

          (c) Notice of Default.  Promptly after the Borrower knows that any
Default or any Material Adverse Effect has occurred, a notice of such Default or
Material Adverse Effect, describing the same in reasonable detail and the action
the Borrower proposes to take with respect thereto.

          (d) Other Accounting Reports.  Promptly upon receipt thereof, a copy
of each other report or letter (excluding routine correspondence and audit
request letters) submitted to the Borrower by independent accountants in
connection with any annual, interim or special audit made by them of the books
of the Borrower, and a copy of any response by the Borrower to such letter or
report (including responses to any audit request letters).

          (e) SEC Filings, Etc.  Promptly upon its becoming available, each
financial statement, report, notice or proxy statement sent by the Borrower to
stockholders generally and each regular or periodic report and any registration
statement, prospectus or written communication (other than transmittal letters)
in respect thereof filed by the Borrower with or received by the Borrower in
connection therewith from any securities exchange or the Commission or any
successor agency.

          (f) Notices Under Other Loan Agreements.  Promptly after the
furnishing thereof, copies of any statement, report or notice furnished to any
Person pursuant to the terms of any indenture, loan or credit or other similar
agreement, other than this Indenture and not otherwise required to be furnished
to the Agent or the Trustee pursuant to any other provision of this Section
7.01.

          (g) Other Matters.  Subject to any applicable restrictions on
disclosure, from time to time such other information regarding the business,
affairs or financial condition of the Borrower (including, without limitation,
any Plan or Multiemployer Plan and any reports or other information required to
be filed under ERISA) as may be requested by and provided to the Senior Lender
or Senior Loan Agent.

          (h) Annual Budgets.  Concurrent with the First Reserve Report and each
January 1 Reserve Report thereafter, a one-year financial projection for the
Borrower and its Subsidiaries in form acceptable to the Senior Loan Agent (or in
the absence of a Senior Loan or Senior Loan Agent, the Agent), which projection
shall include revenues, expenses and capital expenditures.

          (i) Monthly Operating Statements.  As soon as available and in any
event within 30 days after the end of each month, monthly operating statements
of BOG including, without limitation, production reports and general and
administrative cost summaries by lease for its Oil and Gas Properties, which
reports shall include quantities or volume of production, revenue, realized
product prices, taxes, capital expenditures by category and lease 

                                      -23-
<PAGE>   28
 
operating costs which have accrued to BOG's accounts in such period, and such
other information with respect thereto as the Senior Loan Agent (or in the
absence of a Senior Loan or Senior Loan Agent, the Agent) may require.

The Borrower will furnish to the Agent, at the time it furnishes each set of
financial statements pursuant to paragraph (a) or (b) above, a certificate
substantially in the form of Exhibit C-2 to the Senior Credit Agreement executed
by a Responsible Officer (i) certifying as to the matters set forth therein and
stating that no Default has occurred and is continuing (or, if any Default has
occurred and is continuing, describing the same in reasonable detail), (ii)
setting forth in reasonable detail the computations necessary to determine
whether the Borrower is in compliance with Sections 8.01 and 8.16 as of the end
of the respective fiscal quarter or fiscal year, and (iii) certifying that said
financial statements fairly present the consolidated and consolidating financial
condition and consolidated results of operations in accordance with GAAP, as at
the end of, and for, such period (subject to normal year-end audit adjustments).

     Section 7.02  Litigation.  The Borrower shall promptly give to the Agent
notice of: (i) all legal or arbitral proceedings, and of all proceedings before
any Governmental Authority involving the Borrower or any Guarantor, except
proceedings which, if adversely determined within any reasonable range of loss,
would not have a Material Adverse Effect, and (ii) of any material litigation or
material proceeding against the Borrower or any Guarantor in which the amount
involved is not covered in full by insurance (subject to normal and customary
deductibles), or in which injunctive or similar relief is sought.  The Borrower
will, and will cause each of the Guarantors to, promptly notify the Agent of any
claim, judgment, Lien or other encumbrance affecting any Property of the
Borrower or any Guarantor if the value of the claim, judgment, Lien, or other
encumbrance affecting such Property shall exceed $1,000,000.

     Section 7.03  Maintenance, Etc.

          (a) The Borrower shall and shall cause each Subsidiary to: upon
reasonable notice, permit representatives of the Agent, during normal business
hours, to examine, copy and make extracts from its financial books and records,
to inspect its Properties, and to discuss its business and affairs with its
officers, all to the extent reasonably required by the Agent; keep, or cause to
be kept, insured by financially sound and reputable insurers all Property of a
character usually insured by Persons engaged in the same or similar business
similarly situated against loss or damage of the kinds and in the amounts
customarily insured against by such Persons and carry such other insurance as is
usually carried by such Persons including, without limitation, environmental
risk insurance to the extent reasonably available; and, where failure to do so
would have a Material Adverse Effect: preserve and maintain its corporate
existence and all of its material attendant rights, privileges and franchises,
keep appropriate books of record and account in relation to its business and
activities, comply with all Governmental Requirements, pay and discharge all
taxes, assessments and governmental charges or levies imposed on it or on its
income or profits or on any of its Property, except for any such tax,
assessment, charge or levy the payment of which is being contested in 

                                      -24-
<PAGE>   29
 
good faith and by proper proceedings and against which adequate reserves are
being maintained.

          (b) Contemporaneously with the delivery of the financial statements
required by Section 7.01(a) to be delivered for each year, the Borrower will
furnish or cause to be furnished to the Agent a certificate of insurance
coverage from the insurer in form and scope reasonably satisfactory to the Agent
and, if required by the Agent, will furnish the Agent copies of the applicable
policies.

          (c) The Borrower will and will cause each Subsidiary to maintain and
operate its Oil and Gas Properties and other material Properties or cause or
make reasonable and customary efforts to cause such Oil and Gas Properties and
other material Properties to be maintained and operated in all material respects
in a good and workmanlike manner in accordance with the practices of the
industry and in compliance with all applicable contracts and agreements and in
compliance in all material respects with all Governmental Requirements.  The
covenants contained in this Section 7.03(c) shall not apply to insignificant
Properties unless a failure of such covenant could have a Material Adverse
Effect.

     Section 7.04  Environmental Matters.

          (a) To the extent that a reasonably prudent owner or operator would do
so under the same or similar circumstances, the Borrower will and will cause
each Subsidiary to establish and implement such procedures as may be reasonably
necessary to periodically determine and assure that all Oil and Gas Properties
of the Borrower and the Subsidiaries and the operations conducted thereon and
other activities of the Borrower and the Subsidiaries are in compliance with and
do not violate the requirements of any Environmental Laws, where failure of the
foregoing would have a Material Adverse Effect.

          (b) The Borrower will promptly notify the Agent in writing of any
threatened action, investigation or inquiry by any Governmental Authority of
which the Borrower has knowledge in connection with any Environmental Laws with
respect to the Property of the Borrower or any Subsidiary, excluding routine
testing, compliance and correction action.

     Section 7.05  Further Assurances.  The Borrower will and will cause each
Guarantor to cure promptly any defects in the creation and issuance of the Notes
and the execution and delivery of the Basic Documents.  The Borrower at its
expense will and will cause each Guarantor to promptly execute and deliver to
the Agent upon request all such other documents, agreements and instruments  to
further evidence and more fully describe the collateral intended as security for
the Notes, or to correct any omissions in the Basic Documents, or to state more
fully the security obligations set out herein or in any of the Basic Documents,
or to perfect, protect or preserve any Liens created pursuant to any of the
Basic Documents, or to make any recordings, to file any notices or obtain any
consents, all as may be necessary or appropriate in connection therewith.

                                      -25-
<PAGE>   30
 
     Section 7.06  Performance of Obligations.  The Borrower will pay the Notes
according to the reading, tenor and effect thereof; and the Borrower will and
will cause each Guarantor to do and perform every act and discharge all of the
obligations to be performed and discharged by them under the Basic Documents, at
the time and times and in the manner specified.

     Section 7.07  Engineering Reports.

          (a) Not less than 30 days prior to the First Borrowing Base
Determination Date, the Borrower shall furnish to the Agent a Reserve Report
prepared as of December 1, 1998 or later (the "First Reserve Report") and as
provided in clause 7.07(b) below.

          (b) On January 31, 1999 and not less than 30 days prior to each
Scheduled Redetermination Date thereafter, commencing with the Scheduled
Redetermination Date to occur on September 30, 1999, the Borrower shall furnish
to the Agent a Reserve Report.  The Reserve Report furnished for the September
30 Scheduled Redetermination Date shall be prepared as of the preceding July 1
and the Reserve Report furnished for the March Scheduled Redetermination Date
(as well as the Reserve Report furnished on January 31, 1999) shall be prepared
as of the preceding January 1.  The Reserve Report furnished on January 31, 1999
and the January 1 Reserve Report of each year beginning January 1, 2000 shall be
prepared by certified independent petroleum engineers or other independent
petroleum consultant(s) acceptable to the Agent and the First Reserve Report and
the July 1 Reserve Report of each year shall be prepared by or under the
supervision of the chief engineer or Vice President of Operations of the
Borrower who shall certify such Reserve Report to have been prepared in
accordance with the procedures used in the immediately preceding First Reserve
Report or January 1 Reserve Report, as appropriate.  At Borrower's option, the
July 1 Reserve Report of each year may instead consist of a report from the
independent petroleum engineers referred to above on any new wells and a roll-
forward by Borrower on any wells previously reported on.

          (c) In addition, the Borrower shall furnish to the Agent copies of any
additional Reserve Reports (other than those specified in Sections 7.07(a) and
(b) above) that Borrower or any of its Subsidiaries deliver to the Senior Loan
Agent or Senior Lenders pursuant to the Senior Loan Documents.

          (d) With the delivery of each Reserve Report, the Borrower shall
provide to the Agent:

              (i)    a certificate from a Responsible Officer certifying that,
     to the best of his knowledge and in all material respects: (i) the most
     recently delivered Reserve Report does not in the belief of such officer
     and based upon information in the Borrower's possession, materially
     overstate the oil and gas reserves of the Borrower and the Subsidiaries as
     a whole bearing in mind that reserves are evaluated based upon estimates
     and assumptions with respect to which reasonable minds of competent
     engineers may differ, (ii) except as set forth in such Reserve Report or on

                                      -26-
<PAGE>   31
 
     an exhibit to the certificate, on a net basis there are no gas imbalances,
     take or pay or other prepayments with respect to its Oil and Gas Properties
     evaluated in such Reserve Report which would violate Section 8.14, (iii)
     none of its proved Hydrocarbon Interests have been sold since the date of
     the last Borrowing Base determination except as set forth on an exhibit to
     the certificate, which certificate shall list all of its proved Hydrocarbon
     Interests sold and in such detail as reasonably required by the Agent, (iv)
     attached to the certificate is a list of its proved Hydrocarbon Interests
     added to and deleted from the immediately prior Reserve Report and a list
     showing any change in working interest or net revenue interest in its
     Hydrocarbon Interests occurring, (v) at the Agent's request, attached to
     the certificate is a list of all Persons disbursing proceeds to the
     Borrower from its Oil and Gas Properties and (vi) except as set forth on a
     schedule attached to the certificate all of the proved Hydrocarbon
     Interests evaluated by such Reserve Report are Mortgaged Property; and

              (ii)   a certificate from a Responsible Officer certifying that,
     to the best of his knowledge and in all material respects (i) the
     representations of the Borrower in Section 4.10 are true and correct and
     apply to the Hydrocarbon Interests evaluated in the Reserve Report that are
     described in the Mortgage and (ii) the Borrower has, with respect to those
     material Hydrocarbon Interests that are evaluated in the most recently
     delivered Reserve Report, but that are not covered by a Mortgage, conducted
     overall title due diligence that, in all material respects, equals or
     exceeds industry standards given the applicable facts and circumstances.

          (e) In addition to the foregoing, on August 30, 1998, the Borrower
shall furnish to the Agent a Reserve Report prepared as of July 1, 1998, by or
under the supervision of the chief engineer or Vice President of Operations of
the Borrower who shall certify such Reserve Report to have been prepared in
accordance with the procedures used in the immediately preceding Initial Reserve
Report.

          (f) Notwithstanding the foregoing, so long as there is a Senior Credit
Agreement in effect which requires the semi-annual delivery to the Senior
Lenders of reserve reports evaluating the Borrower's and its Subsidiaries' Oil
and Gas Properties, delivering the Agent and Noteholders with a copy of each
such reserve report and any accompanying officer's certificate (certified to
Agent and the Noteholders) required thereunder shall satisfy the Borrower's
obligations under this Section 7.07, so long as such reserve report includes a
calculation of reserve value based upon pricing assumptions consistent with
Commission reporting requirements at the time.

     Section 7.08  Intentionally Omitted.

     Section 7.09  Additional Collateral.

          (a) Should any of the Borrower's or any Subsidiary's Properties which
are not Mortgaged Property be pledged as collateral for the payment of all or
any portion of the 

                                      -27-
<PAGE>   32
 
Senior Loan Obligations, the Borrower will simultaneously with such pledge in
favor of the Senior Lenders (or Senior Loan Agent) grant or cause such
Subsidiary to grant to the Trustee as security for the Obligations a second-
priority Lien interest (subject only to Excepted Liens, the matters set out on
Schedule 4.10 of the Securities Purchase Agreement, and any additional
qualifications and exceptions accepted by the Senior Lenders under any mortgage
of such Property to the Senior Agent) in the Borrower's or the Subsidiary's
interest in such Properties not already subject to a Lien of the Basic
Documents, which Lien will be created and perfected by and in accordance with
the provisions of deeds of trust, security agreements and financing statements,
or other Basic Documents, all in form substantially the same as the previous
Collateral Documents and in sufficient executed (and acknowledged where
necessary or appropriate) counterparts for recording purposes.

          (b) Concurrently with the granting of the Lien or other action
referred to in Section 7.09(a) above, the Borrower will provide to the Agent all
title information provided to the Senior Lenders or Senior Loan Agent in
connection therewith and any legal opinion (addressed to the Agent as well)
provided to the Seniors Lenders or Senior Loan Agent in connection therewith.

     Section 7.10  ERISA Information and Compliance.  Immediately after any
Responsible Officer of the Borrower knows or has reason to know any of the
following items are true, the Borrower will deliver to the Agent a certificate
of a Responsible Officer of the Borrower setting forth details as to such
occurrence and such action, if any, the Borrower or any ERISA Affiliate is
required or proposes to take, together with any notices required or proposed to
be given to or filed with or by the Borrower or its ERISA Affiliate with respect
thereto: that a Reportable Event has occurred or that an application may be or
has been made to the Secretary of the Treasury for a waiver or modification of
the minimum funding standard; that a Multiemployer Plan has been or may be
terminated, reorganized, partitioned or declared insolvent under Title IV of
ERISA; that any required contribution which is material to a Plan, Multiemployer
Plan or Employee Plan has not been or may not be timely made; that proceedings
may be or have been instituted under Section 4069(a) of ERISA to impose
liability on the Borrower or an ERISA Affiliate or under Section 4042 of ERISA
to terminate a Plan or appoint a trustee to administer a Plan; that the Borrower
or any ERISA Affiliate has incurred or may incur any liability (including any
contingent or secondary liability) on account of the termination of or
withdrawal from a Plan or a Multiemployer Plan; and that the Borrower or any
ERISA Affiliate may be required to provide security to a Plan under Section
401(a)(29) of the Code; or any other condition(s) exist(s) or may occur with
respect to one or more Plans, Employee Plans and/or Multiemployer Plans which
would reasonably be expected to result, individually or in the aggregate, in a
Material Adverse Effect.

     Section 7.11  Subsidiary Security.  Should the Borrower grant to the
Senior Loan Agent for the benefit of the Senior Lenders, or to the Senior
Lenders, a security interest and pledge of the Capital Stock of any Subsidiary
(whether existing as of the Closing Date or created or acquired thereafter), the
Borrower will, simultaneously with such pledge in favor of the Senior Loan Agent
or Senior Lenders, grant to the Trustee for the benefit of the Noteholders, a
second in priority security interest and pledge of such Capital Stock in form

                                      -28-
<PAGE>   33
 
and substance satisfactory to the Agent and if any Subsidiary should guaranty
all or any portion of the Senior Loan, the Borrower will cause such Subsidiary
to enter into a Guaranty Agreement of the Obligations in substantially the same
form as the Guaranty Agreement given by Brigham, Inc. on the Closing Date or
otherwise in form and substance satisfactory to the Agent.  The delivery of such
security and guaranty shall be accompanied by such back up corporate authority
and opinions of counsel (addressed to the Agent as well as the Senior Loan
Agent) as are provided to the Senior Loan Agent.


                                 ARTICLE VIII
                              NEGATIVE COVENANTS

     Unless the Agent's prior written consent to the contrary is obtained, for
the benefit of each of the Noteholders, the Borrower will at all times comply
with the covenants contained in this Article VIII (or cause each Subsidiary's
compliance with the applicable covenants), from the date hereof and for so long
as any part of the Obligations is outstanding.

     Section 8.01  Debt.  Neither the Borrower nor any Subsidiary will:

          (a) Incur, create or assume any Debt, other than Permitted Debt, such
that the ratio of the Borrower's Adjusted Consolidated Net Tangible Assets (as
at the end of the immediately preceding calendar quarter) to the sum of (i)
Borrower's Consolidated Indebtedness (after such incurrence, creation or
assumption of additional Debt other than Permitted Debt) plus (ii) past due
interest on Debt, is less than 1.5 to 1.0.  This covenant shall also apply to
any such Debt incurred or assumed as a result of a merger or consolidation with
any other Person.  Any such Debt so incurred, created or assumed (without
violation of this Section 8.01) must be fully subordinated to the Obligations
unless the Agent agrees otherwise, provided that, so long as ECT has been given
a first look and right to make a proposal for any future subordinated
indebtedness, up to $25,000,000 (less the maximum potential balance at the time
in question of the Schedule 8.02 Payables) in the aggregate of such Debt may be
incurred that is pari passu in right of payment with the Notes.  Notwithstanding
the foregoing, in the event of any refinancing of the Senior Loan, which
refinancing does not violate, on a proforma basis for the four fiscal quarters
of the Borrower after the refinancing, the interest coverage test of Section
8.16, the current ratio test of Section 8.17, or, provided the amount of such
refinanced Senior Loan is more than $75,000,000, the covenant in the first
sentence of this subsection (a), the refinanced Senior Loan shall remain senior
to (and shall not be subordinate to) the Obligations; or

          (b) Incur, create, suffer or assume any accounts payable for the
deferred purchase price of Property or services or any Trade Payables which are
more than 75 days past the invoice or billing date, unless such accounts payable
are either (i) being contested in good faith by appropriate proceedings and
reserves as required under GAAP shall have been established therefor, or (ii)
Schedule 8.02 Payables which are not past due.

                                      -29-
<PAGE>   34
 
Notwithstanding the foregoing, if at any time the ratio of the Borrower's
Adjusted Consolidated Net  Tangible Assets to the sum of (a) Borrower's
Consolidated Indebtedness plus (b) past due interest on Debt, is less than 1.5
to 1.0, the Agent shall have the right to require, and the Borrower covenants
and agrees to convey (or cause to be conveyed) to the Trustee or the Agent for
the benefit of the Agent and the Noteholders, such additional Potential
Collateral as the Agent shall require (subject to the Senior Lenders' rights to
a first and prior lien in such Potential Collateral).  Such conveyance shall be
made within 30 days following receipt of written notice from the Agent and shall
be deemed a pledge of additional Collateral in accordance with Section 7.09.  As
used in this paragraph, "Potential Collateral" means any of Borrower's or any
Subsidiary's Oil and Gas Properties (which are not already Collateral) which are
identified as containing proved Hydrocarbon reserves, whether currently existing
or hereafter acquired.

     Section 8.02  Liens.  Neither the Borrower nor any Subsidiary will
create, incur, assume or permit to exist any Lien on any of its Properties (now
owned or hereafter acquired), except:

          (a) Liens securing the Senior Loan; provided the Trustee or the Agent
is granted a second Lien in such Property securing the payment of the
Obligations;

          (b) Liens securing the payment of the Obligations;

          (c) Excepted Liens;

          (d) Liens securing leases allowed under clause (e) of the definition
of Excepted Liens but only on the Property under lease;

          (e) Liens disclosed on Schedule 8.02; and

          (f) Any Permitted Encumbrances as described in the Mortgage.

     Section 8.03  Investments, Loans and Advances.  Neither the Borrower nor
any Subsidiary will make or permit to remain outstanding any loans or advances
to or investments in any Person, except that the foregoing restriction shall not
apply to:

          (a) investments, loans or advances reflected in the Financial
Statements or which are disclosed to the Noteholders in Schedule 8.03;

          (b) accounts receivable arising in the ordinary course of business;

          (c) direct obligations of the United States or any agency thereof, or
obligations guaranteed by the United States or any agency thereof, in each case
maturing within one year from the date of creation thereof;

                                      -30-
<PAGE>   35
 
          (d) commercial paper maturing within one year from the date of
creation thereof rated in the highest grade by Standard & Poors Corporation or
Moody's Investors Service, Inc.;

          (e) deposits maturing within one year from the date of creation
thereof with, including certificates of deposit issued by any office located in
the United States, Canada, or England of, any bank or trust company which is
organized under the laws of the United States, Canada, England or any state or
province thereof, which has capital, surplus and undivided profits aggregating
at least $100,000,000.00 (as of the date of such bank or trust company's most
recent financial reports) and has a short term deposit rating of no lower than
A2 or P2, as such rating is set forth from time to time, by Standard & Poors
Corporation or Moody's Investors Service, Inc. (or their successors),
respectively;

          (f) deposits in money market funds investing exclusively in
investments described in Section 8.03(c), 8.03(d) or 8.03(e);

          (g) investments of up to $400,000 in the aggregate in Quest Resources
L.L.C.;

          (h) (i) investments, distributions, loans and advances by the Borrower
in or to any Subsidiary of the Borrower which is a Guarantor, (ii) investments,
distributions, loans and advances by the Borrower in or to any Subsidiary of the
Borrower which is not a Guarantor, provided that such Subsidiary has direct or
indirect ownership interests in Oil and Gas Properties or gas gathering systems,
gas plants, and similar assets related thereto and the aggregate outstanding
amount of such investments, distributions, loans and advances under this clause
(ii) shall not exceed $1,000,000 at any time, or (iii) investments in equity
interests in any Person (other than a Subsidiary as provided in clauses (i) or
(ii)) whose business is the acquisition, exploration and development of Oil and
Gas Properties, gas gathering systems, gas plants, or any line of business which
is closely related thereto, provided that the aggregate outstanding amount of
any such investments under this clause (iii) shall not exceed $1,000,000 at any
time;

          (i) investments, distributions, loans and advances by a Subsidiary to
the Borrower;

          (j) extensions of credit to purchasers, working interest owners,
employees and other persons in the ordinary course of business, up to an
aggregate of $1,000,000 at any one time.

     Section 8.04  Dividends, Distributions and Redemptions.  Neither the
Borrower or any Subsidiary will declare or pay any dividend, purchase, redeem or
otherwise acquire for value any of its stock now or hereafter outstanding,
return any capital to its stockholders or make any distribution of its assets to
its partners, except to the Borrower or any Subsidiary.

                                      -31-
<PAGE>   36
 
     Section 8.05  Sales and Leasebacks.  Neither the Borrower nor any
Subsidiary will enter into any arrangement, directly or indirectly, with any
Person whereby the Borrower or any Subsidiary shall sell or transfer any of its
Property, whether now owned or hereafter acquired, and whereby the Borrower or
any Subsidiary shall then or thereafter rent or lease as lessee such Property or
any part thereof or other Property which the Borrower or any Subsidiary intends
to use for substantially the same purpose or purposes as the Property sold or
transferred.

     Section 8.06  Nature of Business. Neither the Borrower nor any Subsidiary
will allow any material change to be made in the character of its business as an
independent oil and gas exploration and production company.

     Section 8.07  Mergers, Etc.  The Borrower will not and will not permit
any Subsidiary to merge into or with or consolidate with any other Person (other
than the Borrower or a Subsidiary) or sell, lease or otherwise dispose of
(whether in one transaction or in a series of transactions) all or substantially
all of its Property or assets to any other Person (other than the Borrower or a
Subsidiary) unless (i) no Default or Event of Default exists and after giving
effect to such merger, no Default or Event of Default shall exist, (ii) after
giving effect to such merger or consolidation, the surviving entity (as the
Borrower hereunder), or in the event of a merger or consolidation of a
Subsidiary, the Borrower, would be able to incur at least $1 in additional Debt
(other than Permitted Indebtedness), and (iii) the surviving entity ratifies and
confirms its Obligations under the Basic Documents and the Notes to the
reasonable satisfaction of the Agent and each Guarantor whose Guaranty Agreement
is in full force and effect ratifies and confirms its Guaranty Agreement to the
reasonable satisfaction of the Agent.

     Section 8.08  Proceeds of Notes.  The Borrower will not permit proceeds
of the Notes to be used for any purpose other than the partial payment of the
Senior Loan.  Neither the Borrower nor any Person acting on behalf of the
Borrower has taken or will take any action which might cause any of the Basic
Documents to violate Regulation G, U or X or any other regulation of the Board
of Governors of the Federal Reserve System or to violate Section 7 of the
Securities Exchange Act of 1934 or any rule or regulation thereunder, in each
case as now in effect or as the same may hereinafter be in effect.

     Section 8.09  ERISA Compliance.  The Borrower will not at any time:

          (a) Engage in, or permit any ERISA Affiliate to engage in, any
transaction in connection with which the Borrower or any ERISA Affiliate could
be subjected to either a civil penalty assessed pursuant to section 502(c), (i),
or (l) of ERISA or a tax imposed by Chapter 43 of Subtitle D of the Code, which
could reasonably be expected to have a Material Adverse Effect;

          (b) Terminate, or permit any ERISA Affiliate to terminate, any Plan in
a manner, or take any other action with respect to any Plan, which could
reasonably be 

                                      -32-
<PAGE>   37
 
expected to result in any liability of the Borrower or any ERISA Affiliate to
the PBGC, which could have a Material Adverse Effect;

          (c) Permit to exist, or allow any ERISA Affiliate to permit to exist,
any accumulated funding deficiency within the meaning of Section 302 of ERISA or
section 412 of the Code, whether or not waived, with respect to any Plan which,
if funded, could reasonably be expected to have a Material Adverse Effect;

          (d) Permit, or allow any ERISA Affiliate to permit, the actuarial
present value of the benefit liabilities under any Plan maintained by the
Borrower or any ERISA Affiliate which is regulated under Title IV of ERISA to
exceed the current value of the assets (computed on a plan termination basis in
accordance with Title IV of ERISA) of such Plan allocable to such benefit
liabilities by an amount which could, if such benefits become payable,
reasonably be expected to have a Material Adverse Effect.  The term "actuarial
present value of the benefit liabilities" shall have the meaning specified in
section 4041 of ERISA;

          (e) Contribute to or assume an obligation to contribute to, or permit
any ERISA Affiliate to contribute to or assume an obligation to contribute to,
any Multiemployer Plan;

          (f) Incur, or permit any ERISA Affiliate to incur, a liability to or
on account of a Plan under sections 515, 4062, 4063, 4064, 4201 or 4204 of ERISA
which, in the aggregate for all such liabilities, could reasonably be expected
to have a Material Adverse Effect;

          (g) Contribute to or assume an obligation to contribute to, or permit
any ERISA Affiliate to contribute to or assume an obligation to contribute to,
any employee welfare benefit plan, as defined in section 3(1) of ERISA,
including, without limitation, any such plan maintained to provide benefits to
former employees of such entities, that may not be terminated by such entities
in their sole discretion at any time without any material liability; or

          (h) Amend or permit any ERISA Affiliate to amend, a Plan resulting in
an increase in current liability such that Borrower or any ERISA Affiliate is
required to provide security to such Plan under section 401(a)(29) of the Code.

     Section 8.10  Sale of Oil and Gas Properties.  The Borrower will not,
and will not permit any Subsidiary to, sell, assign, farm-out, convey or
otherwise transfer any Hydrocarbon Interests except for (i) the sale of
Hydrocarbons in the ordinary course of business; (ii) assignments, farmouts, and
other disposition of Hydrocarbon Interests which do not contain identified
proved Hydrocarbon reserves, provided such assignments, farmouts, and other
dispositions are in the normal course of business (e.g., in bringing in
participants or disposing of unattractive prospects); (iii) the sale or transfer
of equipment that is no longer necessary for the business of the Borrower or
such Subsidiary or is replaced by equipment 

                                      -33-
<PAGE>   38
 
of at least comparable value and use and (iv) during any consecutive four fiscal
quarters, sales of Hydrocarbon Interests containing identified proved
Hydrocarbon reserves which, when taken together with the proceeds of any
permitted sales of Subsidiaries during such four quarters under the next
sentence of this Section 8.10, shall not exceed $3,000,000 in the aggregate. The
Borrower will not sell, and will not permit the sale of, any interest in any
Subsidiary unless all or substantially all of the Borrower's interest in such
Subsidiary is sold and, during any consecutive four fiscal quarters, the
proceeds of any such sale taken together with the proceeds of any sale of
Hydrocarbon Interests permitted under clause (iv) of this Section 8.10 does not
exceed $3,000,000.

     Section 8.11  Environmental Matters.  Neither the Borrower nor any
Subsidiary will knowingly cause or permit any of its Property to be in violation
of, or knowingly do anything or permit anything to be done which will subject
any such Property to any remedial obligations under any Environmental Laws,
assuming disclosure to the applicable Governmental Authority of all relevant
facts, conditions and circumstances, if any, pertaining to such Property, where
such violations or remedial obligations would have a Material Adverse Effect.

     Section 8.12  Transactions with Affiliates.  Neither the Borrower nor
any Subsidiary will enter into any transaction, including, without limitation,
any purchase, sale, lease or exchange of Property or the rendering of any
service, with any Affiliate (other than the Borrower or a Subsidiary) unless
such transaction (a) is otherwise not in violation of this Indenture, and (b)
unless approved by a majority of the disinterested members of the Board of
Directors, is in the ordinary course of its business and is upon fair and
reasonable terms no less favorable to it than it would obtain in a comparable
arm's length transaction with a Person not an Affiliate.

     Section 8.13  Negative Pledge Agreements.  The Borrower will not and
will not permit any Subsidiary to create, incur, assume or suffer to exist any
contract, agreement or understanding (other than the Basic Documents) which in
any way prohibits or restricts any Subsidiary from paying dividends or making
any other distribution to the Borrower or which requires the consent of a notice
to other Persons in connection with any of the foregoing, other than the
restrictions contained in the Senior Loan Documents as they exist on the day
hereof.

     Section 8.14  Gas Imbalances, Take-or-Pay Prepayments.  The Borrower
will not allow gas imbalances, take-or-pay or other prepayments with respect to
the Hydrocarbon Interests of the Borrower and its Subsidiaries which would
require the Borrower or its Subsidiaries to deliver five percent (5%) or more of
the Borrower's and its Subsidiaries' Hydrocarbons produced on a monthly basis
from the Hydrocarbon Interests at some future time without then or thereafter
receiving full payment therefor.

     Section 8.15  Borrower as Operator.  The Borrower will not and will not
allow any of its Subsidiaries to voluntarily resign as operator of more than
twenty-five percent (25%) of their currently operated Oil and Gas Properties,
unless a substitute operator is appointed 

                                      -34-
<PAGE>   39
 
that is another Subsidiary of the Borrower or is otherwise acceptable to the
Majority Noteholders, approval of such substitute operator not to be
unreasonably withheld.

     Section 8.16  Consolidated Interest Coverage Ratio.  As of the last day
of each fiscal quarter, the Borrower will not permit the Consolidated Interest
Coverage Ratio to be less than (i) 1.5 to 1.0 as of the end of the first four
(4) fiscal quarters following the Closing Date and (ii) 2.0 to 1.0 as of the end
of each fiscal quarter thereafter.

     Section 8.17  Current Ratio.  The Borrower will not permit its ratio of
(i) consolidated current assets of the Borrower and its Consolidated
Subsidiaries (including, without limitation, any unused and available
commitments under the Senior Credit Agreement) to (ii) their consolidated
current liabilities (excluding any principal or interest payments due on the
Senior Loan or the Notes), to be less than .8 to 1.0 at any time.

                                  ARTICLE IX
                             PAYMENT OF THE NOTES

     Section 9.01  Repayment.  The Borrower shall pay to the Noteholders on the
Maturity Date an amount equal to the outstanding principal amount of the Notes
plus the accrued and unpaid interest on the outstanding principal amount of the
Notes.  The Borrower may prepay the Obligations at any time in whole or in part
without penalty or premium.

     Section 9.02  Interest.

          (a) Subject to the provisions of Section 9.02(b), the outstanding
principal amount of the Notes shall bear interest at the following rates per
annum:

<TABLE>
<CAPTION>
                Period                               Rate
<S>                                                 <C>
          Funding Date through August 20, 2001        12%

          August 21, 2001 through August 20, 2002     13%

          August 21, 2002 through Maturity Date       14%
</TABLE>

The foregoing rates shall apply only to interest which is paid in cash.  In the
event the Borrower should elect to make any interest payments in kind as
permitted by Section 9.02(b), the rates applicable to such payments shall be as
set forth in Section 9.02(b).

          (b) So long as there exists no Event of Default, if on any Interest
Payment Date either (i) there exists a "Borrowing Base Deficiency" under the
Senior Credit Agreement or (ii) the payment in cash of interest accrued on the
Notes would cause the Borrower to be in violation of any covenant or other
restriction set forth in the Senior Loan Documents or any Basic Document, the
Borrower may pay such interest in kind, as provided in this Section 9.02(b).  In
such event the accrued interest due on such Interest Payment 

                                      -35-
<PAGE>   40
 
Date shall be calculated at the rates set forth in this Section 9.02(b) and the
interest due (calculated at the rates set forth in this Section 9.02(b)) shall
be deemed an advance of principal under the Notes and, as of the Interest
Payment Date, shall be added to the outstanding principal balance of the Notes
(notwithstanding that the outstanding principal balance may exceed, in the
aggregate, the face amount of the Notes). In order to exercise its option to pay
interest in kind under this Section 9.02(b), the Borrower shall, on or before
the applicable Interest Payment Date, deliver written notice to the Agent
executed by a Responsible Officer specifying the applicable covenant or
restriction of the Senior Loan Documents or the Basic Documents that will be
violated by payment of accrued interest in cash and notifying Agent of its
election to pay interest in kind. Any such election must be made as to all
Notes. Should Borrower fail to deliver such written notice in a timely fashion
Borrower shall be deemed to have irrevocably elected to make payment of accrued
interest in cash and any subsequent failure to do so in a timely fashion
(subject to the thirty (30) day grace period provided in Section 10.01(a)) shall
constitute an Event of Default hereunder. Notwithstanding anything contained
herein to the contrary, the Borrower may not pay interest in kind over the term
of the Notes for more than six (6) calendar quarters. In the event the Borrower
elects to pay interest in kind, such interest to be paid shall be calculated at
the following rates commencing on the immediately preceding Interest Payment
Date:

                 Period                              Rate

          Funding Date through August 20, 2001        13%

          August 21, 2001 through August 20, 2002     14%

          August 21, 2002 through Maturity Date       15%

          (c) In the event any sum due and payable hereunder is not paid when
due such past due amount shall accrue interest at the Default Rate from the date
due until paid.  Should an Event of Default occur hereunder, interest on the
Obligations shall accrue at the Default Rate from the date of occurrence of the
Default to which such Event of Default is attributable, until such Event of
Default is cured or waived.

          (d) Interest shall be computed based on a year of 360 days and twelve
30-day months (pro-rated appropriately for the period from the Funding Date
until the first Interest Payment Date and for any period of less than three
months for which interest may be due as a result of the prepayment or
acceleration of the Notes).  The rates of interest applicable to the Notes
provided in Sections 9.02(a) and (b) shall commence on the first day immediately
following the Funding Date or the applicable anniversary of the Funding Date and
remain in effect through the next succeeding anniversary of the Funding Date, or
the Maturity Date, as applicable.

          (e) Accrued interest on the Notes shall be due and payable in cash or,
if permitted by Section 9.02(b), in kind, quarterly on each Interest Payment
Date (including the 

                                      -36-
<PAGE>   41
 
Maturity Date) or, in the event the maturity of the Notes is accelerated
pursuant to the terms of the Basic Documents, such earlier date as the Notes
become due and payable, or the date the Notes are paid in full, whichever first
occurs. If any Interest Payment Date is not a Business Day, the interest payment
that would be due thereon shall instead be due on the next following Business
Day.

          (f) Notwithstanding anything herein or in the other Basic Documents to
the contrary, it is the intention of the parties hereto to conform strictly to
usury laws applicable to this transaction.  Accordingly, if the transactions
contemplated hereby would be usurious under applicable law, then, in that event,
notwithstanding anything to the contrary in the Notes, this Indenture or in any
other Basic Document or agreement entered into in connection with or as security
for the Notes, it is agreed as follows:  (a) the aggregate of all consideration
which constitutes interest under law applicable to the Noteholders that is
contracted for, taken, reserved, charged or received under the Notes, this
Indenture or under any of the other Basic Documents or agreements or otherwise
in connection with this transaction shall under no circumstances exceed the
maximum amount allowed by such applicable law, and any excess shall be canceled
automatically and, if already paid, shall be credited by the Noteholders on the
principal amount of the Obligations (or, to the extent that the principal amount
of the Obligations shall have been or would thereby be paid in full, refunded to
the Borrower); and (b) in the event that the maturity of the Notes is
accelerated by reason of any Event of Default under this Indenture or otherwise,
or in the event of any required or permitted prepayment, then such consideration
that constitutes interest under law applicable to this transaction may never
include more than the maximum amount allowed by such applicable law, and (c)
excess interest, if any, provided for in this Indenture or otherwise in
connection with the Notes shall be canceled automatically and, if already paid,
shall be credited by the Noteholders on the principal amount of the Obligations
(or, to the extent that the principal amount of the Obligations shall have been
or would thereby be paid in full, refunded by the Noteholders to the Borrower).
All sums paid or agreed to be paid to the Noteholders for the use, forbearance
or detention of sums included in the Obligations shall, to the extent permitted
by applicable law, be amortized, prorated, allocated and spread throughout the
full term of the Notes until payment in full so that the rate or amount of
interest on account of the Obligations does not exceed the applicable usury
ceiling, if any.  As used in this Section 9.02(f), the term "applicable law"
shall mean the laws which govern this Indenture as described in Section 12.07
(or the law of any other jurisdiction whose laws may be mandatorily applicable
notwithstanding other provisions of this Indenture), or law of the United States
of America applicable to the Noteholders and the Notes which would permit the
Noteholders to contract for, charge, take, reserve or receive a greater amount
of interest than under any other applicable law.  If the stated rate of interest
under this Indenture ever exceeds the Maximum Rate, then the outstanding
principal amount of the Notes made hereunder shall bear interest at the Maximum
Rate until the difference between the interest which would have been due at the
stated rates of interest and the amount due at the Maximum Rate (the "Lost
Interest") has been recaptured by the Noteholders.  If the Notes are repaid in
full and the Lost Interest has not been fully recaptured by the Noteholders
pursuant to the preceding sentence, then the Notes shall be deemed to have
accrued interest at the Maximum Rate since the date the initial advance under
the Notes was 

                                      -37-
<PAGE>   42
 
made to the extent necessary to recapture the Lost Interest not recaptured
pursuant to the preceding sentence and, to the extent allowed by law, the
Borrower shall pay to the Noteholders the amount of the Lost Interest remaining
to be recaptured by the Noteholders.

     Section 9.03  Payments and Computations.

          (a) All payments and obligations by Borrower under the Notes or any
other Basic Document shall be made to the Agent, without any presentment and
without any notation of such payment being made on the Notes (i) by wire
transfer in immediately available funds to such account as the Agent may
designate from time to time by written notice to the Borrower (the "Agent's
Account") or (ii) in such other manner as may be designated in writing to the
Borrower by the Agent.

          (b) The Borrower shall make each payment under this Indenture and
under the Notes not later than 2:00 p.m. (Houston, Texas time) on the day when
due in U.S. Dollars to the Agent at the location specified in paragraph (a)
above in immediately available funds. All payments by the Borrower hereunder
shall be made without any offset, abatement, withholding, or reduction.

          (c) Whenever any payment under the Basic Documents shall be stated to
be due on a day other than a Business Day, such payment shall be made on the
next succeeding Business Day, and (other than an interest payment subject to
Section 9.02(e) above) such extension of time shall in such case be included in
the computation of payment of interest.  If the time for payment for an amount
payable is not specified in the Basic Documents, or in any other document, the
payment shall be due and payable ten days after the date on which the Agent or
any Noteholder demands payment therefor.

          (d) Following receipt of payment in cash of any obligations due under
the Notes or any other Basic Document the Agent will promptly thereafter cause
to be distributed like funds relating to the payment of principal, interest or
fees ratably to the Noteholders at their respective Noteholder's Account.  If
and to the extent that the Agent receives any payment or prepayment from the
Borrower and fails to distribute such payment or prepayment to the Noteholders
ratably on the basis of their respective Participations on the day the Agent
receives such payment or prepayment (if received prior to 1:00 P.M. (Houston,
Texas time) on such day) or the next Business Day (if received after 1:00 P.M.
(Houston, Texas time) on such day), then the Agent shall pay to each Noteholder
such Noteholder's Participation of such payment or prepayment together with
interest thereon at the Federal Funds Rate for each day from the date such
amount should have been distributed by the Agent until such payment or
prepayment is actually distributed to the Noteholders.  All payments and
prepayments received shall be applied first to accrued interest and second to
the reduction of principal.

          (e) Unless the Agent shall have received written notice from the
Borrower prior to the date on which any payment is due to the Noteholders that
the Borrower will not make such payment in full or will make such payment in
kind pursuant to Section 9.02(b), 

                                      -38-
<PAGE>   43
 
the Agent may assume that the Borrower has made such payment in full, in cash,
to the Agent on such date and the Agent may, in reliance upon such assumption,
cause to be distributed to each Noteholder on such date an amount equal to the
amount then due such Noteholder. If and to the extent the Borrower shall not
have so made such payment in full, in cash, to the Agent, each Noteholder shall
repay to the Agent forthwith on demand such amount distributed to such
Noteholder, together with interest, for each day from the date such amount is
distributed to such Noteholder until the date such Noteholder repays such amount
to the Agent, at the Federal Funds Rate for such day.


                                   ARTICLE X
                             DEFAULT AND REMEDIES

     Section 10.01  Events of Default.  The occurrence of any of the following
shall be an "Event of Default" for the purposes of this Indenture and the Notes:

          (a) the Borrower shall default in the payment or prepayment when due
of any Obligations, and such default, other than a default of a payment or
prepayment of principal (which shall have no cure period), shall continue
unremedied for a period of thirty (30) days after such Obligations become due,
in the case of interest, or thirty (30) days after the Borrower receives notice
from the Agent that such Obligations are due, in the case of Obligations other
than principal or interest; or

          (b) (i) The Borrower or any Guarantor shall, as to any Debt (other
than the Obligations and the Senior Loan) aggregating more than $2,000,000
default in the payment when due of any principal of or interest thereon, or any
event specified in any note, agreement, indenture or other document evidencing
or relating to any such Debt shall occur if the effect of such event is to
cause, or (with the giving of any notice or the lapse of time or both) to permit
the holder or holders of such Debt (or a trustee or agent on behalf of such
holder or holders) to cause, such Debt to become due prior to its stated
maturity, or (ii) as to the Senior Loan, there shall have occurred a default
thereunder and the holders of the Senior Loan shall have elected to accelerate
the payment of the Senior Loan (or it shall be accelerated automatically or
otherwise be due and payable in full); or

          (c) any representation, warranty or certification made or deemed made
herein or in any other Basic Document by the Borrower or any Guarantor, or any
certificate furnished by the Borrower or any Guarantor to the Trustee, any
Noteholder or the Agent pursuant to the provisions hereof or any other Basic
Document, shall prove to have been false or misleading as of the time made or
furnished in any material and adverse respect and such default shall continue
unremedied for a period of forty-five (45) days after notice thereof to the
Borrower by the Agent; or

          (d) the Borrower shall default in the performance of any of its
obligations under Article VIII which are not capable of being cured, or under
Sections 8.01, 8.16, 8.17  or 7.01(c); or the Borrower shall default in the
performance of any of its obligations under 

                                      -39-
<PAGE>   44
 
Article VIII which are capable of being cured (other than Sections 8.01, 8.16
and 8.17) or any other Article of this Indenture (other than 7.01(c)) or under
any other Basic Document to which it is a party (other than the payment of
amounts due which shall be governed by Section 10.01(a)) and such default shall
continue unremedied for a period of forty-five (45) days after notice thereof to
the Borrower by the Agent; or

          (e) any Guarantor shall default in the performance of its obligation
to pay the Liabilities (as defined in the Guaranty Agreement) at maturity, or
any Guarantor shall default in the performance of any of its other obligations
under its Guaranty Agreement and such default shall continue unremedied for a
period of forty-five (45) days after notice thereof to the Guarantor by the
Agent; or

          (f) the Borrower shall admit in writing its inability to, or be
generally unable to, pay its debts as such debts become due; or

          (g) the Borrower shall (i) apply for a consent to the appointment of,
or the taking of possession by, a receiver, custodian, trustee or liquidator of
itself or of all or a substantial part of its property, (ii) make a general
assignment for the benefit of its creditors, (iii) commence a voluntary case
under the Federal Bankruptcy Code (as now or hereafter in effect), (iv) file a
petition seeking to take advantage of any other law relating to bankruptcy,
insolvency, reorganization, winding-up, liquidation or composition or
readjustment of debts, (v) fail to controvert in a timely and appropriate
manner, or acquiesce in writing to, any petition filed against it in an
involuntary case under the Federal Bankruptcy Code, or (vi) take any corporate
action for the purpose of effecting any of the foregoing, or

          (h) a proceeding or case shall be commenced, without the application
or consent of the Borrower, in any court of competent jurisdiction, seeking (i)
its liquidation, reorganization, dissolution or winding-up, or the composition
or readjustment of its debt; (ii) the appointment of a trustee, receiver,
custodian, liquidator or the like of the Borrower of all or any substantial part
of its assets, or (iii) similar relief in respect of the Borrower under any law
relating to bankruptcy, insolvency, reorganization, winding-up, or composition
or adjustment of  debts, and such proceeding or case shall continue undismissed,
or an order, judgement or decree approving or ordering any of the foregoing
shall be entered and continue unstayed and in effect, for a period of 60 days;
or an order for relief against the Borrower shall be entered in an involuntary
case under the Federal Bankruptcy Code; or

          (i) a judgment or judgments for the payment of money in excess of
$2,000,000 in the aggregate shall be rendered by a court against the Borrower
and the same shall not be discharged (or provision shall not be made for such
discharge), or a stay of execution thereof shall not be procured, within forty-
five (45) days from the date of entry thereof and the Borrower shall not, within
said period of 45 days, or such longer period during which execution of the same
shall have been stayed, appeal therefrom and cause the execution thereof to be
stayed during such appeal; or

                                      -40-
<PAGE>   45
 
          (j) any of the Basic Documents after delivery thereof shall for any
reason, except to the extent permitted by the terms thereof, cease to be in full
force and effect and valid, binding and enforceable in all material respects in
accordance with their terms, or cease in any material respect to create a valid
and perfected Lien of the priority required thereby on any of the collateral
purported to be covered thereby, except to the extent permitted by the terms of
this Indenture, or the Borrower or any Guarantor shall so state in writing, and
such Default shall continue unremedied for a period of forty-five (45) days
after notice thereof to the Borrower by the Agent; or

          (k) any Guarantor takes, suffers or permits to exist any of the
events or conditions referred to in paragraphs (f), (g), (h) or (i) hereof or if
any Guaranty Agreement related thereto shall for any reason cease to be valid
and binding on such Guarantor in all material respects or if such Guarantor
shall so state in writing, and such Default shall continue unremedied for a
period of forty-five (45) days after notice thereof to the Guarantor by the
Agent; or

          (l) there occurs a Change in Control; or

          (m) any annual audited financial statement delivered to Agent pursuant
to Section 7.01(a) is qualified (as to going concern or similar qualifications).

     Section 10.02  Remedies.

          (a) At any time during the continuance of any Event of Default
specified in Section 10.01 (other than clauses (f), (g) or (h) of Section
10.01), or in clause (k) as it relates to clauses (f), (g) or (h) thereof, the
Agent may by written notice to the Borrower declare the entire principal amount
of all Obligations then outstanding, including interest accrued thereon, to be
immediately due and payable without presentment, demand, protest, notice of
protest or dishonor, notice of intent to accelerate,  or other notice of default
of any kind, all of which are hereby expressly waived by the Borrower.  Once an
acceleration has been declared pursuant to the foregoing, no subsequent cure of
the Event of Default shall negate such acceleration or the rights and remedies
of the Trustee, Agent or Noteholders with respect thereto without the express
written consent of the Agent.

          (b) Upon the happening of any Event of Default specified in clauses
(f), (g) or (h) of Section 10.01, or clause (k) as it relates to clauses (f),
(g) or (h), the entire principal amount of all Obligations then outstanding,
including interest accrued thereon, shall, without notice or action by the
Trustee, the Agent or the Noteholders be immediately due and payable without
presentment, demand, protest, notice of protest or dishonor, notice of intent to
accelerate or other notice of default of any kind, all of which are hereby
expressly waived by the Borrower.

          (c) In addition to the foregoing, upon the happening of any of the
events described in subsections (a) and (b) above, the Trustee, at the direction
of the Agent may 

                                      -41-
<PAGE>   46
 
exercise any of the rights or remedies provided in the Collateral Documents and
other Basic Documents or avail itself of any rights or remedies provided by
applicable law.

          (d) All proceeds received after maturity of the Notes, whether by
acceleration or otherwise shall be applied first to reimbursement of expenses
and indemnities provided for in the Basic Documents; second to accrued interest
on the Notes; third to fees; fourth pro rata to principal outstanding on the
Notes and other Obligations; and any excess shall be paid to the Borrower or as
otherwise required by any Governmental Requirement.

     Section 10.03 Production and Proceeds.  Notwithstanding that, by the terms
of the various Mortgages and other Basic Documents, the Borrower and any other
mortgagors are and will be assigning to the Trustee all of the Hydrocarbons
covered thereby and all of the products thereof and proceeds and revenues
attributable thereto and all payments in lieu of such Hydrocarbons (in this
section collectively called the "Production and Proceeds"), so long as no
Default has occurred and is continuing (a) the Borrower and such mortgagors may
continue to receive all such Production and Proceeds, subject, however, to the
Liens created under the Mortgages and other Basic Documents, and (b) upon the
Borrower's request the Agent will confirm to any purchasers of Hydrocarbons,
title examiners, or other Persons that the Borrower and such mortgagors continue
to have the right so to receive such Production and Proceeds until notification
by the Agent of the occurrence of a Default.  During the continuance of an Event
of Default, however, the Trustee at the direction of the Agent may (subject to
all rights of the Senior Loan Agent and the Senior Lenders under the Senior Loan
Documents) exercise its rights and remedies granted under the Mortgages and the
other Basic Documents, including the rights and remedies granted under the
Mortgages and the other Basic Documents, including the right to obtain
possession of all Production and Proceeds then held by the Borrower and such
mortgagors and to receive directly from the purchasers of Hydrocarbons all other
Production and Proceeds.  In no case shall any failure by the Trustee to collect
directly any such Production and Proceeds constitute in any way a release of any
of its or the Agent's rights under the Basic Documents.

     Section 10.04 Set-Off.  Upon the occurrence of any Event of Default, any
Noteholder shall have the right to set-off any funds of the Borrower in the
possession of the Noteholder against any Debt (or accrued interest on Debt) then
due by the Borrower to the Noteholder.  The Borrower agrees that any holder of
Notes or a participation in the Notes may exercise any and all rights of
counter-claim, set-off, banker's lien and other liens with respect to any and
all monies owing by the Borrower to such holder as fully as if such holder of a
participation were a holder of a Note in the amount of such participation.

                                  ARTICLE XI
                                   THE AGENT

     Section 11.01  Authorization and Action.  Each Noteholder hereby appoints
and authorizes the Agent to take such action on behalf of such Noteholder and to
exercise such powers under this Indenture as are delegated to the Agent by the
terms hereof and of the other Basic Documents, together with such powers as are
reasonably incidental thereto.  As 

                                      -42-
<PAGE>   47
 
to any matters not expressly provided for by this Indenture or any other Basic
Document (including, without limitation, enforcement or collection of the
Notes), the Agent shall not be required to exercise any discretion or take any
action, but shall be required to act or to refrain from acting (and shall be
fully protected in so acting or refraining from acting) only upon the
instructions of the Majority Noteholders, and such instructions shall be binding
upon Noteholders; provided, however, that the Agent shall not be required to
take any action which exposes the Agent to personal liability or which is
contrary to this Indenture, any other Basic Document, or applicable law.

     Section 11.02  Agent's Reliance, Etc.  Neither the Agent nor any of the
Agent's directors, officers, agents or employees shall be liable for any action
taken or omitted to be taken (including the Agent's own negligence) by it or
them under or in connection with this Indenture or the other Basic Documents,
except for its or their own gross negligence or willful misconduct.  Without
limitation of the generality of the foregoing, the Agent:  (a) may treat the
payee of any Note as the holder thereof until the Agent receives written notice
of the assignment or transfer thereof signed by such payee and in form
satisfactory to the Agent; (b) may consult with legal counsel (including counsel
for the Borrower), independent public accountants and other experts selected by
it and shall not be liable for any action taken or omitted to be taken in good
faith by it in accordance with the advice of such counsel, accountants or
experts; (c) makes no warranty or representation to any Noteholder and shall not
be responsible to any Noteholder for any statements, warranties or
representations made in or in connection with this Indenture or the other Basic
Documents; (d) shall not have any duty to ascertain or to inquire as to the
performance or observance of any of the terms, covenants or conditions of this
Indenture or any other Basic Document on the part of the Borrower or any
Subsidiary or to inspect the Property (including the books and records) of such
Persons; (e) shall not be responsible to any Noteholder for the due execution,
legality, validity, enforceability, genuineness, sufficiency or value of this
Indenture or any other Basic Document; and (f) shall incur no liability under or
in respect of this Indenture or any other Basic Document by acting upon any
notice, consent, certificate or other instrument or writing (which may be by
telecopy) reasonably believed by it to be genuine and signed or sent by the
proper party or parties.

     Section 11.03  The Agent and Its Affiliates.  With respect to its
Participation, and the Note issued to it, the Agent shall have the same rights
and powers under this Indenture as any other Noteholder and may exercise the
same as though it were not an Agent hereunder.  The term "Noteholder" or
"Noteholders" shall, unless otherwise expressly indicated, include the Agent in
its individual capacity.  The Agent and its Affiliates may accept deposits from,
lend money to, act as trustee under indentures of, and generally engage in any
kind of business with, the Borrower or any Subsidiary, and any Person who may do
business with or own securities of the Borrower, or any Subsidiary, all as if
the Agent were not an agent hereunder and without any duty to account therefor
to the Noteholders.

     Section 11.04 Noteholders Loan Decision. Each Noteholder acknowledges that
it has, independently and without reliance upon the Agent or any other
Noteholder and based on the Financial Statements and such other documents and
information as it has deemed

                                      -43-
<PAGE>   48
 
appropriate, made its own credit analysis and decision to enter into the Basic
Documents. Each Noteholder also acknowledges that it will, independently and
without reliance upon the Agent or any other Noteholder and based on such
documents and information as it shall deem appropriate at the time, continue to
make its own credit decisions in taking or not taking action under this
Indenture.

     Section 10.05  Indemnification.  The Noteholders severally agree to
indemnify the Agent and each Affiliate thereof and their respective directors,
officers, employees and agents (to the extent not reimbursed by the Borrower),
according to their respective Participations from and against any and all
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements of any kind or nature whatsoever which may be
imposed on, incurred by, or asserted against the Agent in any way relating to or
arising out of this Indenture or any action taken or omitted by the Agent under
this Indenture or any other Basic Document (INCLUDING THE AGENT'S OWN
NEGLIGENCE), provided that no Noteholder shall be liable for any portion of such
liabilities, obligations, losses, damages, penalties, actions, judgments, suits,
costs, expenses or disbursements resulting from the Agent's gross negligence or
willful misconduct.  Without limitation of the foregoing, each Noteholder agrees
to reimburse the Agent promptly upon demand for its ratable share of any out-of-
pocket expenses (including counsel fees) incurred by the Agent in connection
with the preparation, execution, delivery, administration, modification,
amendment or enforcement (whether through negotiations, legal proceedings or
otherwise) of, or legal advice in respect of rights or responsibilities under,
this Indenture or any other Basic Document, to the extent that the Agent is not
reimbursed for such expenses by the Borrower.

     Section 11.06 Successor Agent. The Agent may resign at any time by giving
written notice thereof to the Noteholders and the Borrower and may be removed at
any time with cause by the Majority Noteholders upon receipt of written notice
from the Majority Noteholders to such effect. Upon receipt of notice of any such
resignation or removal, the Majority Noteholders shall have the right to appoint
a successor Agent with, if no Default exists, the consent of the Borrower, which
consent shall not be unreasonably withheld. If no successor Agent shall have
been so appointed by the Majority Noteholders with the consent of the Borrower,
if required, and shall have accepted such appointment, within 30 days after the
retiring Agent's giving of notice of resignation or the Majority Noteholders,
removal of the retiring Agent, then the retiring Agent may, on behalf of the
Noteholders and the Borrower, appoint a successor Agent. Upon the acceptance of
any appointment as Agent by a successor Agent, such successor Agent shall
thereupon succeed to and become vested with all the rights, powers, privileges
and duties of the retiring Agent, and the retiring Agent shall be discharged
from its duties and obligations under this Indenture and the other Basic
Documents. After any retiring Agent's resignation or removal hereunder as Agent,
the provisions of this Article XI shall inure to its benefit as to any actions
taken or omitted to be taken by it while it was Agent this Indenture and the
other Basic Documents.

                                      -44-
<PAGE>   49
 
                                  ARTICLE XII
                                    TRUSTEE

     Section 12.01  Duties of Trustee.

          (a) If an Event of Default has occurred and is continuing, the Trustee
shall exercise such rights and powers vested in it by this Indenture and use the
same degree of care and skill in such exercise as a prudent person would
exercise or use under the circumstances in the conduct of such person's own
affairs.

          (b) Except during the continuance of an Event of Default:

              (i)    The Trustee need perform only those duties that are
     specifically set forth (or incorporated by reference) in this Indenture and
     no others.

              (ii)   In the absence of bad faith on its part, the Trustee may
     conclusively rely, as to the truth of the statements and the correctness of
     the opinions expressed therein, upon certificates or opinions furnished to
     the Trustee and conforming to the requirements of this Indenture.  However,
     in the case of any such certificates or opinions which by any provision
     hereof are specifically required to be furnished to the Trustee, the
     Trustee shall be under a duty to examine the same to determine whether or
     not they conform to the requirements of this Indenture (but need not
     confirm or investigate the accuracy of mathematical calculations or other
     facts stated therein).

          (c) The Trustee may not be relieved from liability for its own
negligent action, its own negligent failure to act, or its own willful
misconduct, except that:

              (i)    This paragraph (c) does not limit the effect of paragraph
     (b) of this Section.

              (ii)   The Trustee shall not be liable for any error of judgment
     made in good faith by an officer of the Trustee, unless it is proved that
     the Trustee was negligent in ascertaining the pertinent facts.

               (iii) The Trustee shall not be liable with respect to action it
     takes or omits to take in good faith in accordance with a direction
     received by it from the Agent, and the Trustee shall be entitled from time
     to time to request such a direction.

          (d) Every provision of this Indenture and each Collateral Document
that in any way relates to the Trustee is subject to paragraphs (a), (b) and (c)
of this Section.

          (e) The Trustee shall be under no obligation and may refuse to perform
any duty or exercise any right or power unless it receives indemnity
satisfactory to it against any loss, liability or expense.  No provision of this
Indenture or any Collateral Document shall 

                                      -45-
<PAGE>   50
 
require the Trustee to expend or risk its own funds or otherwise incur financial
liability in the performance of any of its duties hereunder or in the exercise
of any of its rights or powers, if it shall have reasonable grounds to believe
that repayment of such funds or adequate indemnity against such risk or
liability is not reasonably assured to it.

          (f) The Trustee shall not be liable for interest on any money received
by it except as the Trustee may agree in writing with the Borrower.  Money held
in trust by the Trustee need not be segregated from other funds except to the
extent required by law.

          (g) The Trustee shall not be required to take notice, and shall not be
deemed to have notice, of any Default or Event of Default hereunder, unless the
Trustee shall be notified specifically of the Default or Event of Default in a
written instrument or document delivered to it by the Borrower or any Guarantor,
or by the Agent or the Majority Noteholders.  In the absence of delivery of a
notice satisfying those requirements, the Trustee may assume that there is no
Default or Event of Default, except as noted above.

     Section 12.02  Rights of Trustee.

          (a) The Trustee may conclusively rely on and shall be fully protected
in acting or refraining from acting upon any document believed by it to be
genuine and to have been signed or presented by the proper person.  The Trustee
shall not be bound to make any investigation into the facts or matters stated in
any resolution, certificate, statement, instrument, opinion, report, notice,
request, direction, consent, order, bond, debenture or other paper or document,
but the Trustee, in its discretion, may make such further inquiry or
investigation into such facts or matters as it may see fit, and, if the Trustee
shall determine to make such further inquiry or investigation, it shall be
entitled to examine the books, records and premises of the Borrower, personally
or by agent or attorney, to the extent reasonably required by such inquiry or
investigation at the sole expense of the Borrower and shall incur no liability
or additional liability of any kind by reason of such inquiry or investigation.

          (b) Before the Trustee acts or refrains from acting, it may require an
Officers, Certificate or an Opinion of Counsel.  The Trustee shall not be liable
for any action it takes or omits to take in good faith in reliance on such
certificate or opinion.

          (c) The Trustee may act through agents and shall not be responsible
for the misconduct or negligence of any agent appointed with due care.

          (d) The Trustee shall not be liable for any action it takes or omits
to take in good faith which it believes to be authorized or within its rights or
powers.

          (e) The Trustee may consult with counsel of its selection and the
advice of such counsel or any Opinion of Counsel shall be full and complete
authorization and protection in respect of any action taken, suffered or omitted
by it hereunder in good faith and in reliance thereon.

                                      -46-
<PAGE>   51
 
          (f) The Trustee will not, without the consent of the Agent, give any
consent, waiver or approval required under the Collateral Documents or by the
terms hereof with respect to the Collateral or agree to any amendment or
modification of the Collateral Documents.

          (g) The Trustee may settle or compromise at any time any and all
claims against it which may be asserted by any governmental body or private
party for the alleged violation of any Environmental Laws affecting any of the
Collateral, and may disclaim (as to itself, but not as to the Indenture or any
successor Trustee) any power (including, without limitation, the power to sell
the Collateral) granted by the Indenture, the Collateral Documents or any
statute or rule of law, the exercise of which power may, in the sole discretion
of the Trustee, as advised by counsel, cause the Trustee to incur corporate or
personal lability under any Environmental Laws.

     Section 12.03  Individual Rights of Trustee.  The Trustee in its individual
or any other capacity may become the owner or pledgee of Notes and may otherwise
deal with the Borrower or its Subsidiaries or Affiliates with the same rights it
would have if it were not Trustee.  The provision of this Section shall extend
to Affiliates of the Trustee.  Any Agent may do the same with like rights.
However, the Trustee must comply with Sections 12.10 and 12.11.

     Section 12.04  Trustee's Disclaimer.

     The Trustee makes no representation as to the value or condition of the
Collateral or any part thereof, or as to the title of the Borrower or any
Subsidiary thereto, or as to the security afforded thereby or hereby, or as to
the validity or genuineness of any Collateral pledged and deposited with the
Trustee, or the validity or adequacy of this Indenture or the Notes, it shall
not be accountable for the Borrower's use of the proceeds from the Notes or any
offering memorandum or solicitation documents, and it shall not be responsible
for any statement in the Basic Documents other than its certificate of
authentication.

     Section 12.05  Notice of Defaults.

     If a Default occurs and is continuing and if it is actually known to a
Responsible Officer of the Trustee pursuant to Section 12.01(g), the Trustee
shall mail to each Noteholder and the Agent pursuant to Section 13.05 a notice
of the Default within 90 days after it occurs.  Except in the case of a Default
in any payment on any Note, the Trustee may withhold the notice if and so long
as the board of directors, executive committee or a trust committee of officers
in good faith determines that withholding the notice is in the interests of the
Noteholders.

     Section 12.06  Reports by Trustee to Noteholders.

     Within 60 days after each November 15, beginning with the November 15
following the date of this Indenture, the Trustee shall mail to each Noteholder
a brief report dated as 

                                      -47-
<PAGE>   52
 
of such November 15, that complies with TIA (S)313(a), but only if such report
is required in any year under TIA (S)313(a). The Trustee also shall comply with
TIA (SS)313(b) and 313(c).

     A copy of each report at the time of its mailing to Noteholders shall be
filed with the SEC and each stock exchange on which the Notes are listed.  The
Borrower shall promptly notify the Trustee in writing when the Notes become
listed on any national securities exchange or of any delisting thereof.

     Section 12.07  Compensation and Indemnity.

     The Borrower and the Guarantors jointly and severally agree to pay the
Trustee from time to time such compensation as shall be agreed in writing
between the Borrower and the Trustee for its services (which compensation shall
not be limited by any provision of law in regard to the compensation of a
trustee of an express trust).  The Borrower and the Guarantors jointly and
severally agree to reimburse the Trustee upon request for all reasonable out-of-
pocket expenses, disbursements and advances incurred by. it.  Such expenses
shall include when applicable the reasonable compensation and expenses of the
Trustee's agents and counsel.

     The Borrower and the Guarantors jointly and severally agree to indemnify
each of the Trustee and any predecessor Trustee against any and all loss,
liability, damage, claim or expenses, including taxes (other than taxes based on
the income of the Trustee) incurred by it arising out of or in connection with
the acceptance and administration of the trust and its duties hereunder as
Trustee and/or Note Registrar, including the costs and expenses of enforcing
this Indenture against the Borrower (including with respect to this Section
12.07) and of defending itself against any claim or liability in connection with
the exercise or performance of any of its powers or duties hereunder.  The
Trustee shall notify the Borrower and the Guarantors of any claim for which it
may seek indemnity; however, unless the position of the Borrower is materially
prejudiced by such failure, the failure of the Trustee to promptly notify the
Borrower shall not limit its right to indemnification.  The Borrower shall
defend each such claim and the Trustee shall cooperate in the defense.  The
Trustee may retain separate counsel and the Borrower shall reimburse the Trustee
for the reasonable fees and expenses of such counsel if the Borrower is advised
by an Opinion of Counsel that the Trustee has separate defenses and that
separate representation is appropriate or if the Trustee reasonably determines
that such joint defense would otherwise involve a conflict of interest.  The
Borrower need not pay for any settlement made without its consent.

     Neither the Borrower nor the Guarantors shall be obligated to reimburse any
expense or indemnify against any loss or liability incurred by the Trustee
through the Trustee's breach of the applicable standard of care for its conduct
under Section 12.01.

     When the Trustee incurs expenses or renders services after the occurrence
of any Event of Default specified in Sections 10.01(f), (g) or (h), the expenses
and the compensation 

                                      -48-
<PAGE>   53
 
for the services are intended to constitute expenses of administration under any
Bankruptcy Law.

     The provisions of this Section 12.07 shall survive the satisfaction and
discharge or other termination of this Indenture.

     Section 12.08  Replacement of Trustee.

     The Trustee may resign by so notifying the Borrower and the Guarantors.
The Agent may remove the Trustee by so notifying the Trustee, in writing.  The
Borrower may remove the Trustee if.

          (a) the Trustee fails to comply with Section 12.10;

          (b) the Trustee is adjudged a bankrupt or an insolvent;

          (c) a receiver or other public officer takes charge of the Trustee or
its property; or

          (d) the Trustee becomes incapable of acting as Trustee hereunder.

     If the Trustee resigns or is removed or if a vacancy exists in the office
of Trustee for any reason, the Borrower shall promptly appoint a successor
Trustee.  Within one year after the successor Trustee takes office, the Agent
may appoint a successor Trustee to replace the successor Trustee appointed by
the Borrower.

     A successor Trustee shall deliver a written acceptance of its appointment
to the retiring Trustee and to the Borrower and the Guarantors.  Immediately
after that, the retiring Trustee shall transfer all property held by it as
Trustee to the successor Trustee the resignation or removal of the retiring
Trustee shall become effective, and the successor Trustee shall have all the
rights, powers and duties of the Trustee under this Indenture.  A successor
Trustee shall mail notice of its succession to each Noteholder.

     If a successor Trustee does not take office within 30 days after the
retiring Trustee resigns or is removed, the retiring Trustee, the Borrower or
the Agent may petition, at the expense of the Borrower, any court of competent
jurisdiction for the appointment of a successor Trustee.

     If the Trustee fails to comply with Section 12.10, the Agent may petition
any court of competent jurisdiction for the removal of the Trustee and the
appointment of a successor Trustee.  Any successor Trustee shall comply with TIA
(S)310(a)(5).

                                      -49-
<PAGE>   54
 
     Section 12.09  Successor Trustee by Merger, etc.

     If the Trustee consolidates, merges or converts into, or transfers all or
substantially all of its corporate trust business to, another corporation, the
successor corporation without any further act shall be the successor Trustee;
provided such corporation or association shall be otherwise eligible and
qualified under this Article.

     Section 12.10  Eligibility, Disqualification.

     This Indenture shall always have a Trustee which satisfies the requirements
of TIA (S)310(a)(1) and (5). The Trustee shall always have a combined capital
and surplus of at least $50,000,000 as set forth in its most recent published
annual report of condition. The Trustee shall also comply with TIA (S)310(b).

     Section 12.11  Preferential Collection of Claims Against Borrower.

     The Trustee shall comply with TIA (S)311(a), excluding any creditor
relationship listed in TIA (S)311(b). A Trustee who has resigned or been removed
shall be subject to TIA (S)311(a) to the extent indicated therein.

     Section 12.12  Appointment of Co-Trustee.

     If the Trustee deems it necessary or desirable in connection with the
Collateral and/or the enforcement of the Collateral Documents, the Trustee may
appoint a co-Trustee with such powers of the Trustee as may be designated by the
Trustee at the time of such appointment (including acting as separate trustee of
any Collateral), and the Borrower shall, on request, execute and deliver to such
co-Trustee any deeds, conveyances or other instruments required by such co-
Trustee so appointed by the Trustee to more fully and certainly vest in and
confirm to such co-Trustee its rights, powers, trusts, duties and obligations
hereunder.

     All rights (including rights to indemnification hereunder), powers, duties
and obligations conferred or imposed upon the Trustee shall be conferred or
imposed upon and exercised or performed by the Trustee or jointly by the Trustee
and such co-Trustees, except to the extent that under any law of any
jurisdiction in which any particular act or acts are to be performed the Trustee
shall be incompetent or unqualified to perform such act or acts, in which event
such rights, powers, duties and obligations shall be exercised and performed by
such co-Trustees.  No Trustee or co-Trustee shall be personally liable by reason
of any act or omission of any other Trustee or co-Trustee hereunder.  Any co-
Trustee appointed pursuant to this Section 12.12 may be removed by the Trustee
pursuant to the terms of this Indenture and may be removed and may resign
pursuant to the provisions of the applicable Collateral Document and of this
Indenture.

     A co-Trustee shall not be responsible for and makes no representation as to
the value or condition of the Collateral or any part thereof, or as to the title
of the Borrower thereto, or as to the security afforded thereby or hereby, or as
to the validity or genuineness of any 

                                      -50-
<PAGE>   55
 
Collateral pledged and deposited with such co-Trustee, or the validity or
adequacy of this Indenture or the Notes; a co-Trustee shall not be accountable
for the Borrower's use of the proceeds from the Notes, and it shall not be
responsible for any statement of the Borrower in this Indenture or any document
issued in connection with the sale of the Notes or any statement in the Notes. A
co-Trustee makes no representations with respect to the effectiveness or
adequacy of this Indenture or any Basic Document or the validity or perfection,
if any, of Liens granted under this Indenture or the Collateral Documents. A co-
Trustee shall not be responsible for independently ascertaining or maintaining
such validity or perfection, if any, and shall be fully protected in relying
upon certificates and opinions delivered to it in accordance with the terms of
this Indenture or the Collateral Documents.

     Section 12.13 No Conflict.

     It is the purpose of this section of the Indenture to remove any potential
conflict of interest in the instance in which Chase Bank of Texas, National
Association ("Chase") is acting as Trustee and, in its commercial banking
capacity, has or may develop a lending relationship with the Borrower or any of
its Subsidiary Guarantors.  Accordingly, in the event that Chase, in its
commercial banking capacity, has or may develop a lending relationship with the
Borrower or any of Subsidiary Guarantors, Chase may, but is not obligated to,
resign as Trustee, such resignation to be effective automatically upon receipt
by the Trustee of notice from the successor Trustee evidencing its assumption of
the duties of Trustee hereunder, without notice to and without prior approval of
any party.  In the event Chase resigns as trustee pursuant to this Section
12.13, First Union National Bank, a national banking association duly organized
and existing under the laws of the United States of America with a corporate
trust office in Jacksonville, Florida, or any successor appointed pursuant to
the "Acceptance of Appointment" attached hereto as Exhibit G, has agreed to and
shall automatically become successor Trustee hereunder for all purposes.  Chase
shall give notice of its resignation in writing to the Borrower, the Agent and
the Noteholders as soon as possible but in any event not less than forty-five
(45) days after its resignation, provided that failure to give such notice shall
not impair the effectiveness of such resignation.  The provisions of this
section shall extend to Affiliates of Chase.


                                 ARTICLE XIII
                                 MISCELLANEOUS

     Section 13.01  Interpretation and Survival of Provisions.  Article,
Section, Schedule, and Exhibit references are to this Indenture, unless
otherwise specified.  All references to instruments, documents, contracts, and
agreements are references to such instruments, documents, contracts, and
agreements as the same may be amended, supplemented, and otherwise modified from
time to time, unless otherwise specified.  The word "including" shall mean
"including but not limited to."  Whenever the Borrower has an obligation under
the Basic Documents, the expense of complying with that obligation shall be an
expense of the Borrower unless otherwise specified.  Whenever any determination,
consent, or approval is to be made or given by the Noteholders, such action
shall be in the Noteholders' sole discretion unless 

                                      -51-
<PAGE>   56
 
otherwise specified in this Indenture. If any provision in the Basic Documents
is held to be illegal, invalid, not binding, or unenforceable, such provision
shall be fully severable and the Basic Documents shall be construed and enforced
as if such illegal, invalid, not binding, or unenforceable provision had never
comprised a part of the Basic Documents, and the remaining provisions shall
remain in full force and effect. The Basic Documents have been reviewed and
negotiated by sophisticated parties with access to legal counsel and shall not
be construed against the drafter. The representations, warranties, and covenants
made in this Indenture, the Notes or any other Basic Document shall remain
operative and in full force and effect regardless of (a) any investigation made
by or on behalf of the Borrower or the Noteholders or (b) acceptance of any of
the Notes and payment therefor and repayment or repurchase thereof. All
indemnification obligations of the Borrower and the provisions of Section 13.02
shall remain operative and in full force and effect unless such obligations are
expressly terminated in a writing referencing those individual Sections,
regardless of any purported general termination of this Indenture or any other
Basic Document.

     Section 13.02  Costs, Expenses and Taxes.

          (a) Intentionally Deleted.

          (b) The Borrower agrees to indemnify the Agent and the Noteholders,
and their respective officers, directors, employees, representatives, agents,
attorneys, and Affiliates (collectively, "Related Parties") from, hold each of
them harmless against and promptly upon demand pay or reimburse each of them
for, any and all actions, suits, proceedings (including any investigations,
litigation, or inquiries), claims, demands, and causes of action, and, in
connection therewith, all reasonable costs, losses, liabilities, damages, or
expenses of any kind or nature whatsoever (collectively the "Indemnity Matters")
which may be incurred by or asserted against or involve any of them (whether or
not any of them is designated a party thereto) as a result of, arising out of,
or in any way related to (i) any actual or proposed use by the Borrower of the
proceeds of any sale of the Notes, (ii) the operations of the business of the
Borrower or any Subsidiary, (iii) any bodily injury or death or property damage
occurring in or upon or in the vicinity of any Collateral, (iv) any claim by any
third Person against any Collateral assigned to or paid to any Noteholder
pursuant to any Collateral Document, (v) the failure of the Borrower or any
Subsidiary to comply with any Governmental Requirement, or (vi) any other aspect
of this Indenture and the other Basic Documents, including, without limitation,
the reasonable fees and disbursements of counsel and all other reasonable
expenses incurred in connection with investigating, defending or preparing to
defend any such action, suit, proceeding (including any investigations,
litigation, or inquiries), or claim and INCLUDING ALL INDEMNITY MATTERS ARISING
BY REASON OF THE ORDINARY NEGLIGENCE OF ANY INDEMNITEE (but excluding all
Indemnity Matters arising solely by reason of claims between the Noteholders or
any Noteholder and the Agent or any Noteholder's shareholders against the Agent
or any Noteholder or by reason of the gross negligence or wilful misconduct of
any Indemnitee).

          (c) The Borrower agrees to pay and hold the Noteholders harmless from
and against any and all present and future stamp and other similar taxes with
respect to this 

                                      -52-
<PAGE>   57
 
Indenture and Basic Documents and save the Noteholders harmless from and against
any and all liabilities with respect to or resulting from any delay or omission
to pay such taxes, and will indemnify the Noteholders for the full amount of
taxes paid by the Noteholders in respect of payments made or to be made under
this Indenture, any Note, or any other Basic Document and any liability
(including penalties, interest, and expenses) arising therefrom or with respect
thereto, whether or not such taxes were correctly or legally asserted.

          (d) The Borrower agrees to indemnify and hold harmless from time to
time the Noteholders, and their respective Related Parties, together with the
Trustee, from and against any and all losses, claims, cost recovery actions,
administrative orders or proceedings, damages, and liabilities to which any such
Person may become subject (i) under any Environmental Law applicable to the
Borrower, any Subsidiary, or any of their respective Properties, (ii) as a
result of the breach or non-compliance by the Borrower or any Subsidiary with
any Environmental Law applicable to the Borrower or any Subsidiary, or any of
their respective Properties, (iii) due to the ownership by the Borrower or any
Subsidiary of their respective Properties or any activity on any of their
respective Properties, or any past activity on any of their respective
Properties which, though lawful and fully permissible at the time, could result
in present liability, (iv) the presence, use, release, storage, treatment, or
disposal of hazardous substances on or at any of the properties owned or
operated by the Borrower or any Subsidiary, or (v) any other environmental,
health, or safety condition in connection with this Indenture or any other Basic
Document.

          (e) In the case of any indemnification hereunder, the Noteholder or
other Person indemnified hereunder shall give notice to the Borrower within a
reasonable period of time of any such claim or demand being made against the
Noteholder or other indemnified Person and the Borrower at its sole cost and
expense shall provide a defense of such claim, provided, however, that (i) if
the Borrower has failed to assume the defense and employ counsel or (ii) if the
defendants in any such action include both the indemnified party and the
Borrower or any Subsidiary and counsel to the indemnified party shall  have
concluded that there may be reasonable defenses available to the indemnified
party that are different from or additional to those available to the Borrower
or such Subsidiary or if the interests of the indemnified party reasonably may
be deemed to conflict with the interests of the  Borrower or such Subsidiary,
then the indemnified party shall have the right to select a separate counsel and
to assume such legal defense and otherwise to participate in the defense of such
action, with the expenses and fees of such separate counsel and other expenses
related to such participation to be reimbursed by the Borrower as incurred.

          (f) No indemnitee may settle any claim to be indemnified without the
consent of the indemnitor, such consent not to be unreasonably withheld;
provided, that the indemnitor may not reasonably withhold consent to any
settlement that an indemnitee proposes if the indemnitor does not have the
financial ability to pay all its obligations outstanding and asserted against
the indemnitee at that time, including the maximum potential claims against the
indemnitee to be indemnified pursuant to this Section 13.02.

                                      -53-
<PAGE>   58
 
          (g) This Section 13.02 shall not apply to actions, suits, proceedings,
investigations, demands, losses, liabilities, claims, damages, deficiencies,
interest, judgments, costs, or expenses relating to any Property to the extent
arising from the acts or omissions of the Agent or any Noteholder during the
period after which such Person, its successors or assigns shall have acquired
possession of such Property (whether through foreclosure or deed in lieu of
foreclosure, as mortgagee in possession or otherwise).

          (h) The Borrower's obligations under this Section 13.02 shall survive
any termination of this Indenture and the payment of the Obligations.

     Section 13.03  No Waiver; Modifications in Writing.

          (a) No failure or delay on the part of the Trustee, the Borrower, the
Agent or the Noteholders in exercising any right, power, or remedy hereunder
shall operate as a waiver thereof, nor shall any single or partial exercise of
any such right, power, or remedy preclude any other or further exercise thereof
or the exercise of any right, power, or remedy.  The remedies provided for
herein are cumulative and are not exclusive of any remedies that may be
available to the Borrower, the Trustee, the Agent or the Noteholders at law or
in equity or otherwise.

          (b) Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective unless signed by the
Borrower and the Majority Noteholders.  The Noteholders have all rights to take
such actions under this Indenture and the other Basic Documents without the
consent or joinder of any holder of the Acquired Shares or Warrants. Any
amendment, supplement or modification of or to any provision of this Indenture
or the Notes or any other Basic Document, any waiver of any provision of this
Indenture, the Notes or any other Basic Document, and any consent to any
departure by the Borrower from the terms of any provision of this Indenture, the
Notes or any other Basic Document, shall be effective only in the specific
instance and for the specific purpose for which made or given.  Except where
notice is specifically required by this Indenture, no notice to or demand on the
Borrower in any case shall entitle the Borrower to any other or further notice
or demand in similar or other circumstances.

     Section 13.04  Binding Effect; Assignment.  This Indenture shall be
binding upon the Borrower, the Trustee, the Agent and the Noteholders, and their
respective successors and permitted assigns. Except as expressly provided in
this Indenture, this Indenture shall not be construed so as to confer any right
or benefit upon any Person other than the Borrower, Trustee, Agent and
Noteholders, and their respective successors and permitted assigns.  Subject to
applicable federal law and state securities law, all or any portion of the
rights and obligations of the Noteholders under this Indenture with respect to
the Basic Documents may be sold, assigned or pledged by any Noteholder.  Upon
any assignment of the Basic Documents, the acquiring Noteholder shall succeed to
all of the selling Noteholder's rights and obligations under the Basic Documents
to the extent assigned and the selling Noteholder 

                                      -54-
<PAGE>   59
 
shall be automatically released from any such obligations hereunder with respect
to the Basic Documents to the extent assigned.

     Section 13.05  Communications.  All notices and demands provided for
hereunder shall be in writing and shall be given by registered or certified
mail, return receipt requested, telecopy, air courier guaranteeing overnight
delivery or personal delivery to the following addresses:

     If to the Trustee:

     Chase Bank of Texas, National Association
     Global Trust Services
     600 Travis Street, Suite 1150
     Houston, Texas  77002
     Attention:  Mauri J. Cowen
     Telephone:  (713) 216-6686
     Telecopier: (713) 216-5474


     If to the Agent:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Shirley Hudler
     Telecopier: (713) 646-8008

     and

     Attention:  Donna Lowry
     Telecopier: (713) 646-4039

     If to the Noteholders:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Shirley Hudler
     Telecopier: (713) 646-8008

     and

                                      -55-
<PAGE>   60
 
     Enron Capital & Trade Resources Corp.
     1400 Smith Street
     Houston, Texas  77002
     Attention:  Donna Lowry
     Telecopier: (713) 646-4039

     If to the Borrower:

     6300 Bridge Point Parkway
     Building 2, Suite 500
     Austin, Texas 78730
     Attention:  Craig M. Fleming
     Telecopier: (512) 472-3400

or to such other address as the Borrower, Agent or any Noteholder may designate
in writing.  All other communications may be by regular mail.  All notices and
communications shall be deemed to have been duly given:  at the time delivered
by hand, if personally delivered; four days after being sent by certified mail,
return receipt requested, if mailed; when receipt acknowledged, if telecopied;
and on the next Business Day if timely delivered to an air courier guaranteeing
overnight delivery.  Notwithstanding the foregoing, notices to the Trustee shall
be effective only upon receipt.

     Section 13.06  Governing Law.  This Indenture will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.

     Section 13.07  Arbitration.

          (a) Binding Arbitration.  Subject to the provisions of subparagraph
(e), on the request of either the Borrower, the Agent or any Noteholder, whether
made before or after the institution of any legal proceeding, any action,
dispute, claim or controversy of any kind now existing or hereafter arising
between any of the parties hereto in any way arising out of, pertaining to or in
connection with this Indenture (a "Dispute") shall be resolved by binding
arbitration in accordance with the terms hereof.  Either the Borrower, the Agent
or any Noteholder may, by summary proceedings, bring an action in court to
compel arbitration of any Dispute.

          (b) Governing Rules.  Any arbitration shall be administered by the
American Arbitration Association (the "AAA") in accordance with the terms of
this Section, the Commercial Arbitration Rules of the AAA, and, to the maximum
extent applicable, the Federal Arbitration Act.  Judgment on any award rendered
by an arbitrator may be entered in any court having jurisdiction.

          (c) Arbitrators.  Any arbitration shall be conducted before a three
person panel of neutral arbitrators.  Such panel shall consist of one person
from each of the 

                                      -56-
<PAGE>   61
 
following categories: (1) an attorney who has practiced in the area of
commercial law for at least 10 years or a retired judge at the Texas or United
States District Court or an appellate court level; (2) a person with at least 10
years experience in commercial lending; and (3) a person with at least 10 years
experience in the energy service industry. The AAA shall submit a list of
persons meeting the criteria outlined above for each category of arbitrator, and
the parties shall select one person from each category in the manner established
by the AAA. If the parties cannot agree on an arbitrator within 30 days after
the request for an arbitration, then any party may request the AAA to select an
arbitrator. The arbitrator may engage engineers, accountants or other
consultants that the arbitrator deems necessary to render a conclusion in the
arbitration proceeding.

          (d) Conduct of Arbitration.  To the maximum extent practicable, an
arbitration proceeding hereunder shall be concluded within 180 days of the
filing of the Dispute with the AAA.  Arbitration proceedings shall be conducted
in Houston, Texas.  At the conclusion of any arbitration proceeding, the
arbitrator shall make specific written findings of fact and conclusions of law.
The arbitrator shall have the power to award recovery of all costs and fees to
the prevailing party.  The Borrower, the Agent and the Noteholders each agree to
keep all Disputes and arbitration proceedings strictly confidential except for
disclosure of information required by applicable law.

          (e) Parties' Rights.  Nothing in the preceding paragraph shall require
arbitration prior to the Agent's or the Noteholders' exercise of any rights and
remedies under Article X.  In addition, nothing in this Section 13.07, nor the
exercise of any right to arbitrate thereunder, shall limit the right of the
Borrower, the Agent, the Trustee or any Noteholder: (a) to foreclose against any
Collateral by the exercise of the power of sale under, or to secure direct
payment of the proceeds of any Collateral as provided under, any deed of trust,
mortgage, or other security agreement or instrument or applicable law; (b) to
exercise self-help remedies such as setoff or repossession; or (c) to obtain
provisional or ancillary remedies or relief such as replevin, injunctive relief,
attachment or appointment of a receiver from a court having jurisdiction,
before, during or after the pendency of any arbitration proceeding.  Any
foreclosure action, or the institution and maintenance of any action for such
judicial relief, or pursuit of provisional or ancillary remedies, or exercise of
self-help remedies shall not constitute a waiver of the right of the exercising
party to submit any claim or dispute to arbitration.

          (f) Costs of Arbitration.  All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Borrower (as to 50%) and the Noteholders (as to 50%) unless
otherwise awarded by the arbitrator.

     Section 13.08  Confidentiality.  In the event that the Borrower or any
Guarantor (hereinafter called the "Subject Entities") provides to the Agent or
the Noteholders written confidential information or, if communicated as
confidential, oral confidential information belonging to any Subject Entity, the
Agent and the Noteholders shall thereafter maintain such information in
confidence in accordance with the standards of care and diligence that each
utilizes in maintaining its own confidential information.  This obligation of
confidence shall 

                                      -57-
<PAGE>   62
 
not apply to such portions of the information which (i) are in the public
domain, (ii) hereafter become part of the public domain without the Agent or the
Noteholders breaching their obligation of confidence to any Subject Entity,
(iii) are previously known by the Agent or the Noteholders from some source
other than any Subject Entity, (iv) are hereafter developed by the Agent or the
Noteholders without using a Subject Entity's information, (v) are hereafter
obtained by or available to the Agent or the Noteholders from a third party who
owes no obligation of confidence to any Subject Entity with respect to such
information, (vi) are disclosed with a Subject Entity's consent, (vii) must be
disclosed either pursuant to any Governmental Requirement or to Persons
regulating the activities of the Agent or the Noteholders, or (viii) may be
required to be disclosed by law or regulation or order of any Governmental
Authority in any judicial, arbitration or governmental proceeding. Further, the
Agent or a Noteholder may disclose any such information to any other Noteholder,
any independent petroleum engineers or consultants, any independent certified
public accounts, any legal counsel employed by such Person in connection with
this Indenture or any other Basic Document, including without limitation, the
enforcement or exercise of all rights and remedies thereunder, or, subject to
Section 13.04, any assignee or participant (including prospective assignees and
participants) in the Obligations; provided, however, that the Agent or the
Noteholders shall receive a confidentiality agreement from the Person to whom
such information is disclosed such that said person shall have the same
obligation to maintain the confidentiality of such information as is imposed
upon the Agent or the Noteholders hereunder. Notwithstanding anything to the
contrary provided herein, this obligation of confidence shall cease three (3)
years from the date the information was furnished, unless the Borrower requests
in writing at least thirty (30) days prior to the expiration of such three (3)
year period, to maintain the confidentiality of such information for an
additional three year period.

     Section 13.09  Execution in Counterparts.  This Indenture may be executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together, shall
constitute but one and the same Agreement.

     Section 13.10 Trust Indenture Act Controls. Whether prior to or following
the qualification of this Indenture under the TIA, if any provision of this
Indenture limits, qualifies, or conflicts with the duties imposed by operation
of TIA (S)318(c) upon an Indenture qualified under the TIA, the imposed duties
shall control under this Indenture.

     Section 13.11 Communication by Noteholders with Other Noteholders.
Noteholders may communicate pursuant to TIA (S)312(b) with other Noteholders
with respect to their rights under this Indenture or the Notes. The Company, the
Guarantors, the Trustee, the Registrar and anyone else shall have the protection
of TIA (S)312(c).

     Section 13.12  Certificate and Opinion as to Conditions Precedent.  Upon
any request or application by the Borrower or any Guarantor to the Trustee to
take any action under this Indenture, the Borrower or such Guarantor, as the
case may be, shall furnish to the Trustee:

                                      -58-
<PAGE>   63
 
          (a) an Officers' Certificate (which shall include the statements set
forth in Section 13.13) stating that, in the opinion of the signers, the
conditions precedent, if any, provided for in this Indenture relating to the
proposed action have been complied with;

          (b) an Opinion of Counsel stating that, in the opinion of such
counsel, such conditions precedent have been complied with; and

          (c) any Opinion of Counsel may assume the existence of non-existence
of facts necessary to support such Opinion unless such counsel has actual
knowledge that such assumption would be contrary to the actual facts.

     Section 13.13  Statements Required in Certificate or Opinion.  Each
certificate or opinion with respect to compliance with a condition or covenant
provided for in this Indenture shall include:

          (a) a statement that each person making such certificate or opinion
has read such covenant or condition;

          (b) a brief statement as to the nature and scope of the examination or
investigation upon which the statements or opinions contained in such
certificate or opinion are based;

          (c) a statement that, in the opinion of each such person, he has made
such examination or investigation as is necessary to enable him to express an
informed opinion as to whether or not such covenant or condition has been
complied with; and

          (d) a statement as to whether or not, in the opinion of each such
person, such covenant or condition has been complied with.

     Section 13.14  Rules by Trustee and Agents.  The Trustee may make
reasonable rules for action by or a meeting of the Noteholders.  The Note
Registrar may make reasonable rules for its functions.

     Section 13.15  Legal Holidays.  A "Legal Holiday" is a Saturday, a
Sunday, or a day on which banks and trust companies in the City of New York are
not required by law or executive order to be open.  If a payment date is a Legal
Holiday at a place of payment, payment may be made at the place on the next
succeeding day that is not a Legal Holiday, without additional interest.

                                      -59-
<PAGE>   64
 
     IN WITNESS WHEREOF, BRIGHAM EXPLORATION COMPANY has caused this Indenture
to be signed by its President or one of its Vice Presidents, and CHASE BANK OF
TEXAS, NATIONAL ASSOCIATION has caused this Indenture to be signed by one of its
duly authorized trust officers, all as of the day and year first above written.

                              BRIGHAM EXPLORATION COMPANY


                              By: /s/ CRAIG M. FLEMING
                                 -----------------------------------
                                 Craig M. Fleming
                                 Vice President and Chief Financial Officer



                              CHASE BANK OF TEXAS, NATIONAL
                              ASSOCIATION, as Trustee


                              By: /s/ MAURI COWEN
                                 -----------------------------------
                              Name:   Mauri J. Cowen
                                   ---------------------------------
                              Title:  Vice President & Trust Officer
                                    --------------------------------

                                      -60-
<PAGE>   65
 
STATE OF TEXAS      (S)
                    (S)
COUNTY OF HARRIS    (S)

     BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared Craig M. Fleming known to me to be the
person and officer whose name is subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said BRIGHAM EXPLORATION
COMPANY, a Delaware corporation, and that he executed the same as the act of
said corporation for the purposes and consideration therein expressed, and in
the capacity therein stated.

     GIVEN UNDER MY HAND AND SEAL OF OFFICE, this 20th day of August, 1998.


                              -------------------------------------------
                              Notary Public in and for the State of Texas

My commission expires:

- ---------------------------

STATE OF TEXAS      (S)
                    (S)
COUNTY OF HARRIS    (S)

     BEFORE ME, the undersigned authority, a Notary Public in and for said
state, on this day personally appeared __________________, known to me to be the
person and officer whose names are subscribed to the foregoing instrument and
acknowledged to me that the same was the act of the said CHASE BANK OF TEXAS,
NATIONAL ASSOCIATION, a national banking association, and that she executed the
same as the act of said national banking association for the purposes and
consideration therein expressed, and in the capacity therein stated.

     GIVEN UNDER MY HAND AND SEAL OF OFFICE, this 20th day of August, 1998.


                              ------------------------------------------- 
                              Notary Public in and for the State of Texas
My commission expires:

- ---------------------------

                                      -61-

<PAGE>   1
                                                                 EXHIBIT 10.1.4


- -------------------------------------------------------------------------------





                              AMENDED AND RESTATED
                        AGREEMENT OF LIMITED PARTNERSHIP




                              -------------------




                            BRIGHAM OIL & GAS, L.P.




                              -------------------




                         Dated as of December 30, 1997





- -------------------------------------------------------------------------------

<PAGE>   2

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                    PAGE
                                                                                    ----
<S>                                                                                 <C>
ARTICLE I -- Formation of Partnership..................................................2
         Section 1.1.  Formation.......................................................2
         Section 1.2.  Name............................................................2
         Section 1.3.  Business........................................................3
         Section 1.4.  Place of Business and Registered Agent..........................3
         Section 1.5.  Names and Addresses of Partners.................................3
         Section 1.6.  Term............................................................3
         Section 1.7.  Filings.........................................................4
         Section 1.8.  Title to Partnership Property...................................4

ARTICLE II -- Definitions and References...............................................4
         Section 2.1.  Defined Terms...................................................4
         Section 2.2.  References and Titles...........................................6

ARTICLE III -- Capitalization..........................................................6
         Section 3.1.  Capital Contributions of Partners...............................6
         Section 3.2.  Additional Capital Contributions................................6
         Section 3.3.  Non-payment of Capital Contributions............................7
         Section 3.4.  Return of Capital Contributions.................................7
         Section 3.5.  Payments and Advances by General Partner........................7

ARTICLE IV -- Allocations and Distributions............................................8
         Section 4.1.      Allocation of Profits and Losses. ..........................8
         Section 4.2.      Distributions...............................................8

ARTICLE V -- Management................................................................8
         Section 5.1.  Power and Authority of General Partner..........................8
         Section 5.2.  Contracts With Affiliates......................................10
         Section 5.3.  Tax Elections..................................................10
         Section 5.4.  Tax Returns; Tax Matters Partner...............................11
         Section 5.5.  Reimbursement of Expenses......................................11

ARTICLE VI -- Rights of Limited Partner...............................................11
         Section 6.1.  Rights of Limited Partner......................................11
         Section 6.2.  Limitations on Limited Partner.................................11
         Section 6.3.  Liability of Limited Partner...................................12
         Section 6.4.  Withdrawal and Return of Capital Contributions.................12

ARTICLE VII -- Books, Records and Bank Accounts.......................................12
         Section 7.1.  Capital Accounts, Books and Records............................12
         Section 7.2.  Reports........................................................13
         Section 7.3.  Bank Accounts..................................................13
         Section 7.4.  Information Relating to the Partnership........................13
</TABLE>



                                      (ii)
<PAGE>   3


<TABLE>
<CAPTION>
                                                                                    PAGE
                                                                                    ----
<S>                                                                                 <C>
ARTICLE VIII -- Dissolution, Liquidation and Termination..............................13
         Section 8.1.  Dissolution....................................................13
         Section 8.2.  Liquidation and Termination....................................14
         Section 8.3.  Reconstitution.................................................15

ARTICLE IX -- Assignments of Interests................................................15
         Section 9.1.  Assignment by Partners.........................................15

ARTICLE X -- Miscellaneous............................................................16
         Section 10.1.  Notices.......................................................16
         Section 10.2.  Amendment.....................................................16
         Section 10.3.  Partition.....................................................16
         Section 10.4.  Entire Agreement..............................................16
         Section 10.5.  Severability..................................................16
         Section 10.6.  No Waiver.....................................................16
         Section 10.7.  Applicable Law................................................16
         Section 10.8.  Meetings of the Partners......................................17
         Section 10.9.  Successors and Assigns........................................17
         Section 10.10.  Counterparts.................................................17
</TABLE>



                                     (iii)

<PAGE>   4

                              AMENDED AND RESTATED
                        AGREEMENT OF LIMITED PARTNERSHIP

                            BRIGHAM OIL & GAS, L.P.


         THIS AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP (this
"Agreement") dated as of December 30, 1997, is made by and between Brigham,
Inc., a Nevada corporation, as the general partner (the "General Partner"), and
Brigham Holdings I, LLC, a Nevada limited liability company ("BHILLC"), as a
limited partner, and Brigham Holdings II, LLC, a Nevada limited liability
company ("BHIILLC"), as a limited partner (BHILLC and BHIILLC shall
individually referred to herein as a "Limited Partner", and together shall be
referred to as the "Limited Partners").

                              W I T N E S S E T H:

         WHEREAS, Brigham Oil & Gas, L.P., a Delaware limited partnership (the
"Partnership") was formed on May 1, 1992 pursuant to an Agreement of Limited
Partnership by and among Brigham Exploration Company, a Texas corporation
(which subsequently changed its name to Brigham, Inc. ("BI") and was merged
with and into its parent, Brigham I, Inc., a Nevada corporation now know as
Brigham, Inc. ("Brigham Nevada") after the merger), as a general partner, and
certain additional parties, as general and limited partners;

         WHEREAS, the Agreement of Limited Partnership for the Partnership was
amended on three occasions for various purposes, including the admission of
certain additional parties as limited partners (the Agreement of Limited
Partnership as so amended herein called the "Original Agreement");

         WHEREAS, on February 26, 1997, in an exchange (the "Exchange") made
pursuant to an Exchange Agreement dated on such date, all of the shareholders
of BI contributed all of their stock in BI to a newly-organized corporation,
Brigham Exploration Company, a Delaware corporation ("BEC"), and all of the
other partners of the Partnership (the "Other Partners") contributed their
interests in the Partnership to BEC, all in exchange for common stock in BEC;

         WHEREAS, BI's interest in the profits and capital of the Partnership
at the time of the Exchange was approximately 54.00% and the interests of the
Other Partners in profits and capital was approximately 46.00%;

         WHEREAS, at the time of the Exchange, the Partnership was indebted to
RIMCO Partners, LP II, RIMCO Partners, LP III and RIMCO Partners, LP IV
(collectively "RIMCO") in the approximate amount of $16,486,000.00 (the "RIMCO
Debt");

         WHEREAS, RIMCO contributed the RIMCO Debt to BEC as a part of the
Exchange and received therefor common stock in BEC, whereupon BEC contributed
the RIMCO Debt to the Partnership as a contribution to capital;

<PAGE>   5

         WHEREAS, following the contribution of the RIMCO Debt by BEC to the
Partnership as a contribution to capital, the Partnership interests of the of
the partners were 43.23% for BI, and 56.77% for BEC;

         WHEREAS, pursuant to a prospectus dated May 8, 1997, BEC issued
additional shares in an initial public offering, the proceeds of which were
contributed by BEC to the capital of the Partnership, resulting in further
adjustments in the Partnership interests of the partners, with BI's interest
being reduced to 31.5% and BEC's interest being increased to 68.5%; and

         WHEREAS, the partners now wish to amend and restate the Original
Agreement to reflect the current percentage interests of the partners, to
convert BEC's interests in the Partnership into limited partner interests, to
convert BI's interest in the Partnership, which is now held by Brigham Nevada
due to the merger, into a 1% general partner interest and a 30.5% limited
partner interest, to admit Brigham Holdings I, LLC, a Nevada limited liability
company and assignee of BEC's 68.5% limited partner interest, as a limited
partner, to admit Brigham Holdings II, LLC, a Nevada limited liability company
and assignee of BI's 30.5% limited partner interest, as a limited partner, and
to make additional changes to eliminate certain obsolete provisions and
incorporate certain additional provisions to reflect current operations of the
Partnership;

         NOW, THEREFORE, in consideration of the premises, the mutual covenants
and agreements contained herein and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the General Partner
and Limited Partners agree as follows:


                                   ARTICLE I

                            Formation of Partnership

         Section 1.1. Formation. The Partnership was organized on May 1, 1992,
as a limited partnership pursuant to the provisions of the Delaware Revised
Uniform Limited Partnership Act (Del. Code Ann. tit. 6 Sections 17-101 to
17-1109), as amended from time to time, and any successor statute or statutes
(the "Act").

         Section 1.2. Name. The name of the Partnership shall be "Brigham Oil &
Gas, L.P." Subject to all applicable laws, the business of the Partnership
shall be conducted in the name of the Partnership unless under the law of some
jurisdiction in which the Partnership does business such business must be
conducted under another name. In such a case, the business of the Partnership
in such jurisdiction may be conducted under such other name or names (except
the name of the General Partner, any Affiliate of the General Partner or the
name of the Limited Partner) as the General Partner shall determine to be
necessary so long as it does not affect adversely the limited liability of the
Limited Partner hereunder or jeopardize in any manner the title to or ownership
of any Partnership assets. The General Partner shall cause to be filed on
behalf of the Partnership such partnership or


                                      -2-

<PAGE>   6

assumed or fictitious name certificate or certificates or similar instruments
as may from time to time be required by law.

         Section 1.3. Business. The business of the Partnership shall be (a) to
acquire and own or lease all types of real and personal property, specifically
including oil, gas and other mineral interests in real property (the "Oil & Gas
Properties"); (b) explore, drill, develop and operate such Oil & Gas
Properties; (c) produce, collect, store, treat, deliver, market, sell or
otherwise dispose of oil, gas and related hydrocarbons, minerals and other
products from such Oil & Gas Properties; (d) farmout, sell, abandon and
otherwise dispose of such Oil & Gas Properties and other Partnership assets;
(e) obtain and market seismic data; and (g) take all such other actions
incidental to any of the foregoing as the General Partner may determine to be
necessary or desirable.

         Section 1.4. Place of Business and Registered Agent.

         (a) The principal United States office and place of business of the
Partnership and its street address shall be 6300 Bridge Point Parkway, Bldg. 2,
Suite 500, Austin, Texas 78730. The General Partner, at any time and from time
to time, may change the location of the Partnership's principal United States
office and place of business and may establish such additional place or places
of business of the Partnership as the General Partner shall determine to be
necessary or desirable, provided notice thereof is concurrently given to the
Limited Partner.

         (b) The registered office of the Partnership in the State of Delaware
shall be The Corporation Trust Company, Corporation Trust Center, 1209 Orange
Street, Wilmington, Delaware 19801, and the registered agent for service of
process on the Partnership shall be The Corporation Trust Company, a
corporation whose business address is the same as the Partnership's registered
office. The General Partner, at any time and from time to time, may change the
Partnership's registered office or registered agent or both by complying with
the applicable provisions of the Act and giving concurrent notice thereof to
the Limited Partners and may establish, appoint and change additional
registered offices and registered agents of the Partnership in such other
states as the General Partner shall determine to be necessary or advisable.

         Section 1.5. Names and Addresses of Partners. The General Partner is
the sole general partner of the Partnership, and the mailing and street address
of its business is 6300 Bridge Point Parkway, Bldg. 2, Suite 500, Austin, Texas
78730. The Limited Partners are the only limited partners of the Partnership,
and the mailing and street address of each of their businesses, which is the
same for each, is 3773 Howard Hughes Parkway, Suite 300 North, Las Vegas,
Nevada 89109. The General Partner and the Limited Partners may agree to admit
additional Limited Partners to the Partnership, in which case any such
additional Limited Partner shall provide its mailing and street address to the
Partnership.

         Section 1.6. Term. The Partnership shall be formed and commence upon
the completion of filing for record an initial certificate of limited
partnership of the Partnership with the Secretary of State of the State of
Delaware and shall continue until terminated in accordance with Article VIII.


                                      -3-

<PAGE>   7

The General Partner shall not be required to deliver or mail a copy of the
certificate of limited partnership to the Limited Partners.

         Section 1.7. Filings. Upon the request of the General Partner, the
Limited Partners shall promptly execute and deliver all such certificates and
other instruments conforming hereto as shall be necessary for the General
Partner to accomplish all filing, recording, publishing and other acts
appropriate to comply with all requirements for the formation and operation of
the Partnership as a limited partnership under the laws of the State of
Delaware and for the qualification or reformation and operation of the
Partnership as a limited partnership (or a partnership in which the Limited
Partners have limited liability) in all other jurisdictions where the
Partnership shall propose to conduct business. Prior to the conducting of any
business in any jurisdiction, the General Partner shall to the full extent
necessary to establish limited liability for the Limited Partners under the
laws of such jurisdiction and otherwise to comply with the laws of such
jurisdiction, cause the Partnership to comply with all requirements for the
registration, qualification or reformation of the Partnership to conduct
business as a limited partnership (or a partnership in which the Limited
Partners have limited liability) in such jurisdiction. Thereafter, the General
Partner shall cause the Partnership to continue to comply with all such
requirements and all other requirements necessary to maintain the limited
liability of the Limited Partners in each jurisdiction where the Partnership
does business.

         Section 1.8. Title to Partnership Property. All property owned by the
Partnership, whether real or personal, tangible or intangible, shall be deemed
to be owned by the Partnership as an entity, and no Partner, individually,
shall have any ownership of such property. The Partnership shall hold its
property in its own name. The Partnership shall hold all of its assets in the
name of the Partnership unless under the law of some jurisdiction in which the
Partnership owns assets such assets must be held in another name. In such a
case, such assets in such jurisdiction shall be held under such other name or
names (except the name of the General Partner, any Affiliate of the General
Partner or the name of the Limited Partners) as the General Partner shall
determine to be necessary so long as it does not affect adversely the limited
liability of the Limited Partners hereunder or jeopardize in any manner the
title to or ownership of any Partnership assets.


                                   ARTICLE II

                           Definitions and References

         Section 2.1. Defined Terms. When used in this Agreement, the following
terms shall have the respective meanings set forth below:

         "Act" shall mean the Delaware Revised Uniform Limited Partnership Act
(Del. Code Ann. tit. 6 Sections 17-101 to 17-1109), as amended from time to
time, and any successor statute or statutes.


                                      -4-

<PAGE>   8

         "Affiliate" shall mean (a) any person directly or indirectly owning,
controlling or holding with power to vote 10% or more of the outstanding voting
securities of the General Partner, (b) any person 10% or more of whose
outstanding voting securities are directly or indirectly owned, controlled or
held with power to vote by the General Partner, (c) any person directly or
indirectly controlling, controlled by or under common control with the General
Partner, and (d) any officer, director or partner of the General Partner or any
person described in subsection (a), (b) or (c) of this paragraph. As used in
this Agreement, the term "person" shall include an individual, an estate, a
corporation, a partnership, an association, a joint stock company and a trust.

         "Agreed Rate" shall mean a rate per annum which is equal to the lesser
of (a) the rate of interest as published from time to time in the Wall Street
Journal as the "prime rate" (defined as the base rate on corporate loans posted
by at least 75% of the nation's 30 largest banks), adjusted from time to time
to reflect any changes in such rate determined hereunder, or (b) the maximum
rate from time to time permitted by applicable law.

         "BHILLC" shall mean Brigham Holdings I, LLC, a Nevada limited
liability company.

         "BHIILLC" shall mean Brigham Holdings II, LLC, a Nevada limited
liability company.

         "Capital Account" shall have the meaning set forth in Section 7.1(b)
hereof.

         "Capital Contributions" shall mean for any Partner at the particular
time in question the aggregate of the dollar amounts of any cash and the fair
market value of any property contributed to the capital of the Partnership, or,
if the context in which such term is used so indicates, the dollar amounts of
cash and the fair market value of any property agreed to be contributed, or
requested to be contributed, by such Partner to the capital of the Partnership.

         "General Partner" shall mean Brigham, Inc., a Nevada corporation, and
any person who becomes a substituted General Partner of the Partnership
pursuant to the terms hereof.

         "Internal Revenue Code" shall mean the Internal Revenue Code of 1986,
as amended from time to time, and any successor statute or statutes.

         "Limited Partner" shall mean each of BHILLC and BHIILLC, and any
person who becomes a substituted Limited Partner or an additional Limited
Partner of the Partnership pursuant to the terms hereof.

         "Partners" shall mean the General Partner and the Limited Partner.

         "Partnership" shall mean Brigham Oil & Gas, L.P., a Delaware limited
partnership.

         "Sharing Ratio" shall mean 1% for the General Partner, 30.5% for
BHIILLC and 68.5% for BHILLC.


                                      -5-
<PAGE>   9

         Section 2.2. References and Titles. All references in this Agreement
to articles, sections, subsections and other subdivisions refer to
corresponding articles, sections, subsections and other subdivisions of this
Agreement unless expressly provided otherwise. Titles appearing at the
beginning of any of such subdivisions are for convenience only and shall not
constitute part of such subdivisions and shall be disregarded in construing the
language contained in such subdivisions. The words "this Agreement," "herein,"
"hereof," "hereby," "hereunder" and words of similar import refer to this
Agreement as a whole and not to any particular subdivision unless expressly so
limited. Pronouns in masculine, feminine and neuter genders shall be construed
to include any other gender, and words in the singular form shall be construed
to include the plural and vice versa, unless the context otherwise requires.


                                  ARTICLE III

                                Capitalization

         Section 3.1. Capital Contributions of Partners. The General Partner
and the Limited Partners have already made Capital Contributions to the
Partnership in such amounts and at such times as are reflected in the books of
the Partnership. Notwithstanding anything to the contrary contained herein,
such Capital Contributions shall be the maximum contribution to the Partnership
that the Partners shall be required to make (unless the Partners otherwise
elect as provided in Section 3.2).

         Section 3.2. Additional Capital Contributions. At any time after the
making of the Capital Contributions referred to in Section 3.1, the General
Partner may request that each Partner make additional Capital Contributions to
the Partnership in accordance with each Partner's Sharing Ratio for the purpose
of (i) acquiring additional Oil & Gas Properties, or (ii) for such other uses
as are consistent with the purpose of the Partnership. No Partner shall be
obligated to make any such additional Capital Contributions unless and until
such time as each Partner agrees to make such additional Capital Contributions.

         In the event that a Partner shall decline to make all or any portion
of the additional Capital Contributions requested at any time, the General
Partner may elect to take any of the following actions:

         (a) The General Partner may borrow funds in the name of the
Partnership for expenditure for such purposes, subject to Section 5.2(a) ;

         (b) The Partners electing to make additional Capital Contributions may
pay their pro rata share of all of the additional Capital Contributions which a
Partner shall decline to make; and the General Partner shall adjust the Sharing
Ratios accordingly; or

         (c) The General Partner may cause the Partnership and/or the Partners
to take such other actions upon which the Partners shall agree.


                                      -6-

<PAGE>   10

         Section 3.3. Non-payment of Capital Contributions.

         (a) The Partnership shall have the right to pursue any remedy existing
at law or in equity for the collection of the unpaid amount of the Capital
Contributions agreed to be made in Section 3.l or hereafter agreed to be made
in accordance with Section 3.2, including without limitation the prosecution of
a suit against a defaulting Partner.

         (b) The Partnership may retain any revenues otherwise distributable to
a defaulting Partner pursuant to this Agreement in an amount equal to the
amount such Partner failed or refused to contribute as required pursuant to the
terms of this Agreement, together with interest on such past-due amounts at a
rate equal to the Agreed Rate. Any amount so withheld shall be deemed, for all
purposes of this Agreement, to have been distributed to the defaulting Partner
and, other than that portion of such amounts representing interest, be deemed
to have been recontributed by the defaulting Partner to the capital of the
Partnership for the purposes for which contributions were initially requested.
To the extent that a Partner has advanced funds to the Partnership as a result
of the default of a Partner, such Partner shall be entitled to be reimbursed
from the amounts so withheld from the defaulting Partner.

         Section 3.4. Return of Capital Contributions. Except as provided in
Section 3.5, no interest shall accrue on any contributions to the capital of
the Partnership; and no Partner shall have the right to withdraw or be repaid
any capital contributed by such Partner except as provided in Section 8.2 of
this Agreement. All interest which accrues on Partnership funds shall be
allocated and credited to the Partners in accordance with Section 4.1.

         Section 3.5. Payments and Advances by General Partner. The General
Partner shall have the right to pay any indebtedness or obligation of the
Partnership out of funds of the General Partner, and may bill the Partnership
in the same manner that the Partnership may bill the Limited Partners. Further,
if at any time the General Partner advances funds to or on behalf of the
Partnership or the General Partner is required to pay any indebtedness or
obligation of the Partnership in excess of the Capital Contributions of the
General Partner agreed to be made in this Article III, such advance or payment
shall constitute a loan by the General Partner to the Partnership. If any such
advance or payment is outstanding for more than sixty(60) days and except as
provided in Section 3.4, such advance or payment shall bear interest from the
date first made at a rate equal to the Agreed Rate. No such advance or payment
by the General Partner shall be deemed to be a contribution by the General
Partner to the capital of the Partnership. Any advances by the General Partner
(other than (i) for a required payment by the General Partner which is beyond
the control of the General Partner of any indebtedness or obligation of the
Partnership in excess of the Capital Contributions of the General Partner
agreed to be made in this Article III, or (ii) a payment by the General Partner
of any costs and expenses allocated and charged to a Limited Partner upon the
default by the Limited Partner in the payment of any Capital Contributions
previously agreed to be made by the Limited Partner) shall be subject to the
limitations on borrowing specified in Section 5.2(a). Any loan made by the
General Partner hereunder to pay any costs or expenses allocated and charged to
any Partner


                                      -7-

<PAGE>   11

shall be repaid (with payments to be applied first to the payment of interest
and then to the repayment of principal) from the revenues that would otherwise
be next distributed to such Partner hereunder.


                                   ARTICLE IV

                         Allocations and Distributions

         Section 4.1. Allocation of Profits and Losses. Except as may be
otherwise required under Section 704 of the Internal Revenue Code and the
Treasury Regulations promulgated thereunder (including those Regulations
governing allocations with respect to nonrecourse indebtedness and property
carried on the books of the Partnership at an amount which differs from its
adjusted tax basis), each item of income, gain, loss, deduction, and credit of
the Partnership shall be allocated and charged to the Partners in accordance
with their respective Sharing Ratios.

         Section 4.2. Distributions. All cash funds of the Partnership (other
than Capital Contributions and any borrowed funds) which the General Partner
reasonably determines are not needed for the payment of existing or foreseeable
(within 30 days) Partnership obligations and expenditures shall be distributed
to the Partners in proportion to their Sharing Ratios. Payment of all
distributions made by the Partnership to the Limited Partners shall be made by
transfer of immediately available funds in accordance with such written
instructions to the General Partner as may be provided by the Limited Partners
from time to time. All distributions in liquidation of a Partner's interest in
the Partnership shall be made in accordance with Section 8.2.


                                   ARTICLE V

                                   Management

         Section 5.1. Power and Authority of General Partner. The General
Partner shall have full and exclusive power and authority on behalf of the
Partnership to manage, control, administer and operate the properties, business
and affairs of the Partnership and to do or cause to be done any and all acts
deemed by the General Partner to be necessary or appropriate thereto, and the
scope of such power and authority shall encompass all matters in any way
connected with such business or incident thereto, including but not limited to,
the power and authority:

         (a) To purchase or otherwise acquire real or personal property of
every nature considered necessary or appropriate to carry on and conduct the
business of the Partnership;

         (b) To borrow monies for the purchase, development and maintenance of
Partnership assets and other aspects of the Partnership's business and from
time to time to draw, make, execute and issue promissory notes and other
negotiable or non-negotiable instruments and evidences of indebtedness; to
secure the payment of the sums so borrowed and to mortgage, pledge or assign in


                                      -8-

<PAGE>   12

trust all or any part of the property of the Partnership, and to assign any
monies owing or to be owing to the Partnership;

         (c) To enter into any agreements of joint venture or partnership or
for sharing of risks, expenses or profits, with any person, firm, corporation,
government or agency thereof engaged in any business or transaction in which
the Partnership is authorized to engage;

         (d) To maintain, develop, manage and defend Partnership property; to
contract with third parties for such purposes; and to do any and all other
things necessary or appropriate to carry out the terms and provisions of this
Agreement which would or might be done by a normal and prudent businessman in
the development and management of its own property;

         (e) To sell, assign, convey or otherwise dispose of, for such
consideration and upon such terms and conditions as the General Partner may
determine to be in the best interests of the Partnership, all or any part of
the Partnership property, any interest therein, or any interest payable
therefrom, and in connection therewith to execute and deliver such deeds,
assignments and conveyances containing such warranties as the General Partner
may determine to be appropriate;

         (f) To purchase, lease, rent or otherwise acquire or obtain the use of
facilities and all other kinds and types of real or personal property that may
in anyway be deemed necessary, convenient, or advisable in connection with
carrying on the business of the Partnership;

         (g) To pay any amounts necessary or appropriate to the maintenance or
operation of any Partnership property;

         (h) To make and to enter into such agreements and contracts with such
parties and to give such receipts, releases and discharges with respect to any
and all of the foregoing and any matters incident thereto as the General
Partner may deem advisable or appropriate;

         (i) To procure and maintain in force such insurance as the General
Partner shall deem prudent to serve as protection against liability for loss
and damage which may be occasioned by the activities to be engaged in by the
Partnership or the General Partner on behalf of the Partnership;

         (j) To sue and be sued, complain and defend in the name of and on
behalf of the Partnership;

         (k) To quitclaim, surrender, release or abandon any Partnership
property, with or without consideration therefor;

         (l) To execute and deliver all checks, drafts, endorsements and other
orders for the payment of Partnership funds;


                                      -9-

<PAGE>   13

         (m) To employ on behalf of the Partnership agents, employees and
officers (having such duties and titles and having such authority by delegation
from the General Partner as the General Partner shall designate), accountants,
attorneys, brokers, consultants and all other professionals, clerical help and
such other assistance and services as the General Partner may deem proper and
to pay therefor such remuneration as the General Partner may determine to be
reasonable and appropriate;

         (n) To appear and to represent the Partnership before any governmental
authority or regulatory agency and to make all necessary or appropriate filings
before such authority or agency; and

         (o) To take such other action, execute and deliver such other
documents and perform such other acts as may be deemed by the General Partner
to be appropriate to carry out the business and affairs of the Partnership in
accordance with this Agreement.

         Section 5.2. Contracts With Affiliates. The Partnership may enter into
contracts and agreements with the General Partner and its Affiliates for the
rendering of services, the sale and lease of supplies and equipment, provided
that the amount of the compensation, price or rental that can be charged to or
by the Partnership therefor must be no less favorable to the Partnership than
those available from unrelated third parties in the area engaged in the
business of rendering comparable services or selling or leasing comparable
properties, equipment and supplies which could reasonably be made available to
or by the Partnership.

         Section 5.3. Tax Elections. The General Partner shall make the
following elections on behalf of the Partnership:

         (a) To elect a fiscal year of the Partnership to be the calendar year;

         (b) To elect the accrual method of accounting if permitted by
applicable law;

         (c) To elect, in accordance with Sections 195 and 709 of the Internal
Revenue Code and applicable regulations and comparable state law provisions, to
treat all start-up and organization costs of the Partnership as deferred
expenses amortizable over sixty (60) months; and

         (d) To elect with respect to such other federal, state and local tax
matters as shall be deemed to be in the best interests of the Partnership and
the Partners.

         Section 5.4. Tax Returns; Tax Matters Partner. The General Partner
shall be the "tax matters partner" of the Partnership and shall prepare and
timely file all federal, state and local income and other tax returns and
reports as may be required as a result of the business of the Partnership.

         Section 5.5. Reimbursement of Expenses. All direct and indirect costs
and expenses incurred by the General Partner in organizing the Partnership and
in managing and conducting the business and


                                      -10-

<PAGE>   14

affairs of the Partnership, including, without limitation, (i) all costs and
expenses incurred in oil and gas exploration, development, operation,
production and marketing activities including all costs and expenses incurred
in connection with activities in support of or related to directly or
indirectly such oil and gas exploration, development, of operation, production
and marketing activities, (ii) all other costs and expenses incurred in any
business of the Partnership other than oil and gas exploration, development and
production, (iii) secretarial, telephone, office rent and other office
expenses, (iv) salaries and other compensation expenses of employees, officers
and directors, (v) other administrative expenses, (vi) travel expenses, (vii)
legal, accounting, geological, engineering and well supervision costs and
expenses and (viii) expenses incurred in providing or obtaining such other
professional, technical, administrative services and advice as the General
Partner may deem necessary or desirable, shall be paid or reimbursed by the
Partnership as a Partnership expense. The General Partner shall determine which
expenses are allocable to the Partnership in a manner which is fair and
reasonable to the General Partner and the Partnership, and if such allocation
is made by the General Partner in good faith it shall be conclusive in the
absence of manifest error.

                                   ARTICLE VI

                           Rights of Limited Partner

         Section 6.1. Rights of Limited Partner. Each of the Limited Partners
shall have the right to: (a) have the Partnership books and records (including,
without limitation, those required under the Act) kept at the principal United
States office of the Partnership and at all reasonable times to inspect and
copy any of them at the sole expense of such Partner; (b) have on demand true
and full information of all things affecting the Partnership and a formal
account of Partnership affairs whenever circumstances render it just and
reasonable; (c) have dissolution and winding up by decree of court as provided
for in the Partnership; and (d) exercise all rights of a limited partner under
the Partnership (except to the extent otherwise specifically provided herein).

         Section 6.2. Limitations on Limited Partner. Each of the Limited
Partners shall not: (a) be permitted to take part in the business or control of
the business or affairs of the Partnership; (b) have any voice in the
management or operation of any Partnership property; or (c) have the authority
or power to act as agent for or on behalf of the Partnership or any other
Partner, to do any act which would be binding on the Partnership or any other
Partner, or to incur any expenditures on behalf of or with respect to the
Partnership. No Partner shall hold out or represent to any third party that any
of the Limited Partners have any such power or right or that the Limited
Partners are anything other than a "limited partner" in the Partnership.

         Section 6.3. Liability of Limited Partner. Each of the Limited
Partners shall not be liable for the debts, liabilities, contracts or other
obligations of the Partnership except to the extent of any unpaid Capital
Contributions agreed to be made by a Limited Partner as set forth in Section
3.1, any additional Capital Contributions hereafter agreed to be made by a
Limited Partner in accordance with Section 3.2 and a Limited Partner's share of
the assets (including undistributed revenues) of the Partnership; and in all
events, a Limited Partner shall be liable and obligated to make payments of its


                                      -11-

<PAGE>   15

Capital Contributions only as and when such payments are due in accordance with
the terms of this Agreement, and a Limited Partner shall not be required to
make any loans to the Partnership. The Partnership shall indemnify and hold
harmless each of the Limited Partners in the event it (a) becomes liable for
any debt, liability, contract or other obligation of the Partnership except to
the extent expressly provided in the preceding sentence or (b) is directly or
indirectly required to make any payments with respect thereto.

         Section 6.4. Withdrawal and Return of Capital Contributions. Each of
the Limited Partners shall not be entitled to (a) withdraw from the Partnership
except upon the assignment by such Limited Partner of all of its interest in
the Partnership and the substitution of the Limited Partner's assignee as a
Limited Partner of the Partnership in accordance with Section 9.1, or (b) the
return of its Capital Contributions except to the extent, if any, that
distributions made pursuant to the express terms of this Agreement may be
considered as such by law or by unanimous agreement of the Partners, or upon
dissolution and liquidation of the Partnership, and then only to the extent
expressly provided for in this Agreement and as permitted by law.


                                  ARTICLE VII

                        Books, Records and Bank Accounts

         Section 7.1. Capital Accounts, Books and Records.

         (a) The General Partner shall keep books of account for the
Partnership in accordance with the terms of this Agreement. Such books shall be
maintained at the principal office of the Partnership.

         (b) An individual capital account (a "Capital Account") shall be
maintained by the Partnership for each Partner in accordance with the
requirements of the applicable Treasury Regulations under Section 704 of the
Internal Revenue Code.

         Section 7.2. Reports. The General Partner shall deliver to the Limited
Partners such reports and financial statements as the General Partner shall
determine or as the Limited Partners shall reasonably request from time to
time.

         Section 7.3. Bank Accounts. The General Partner shall cause one or
more accounts to be maintained in the name of the Partnership in one or more
banks which each have capital, surplus and undivided profits of at least
$200,000,000, which accounts shall be used for the payment of expenditures
incurred by the General Partner in connection with the business of the
Partnership and in which shall be deposited any and all receipts of the
Partnership. The General Partner may also temporarily invest the cash funds of
the Partnership in any manner it determines to be in the best interests of the
Partnership and the Partners. All amounts shall be and remain the property of
the


                                      -12-

<PAGE>   16

Partnership and shall be received, held and disbursed by the General Partner
for the purposes specified in this Agreement. There shall not be deposited in
any of such accounts any funds other than funds belonging to the Partnership,
and no other funds shall in any way be commingled with such funds.

         Section 7.4. Information Relating to the Partnership. Upon request,
the General Partner shall supply to the Limited Partners any information
requested regarding the Partnership or its activities. During ordinary business
hours, the Limited Partners and its authorized agents and representatives shall
have reasonable access to all books, records and materials in the Partnership's
offices regarding the Partnership or its activities.


                                  ARTICLE VIII

                    Dissolution, Liquidation and Termination

         Section 8.1. Dissolution. The Partnership shall be dissolved upon the
occurrence of any of the following:

         (a) The occurrence of December 31, 2025.

         (b) The sale, disposition or termination of all of the property then
owned by the Partnership.

         (c) The occurrence of an event of withdrawal from the Partnership by
the General Partner as provided for in the Partnership.

         (d) The consent in writing of the General Partner and all of the
Limited Partners.

         (e) The occurrence of any event which, under the Act, causes the
dissolution of a limited partnership.

         Section 8.2. Liquidation and Termination. Upon dissolution of the
Partnership, the General Partner or, if the withdrawal of the General Partner
caused the dissolution of the Partnership, a person selected by all of the
Limited Partners, shall act as liquidator or shall appoint one or more
liquidators who shall have full authority to wind up the affairs of the
Partnership and make final distribution as provided herein. The liquidator
shall continue to operate the Partnership properties with all of the power and
authority of the General Partner. The steps to be accomplished by the
liquidator are as follows:

         (a) As promptly as possible after dissolution and again after final
liquidation, the liquidator, if requested by any Partner, shall cause a proper
accounting to be made by the Partnership's independent accountants of the
Partnership's assets, liabilities and operations through


                                      -13-

<PAGE>   17

the last day of the month in which the dissolution occurs or the final
liquidation is completed, as appropriate.

         (b) The liquidator shall pay all of the debts and liabilities of the
Partnership (including all expenses incurred in liquidation) or otherwise make
adequate provision therefor (including without limitation the establishment of
a cash escrow fund for contingent liabilities in such amount and for such term
as the liquidator may reasonably determine). After making payment or provision
for all debts and liabilities of the Partnership, the Partners' Capital
Accounts shall then be adjusted by (i) assuming the sale of all remaining
assets of the Partnership for cash at their respective fair market values (as
determined by an appraiser selected by the liquidator) as of the date of
termination of the Partnership and (ii) debiting or crediting each Partner's
Capital Account with its respective share of the hypothetical gains or losses
resulting from such assumed sales in the same manner as each such Capital
Account would be debited or credited for gains or losses on actual sales of
such assets. The liquidator shall then by payment of cash or property (valued
as of the date of termination of the Partnership at its fair market value by
the appraiser selected in the manner provided above) distribute to the Partners
such amounts as are required to pay the positive balances of their respective
Capital Accounts. Such a distribution shall be in cash or in kind as determined
by the liquidator. Any distribution to the Partners in liquidation of the
Partnership shall be made by the latter of either the end of the taxable year
in which the liquidation occurs or on a date which is not more than ninety (90)
days after the date of such liquidation. For purposes of the preceding
sentence, the term "liquidation" shall have the same meaning as set forth in
Treasury Regulation Section 1.704-1(b)(2)(ii) as in effect at such time. Each
Partner shall have the right to designate another person to receive any
property which otherwise would be distributed in kind to that Partner pursuant
to this Section 8.2.

         (c) Except as expressly provided herein, the liquidator shall comply
with any applicable requirements of the Act and all other applicable laws
pertaining to the winding up of the affairs of the Partnership and the final
distribution of its assets.

         (d) Notwithstanding any provision in this Agreement to the contrary,
no Partner shall be obligated to restore a deficit balance in its Capital
Account at any time.

         The distribution of cash and/or property to the Partners in accordance
with the provisions of this Section 8.2 shall constitute a complete return to
the Partners of their Capital Contributions and a complete distribution to the
Partners of their interest in the Partnership and all Partnership property.

         Section 8.3. Reconstitution. Notwithstanding the foregoing or any
other provision of this Agreement, upon the occurrence of an event of
dissolution described in Section 8.1, the Partners may unanimously consent to
the reconstitution of the Partnership, and the business of the Partnership
shall be continued without being wound up as provided for in the Act.


                                      -14-

<PAGE>   18

                                   ARTICLE IX

                            Assignments of Interests

         Section 9.1. Assignment by Partners.

         (a) No Partner's interest in the Partnership shall be assigned,
mortgaged, pledged, subjected to a security interest or otherwise encumbered,
in whole or in part, without the prior written consent of all of the other
Partners, and any attempt by a Partner to assign its interest without such
consent shall be void ab initio.

         (b) Unless an assignee becomes a substituted Partner in accordance
with the provisions set forth below, such assignee shall not be entitled to any
of the rights granted to a Partner hereunder, other than the right to receive
allocations of income, gain, loss, deduction, credit and similar items and
distributions to which the assignor would otherwise be entitled, to the extent
such items are assigned.

         (c) An assignee of the interest of a Partner, or any portion thereof,
shall become a substituted Partner entitled to all of the rights of a Partner
if, and only if (i) the assignor gives the assignee such right, (ii) the
Partners consent to such substitution, the granting or denying of which shall
be in each Partner's sole discretion, and (iii) the assignee executes and
delivers such instruments, in form and substance satisfactory to the General
Partner, as the General Partner may deem necessary or desirable to effect such
substitution and to confirm the agreement of the assignee to be bound by all of
the terms and provisions of this Agreement. Upon the satisfaction of such
requirements, the General Partner shall concurrently (or as of such later date
as shall be provided for in any applicable written instruments furnished to the
General Partner) admit any such assignee as a substituted Partner of the
Partnership and reflect such admission and the date thereof in the records of
the Partnership.

         (d) The Partnership and the General Partner shall be entitled to treat
the record owner of any Partnership interest as the absolute owner thereof in
all respects and shall incur no liability for distributions of cash or other
property made in good faith to such owner until such time as a written
assignment of such interest that complies with the terms of this Agreement has
been received by the General Partner.


                                      -15-

<PAGE>   19

                                   ARTICLE X

                                 Miscellaneous

         Section 10.1. Notices. All notices, elections, demands or other
communications required or permitted to be made or given pursuant to this
Agreement shall be in writing and shall be considered as properly given or made
if given by (a) personal delivery, (b) prepaid telegram, telex or facsimile
(provided that such telegram, telex or facsimile is confirmed by expedited
delivery service), or (c) expedited delivery service with proof of delivery,
addressed to the respective addressee(s) specified in Section 1.5. Any Partner
may change its address by giving notice in writing to the other Partners of its
new address.

         Section 10.2. Amendment. This Agreement may be changed, modified or
amended only by an instrument in writing agreed upon by the General Partner and
the Limited Partner.

         Section 10.3. Partition. Each of the Partners hereby irrevocably
waives for the term of the Partnership any right that such Partner may have to
maintain any action for partition with respect to the Partnership property.

         Section 10.4. Entire Agreement. This Agreement constitutes the full
and complete agreement of the parties hereto with respect to the subject matter
hereof.

         Section 10.5. Severability. Every provision in this Agreement is
intended to be severable. If any term or provision hereof is illegal or invalid
for any reason whatsoever, such illegality or invalidity shall not affect the
validity of the remainder of this Agreement.

         Section 10.6. No Waiver. The failure of any Partner to insist upon
strict performance of a covenant hereunder or of any obligation hereunder,
irrespective of the length of time for which such failure continues, shall not
be a waiver of such Partner's right to demand strict compliance in the future.
No consent or waiver, express or implied, to or of any breach or default in the
performance of any obligation hereunder shall constitute a consent or waiver to
or of any other breach or default in the performance of the same or any other
obligation hereunder.

         Section 10.7. Applicable Law. This Agreement and the rights and
obligations of the parties hereunder shall be governed by and interpreted,
construed and enforced in accordance with the laws of the State of Delaware.

         Section 10.8. Meetings of the Partners. The General Partner may hold
meetings with the Limited Partners from time to time to inform and consult with
the Limited Partners concerning such matters as the General Partner deems
appropriate. Such meetings may be held by conference telephone and shall be
held at such times and places, as often and in such manner as shall be
determined by the General Partner. The General Partner shall give notice of the
time, place and topic of each such meeting at least ten business days prior
thereto. Notwithstanding the foregoing


                                      -16-

<PAGE>   20

provisions of this Section 10.8, the Limited Partners shall not be permitted to
take part in the business or control of the business of the Partnership; it
being the intention of the parties that the involvement of the Limited Partners
as contemplated in this Section 10.8 is for the purpose of informing the
Limited Partners with respect to various Partnership matters, explaining any
information furnished to the Limited Partners in connection therewith,
answering any question the Limited Partners may have with respect thereto and
receiving any ideas or suggestions the Limited Partners may have with respect
thereto; it being the further intention of the parties that the General Partner
shall have full and exclusive power and authority on behalf of the Partnership
to manage, control, administer and operate the property, business and affairs
of the Partnership in accordance with this Agreement.

         Section 10.9. Successors and Assigns. This Agreement shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and assigns; provided, however, that no Partner may sell, assign,
transfer or otherwise dispose of all or any part of its rights or interest in
the Partnership or under this Agreement except in accordance with Article IX.

         Section 10.10. Counterparts. This Agreement may be executed in one or
more counterparts, each of which shall be an original and all of which shall
constitute but one and the same document.


                                      -17-

<PAGE>   21

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the day and year first above written.

SHARING RATIO:                       GENERAL PARTNER:

1%                                   BRIGHAM, INC.


                                     By: /s/ Ben M. Brigham
                                        -----------------------------------
                                        Ben M. Brigham,
                                        President


                                     LIMITED PARTNERS:

68.5%                                BRIGHAM HOLDINGS I, LLC



                                     By:      /s/ Ben M. Brigham
                                        -----------------------------------
                                        Ben M. Brigham,
                                        President


30.5%                                BRIGHAM HOLDINGS II, LLC



                                     By       /s/ Ben M. Brigham
                                        --------------------------------
                                        Ben M. Brigham,
                                        President


                                     -18-

<PAGE>   1
                                                                EXHIBIT 10.36.1



                      FIRST AMENDMENT TO CREDIT AGREEMENT

        THIS FIRST AMENDMENT TO CREDIT AGREEMENT (this "Amendment") dated as of
August 20, 1998 is among: BRIGHAM OIL & GAS, L.P., a Delaware limited
partnership (the "Borrower"); each of the Lenders (as defined in the Credit
Agreement as hereinafter defined); and BANK OF MONTREAL, a Canadian bank (in
its individual capacity, "BMO"), as agent for the Lenders (in such capacity,
together with its successors in such capacity, the "Agent").

                                R E C I T A L S

        A. The Borrower, the Agents, and the Lenders have entered into that
certain Credit Agreement dated as of January 26, 1998 (the "Credit Agreement"),
pursuant to which the Lenders have agreed to make certain loans and extensions
of credit to the Borrower upon the terms and conditions as provided therein;
and

        B. The Borrower, the Agents, and the Lenders now desire to make certain
amendments to the Credit Agreement.

        NOW, THEREFORE, in consideration of the premises and other good and
valuable consideration and the mutual benefits, covenants and agreements herein
expressed, the parties hereto now agree as follows:

        Section 1. Certain Definitions. Unless otherwise defined herein, all
terms beginning with a capital letter which are defined in the Credit Agreement
shall have the same meanings herein as therein unless the context hereof
otherwise requires.

        Section 2. Amendments to Credit Agreement.

        (a) Additional Defined Terms. Section 1.02 of the Credit Agreement is
hereby amended and supplemented by adding the following new definitions, which
are read in their entirety as follows:

            "First Amendment" shall mean that certain First Amendment to Credit
        Agreement dated as of August 20, 1998 among the Borrower, the Lenders
        and the Agent.

            "Indenture" shall mean that certain Indenture dated as of August 20,
        1998 between Brigham Exploration, as the issuer of the Subordinated
        Debt, and Chase Bank of Texas, National Association, as the trustee.



<PAGE>   2

            "Securities Purchase Agreement" shall mean that certain Securities
        Purchase Agreement dated August 20, 1998 among Brigham Exploration,
        Enron Capital & Trade Resources Corp., and Joint Energy Development
        Investments II Limited Partnership, as agent for such purchasers
        regarding the Subordinated Debt.

            "Subordinated Debt" shall mean the Debt in the principal amount not
        to exceed $40,000,000 (plus up to an additional $10,000,000 for
        interest paid in kind pursuant to Section 9.02 of the Indenture) of
        Brigham Exploration incurred under the Indenture and expressly
        subordinated to the Indebtedness pursuant to the Subordination
        Agreement.

            "Subordination Agreement" shall mean that certain Intercreditor and
        Subordination Agreement dated as of August 20, 1998, and from time to
        time amended, among Enron Capital & Trade Resources Corp., Joint Energy
        Development Investments 11 Limited Partnership, and Bank of Montreal.

        (b) Section 2.03. Section 2.03 (a) is hereby deleted in its entirety,
and the following is substituted therefor:

            "(a) The Aggregate Commitments shall at all times be equal to
        $65,000,000 until January 31, 1999 after which date it shall be equal
        to the lesser of (i) the Aggregate Maximum Credit Amounts after
        adjustments resulting from reductions pursuant to Section 2.03(b)
        hereof or (ii) the Borrowing Base as determined from time to time."

        (c) Section 2.07. Section 2.07(c) of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

            "(c) Upon any redeterinination of the amount of the Borrowing Base
        in accordance with Section 2.08, if the redetermined Borrowing Base is
        less than the aggregate outstanding principal amount of the Loans plus
        the LC Exposure, then the Borrower shall within ninety (90) days (or
        such shorter period as hereinafter provided) of receipt of written
        notice thereof. (i) prepay the Loans in an aggregate principal amount
        equal to such excess, together with interest on the principal amount
        paid accrued to the date of such prepayment, provided however, that
        upon the first Borrowing Base determination such required prepayment
        shall be made on or before 30 days after such first Borrowing Base
        determination if such deficiency is ten percent (10%) or more of the
        Borrowing Base and (ii) if a Borrowing Base deficiency remains after
        prepaying all of the Loans because of LC Exposure, the Borrower shall
        pay to the Agent on behalf of the Lenders an amount equal to such
        Borrowing Base deficiency to be held as cash collateral as provided in
        Section 2.10(b) hereof."


                                      -2-
<PAGE>   3

        (d) Section 7.21. Section 7.21 of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

            "Restriction on Liens. Neither the Borrower nor any Subsidiary is a
        party to or subject to any agreement or arrangement (other than the
        Loan Documents, the documents described in Section 4.01 (a) through (d)
        of the Indenture, the Indenture, and any other documents permitted
        under Section 9.02(f)), or subject to any order, judgment, writ or
        decree, which either restricts or purports to restrict its ability to
        grant Liens to other Persons on or in respect of their respective
        assets or Properties."

        (e) Section 9.01. Section 9.01 of the Credit Agreement is hereby amended
by adding the following new clause (i):

            "(i) Guarantees of the Borrower and its Subsidiaries which have
        executed prior and senior guarantees of the Indebtedness in form and
        substance satisfactory to the Agent, of the Subordinated Debt, which
        Guarantees are subordinated and otherwise in form and substance
        satisfactory to the Agent consistent with the Subordination Agreement."

        (f) Section 9.02. Section 9.02 of the Credit Agreement is hereby
amended by adding the following new clause (f):

            "(f) Liens securing the Subordinated Debt or Guarantees permitted
        under Section 9.01(i) on Properties upon which prior Liens have been
        granted to secure the Indebtedness pursuant to documents in form and
        substance satisfactory to the Agent, provided such Liens (i) are
        subordinated and are otherwise in form. and substance satisfactory to
        the Agent consistent with the Subordination Agreement and (ii) do not
        directly or indirectly secure any Hedging Agreements."

        (g) Section 9.03. Section 9.03(j)(a) of the Credit Agreement is hereby
deleted in its entirety and the following is substituted therefor:

            "(a) to Brigham Exploration, Brigham, Inc., Brigham Holdings I, LLC
        and/or Brigham Holdings II, LLC

                 (i) to pay Federal or State taxes owing by any of them, payroll
            and payroll related taxes and other reasonable general and
            administrative expenses, or consisting of forgiveness of
            indebtedness, and

                 (ii) so long as no Borrowing Base deficiency exists or will be
            created thereby, no Event of Default or, with respect to Section
            5.2(q), (r), (s) or (u) of the Guaranty Agreement of Brigham
            Exploration, Default, is in existence or will be created thereby,
            to enable Brigham Exploration to pay accrued and unpaid interest
            owing on the "Notes" (as defined in the Indenture)."


                                      -3-
<PAGE>   4

        (h) Section 9.17. Section 9.17 of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

            "Section 9.17 Negative Pledge Agreements. The Borrower will not and
        will not permit any Subsidiary to create, incur, assume or suffer to
        exist any contract, agreement or understanding (other than the Loan
        Documents) which in any way prohibits or restricts (i) the granting,
        conveying, creation or imposition of any Lien on any of its Property
        (other than the Indenture, the documents described in Section 4.01(a)
        through (d) of the Indenture, and any other documents permitted under
        Section 9.02 (f)) or (ii) any Subsidiary from paying dividends or
        making any other distribution to the Borrower or which requires the
        consent of or notice to other Persons in connection with any of the
        foregoing."

        (i) Article IX. Article IX is hereby supplemented by adding the
following new section:

            "Section 9.19 Borrower as Operator. The Borrower will not and will
        not permit any of the Subsidiaries to voluntarily resign as operator of
        more than twenty-five percent (25%) of their currently operated Oil and
        Gas Properties unless the new operator is acceptable to the Majority
        Lenders."

        (j) Section 10.02 Section 10.02(a) of the Credit Agreement is hereby
deleted in its entirety, and the following is substituted therefor:

            "(a) At any time during the continuance of an Event of Default
        other than one referred to in clauses (f), (g) or (h) of Section 10.01
        or in clause (m) to the extent it relates to clauses (f), (g) or (h),
        the Agent, upon request of the Majority Lenders, shall, by notice to
        the Borrower, cancel the Commitments and/or declare the principal
        amount then outstanding of, and the accrued interest on, the Loans and
        all other amounts payable by the Borrower hereunder and under the Notes
        (including without limitation the payment of cash collateral to secure
        the LC Exposure as provided in Section 2.10(b) hereof) to be forthwith
        due and payable, whereupon such amounts shall be immediately due and
        payable without presentment, demand, protest, notice of intent to
        accelerate, notice of acceleration or other formalities of any kind,
        all of which are hereby expressly waived by the Borrower. Once an
        acceleration has been declared pursuant to the foregoing, no subsequent
        cure of the Event of Default shall negate such acceleration or the
        rights and remedies of the Agent and the Lenders with respect thereto
        without the express written consent of all of the Lenders."


                                      -4-
<PAGE>   5

        Section 3. Conditions Precedent. This Amendment shall become binding
upon the receipt by the Agent of the following documents and satisfaction of
the other conditions provided in this Section 3, each of which must be
satisfactory to the Agent in form and substance:

            (a) counterparts of this Amendment executed by the Borrower and the
        Lenders;

            (b) certificates of the Secretary or an Assistant Secretary of the
        Borrower and of the Guarantor setting forth for each of them (i) the
        resolutions of its board of directors with respect to the authorization
        to execute, deliver and perform this Amendment; (ii) the officer of
        such entity authorized to sign this Amendment, and (iii) the signature
        of such authorized officer of such entity;

            (c) evidence of the closing and concurrent funding of the
        Subordinated Debt pursuant to the Indenture and the equity issuance
        pursuant to the Securities Purchase Agreement;

            (d) a copy of the Securities Purchase Agreement and the Indenture
        and all documents executed with respect to the Subordinated Debt all in
        form and substance acceptable to the Lenders; and

            (e) A security agreement executed by Brigham Exploration in favor
        of the Agent granting a first-priority security interest in all of
        Brigham Exploration's right, title and interest to the ownership
        interests of Brigham Holdings I, LLC;

            (f) A security agreement executed by Brigham Inc. in favor of the
        Agent granting a first-priority security interest in all of Brigham
        Inc.'s right, title and interest in and to the ownership interests of
        Brigham Holdings II, LLC and the Borrower;

            (g) such other documents as Agent or its counsel may reasonably
        request.

Upon performance of such conditions satisfactory to the Agent, the Agent shall
be deemed to have consented, on behalf of the Lenders, to the matters described
in the preceding subsections (c), (d), (e) and (f).

        Section 4. Representations and Warranties. The Borrower hereby
reaffirms that as of the effective date of this Amendment, the representations
and warranties made by the Borrower in the Credit Agreement will be true and
correct as though made on and as of the effective date of this Amendment, and
further, the Borrower represents that no Default or Material Adverse Effect
shall have occurred and be continuing on such date.

        Section 5. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or


                                      -5-
<PAGE>   6

condition of the Credit Agreement or any of the other Loan Documents, or (b)
prejudice any right or rights which the Lenders may now have or may have in the
future under or in connection with the Credit Agreement or any of the other
Loan Documents. Except as expressly supplemented, amended or modified hereby,
the terms and provisions of the Credit Agreement or any other Loan Documents
are and shall remain in full force and effect. In the event of a conflict
between this Amendment and any of the foregoing documents, the terms of this
Amendment shall be controlling.

        Section 6. Governing Law. This Amendment and the rights and obligations
of the parties hereunder and under the Credit Agreement shall be construed in
accordance with and be governed by the laws of the State of Texas and the
United States of America.

        Section 7. Descriptive Headings. etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

        Section 8. Counterparts. This Amendment may be executed in any number of
counterparts and by different parties on separate counterparts and all of such
counterparts shall together constitute one and the same instrument.

        IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
executed as of the date first written above.

            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

        THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES
BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS
OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL
AGREEMENT BETWEEN THE PARTIES.


                                      -6-

<PAGE>   7

BORROWER:                              BRIGHAM OIL & GAS, L.P.

                                       By:  Brigham, Inc., its General Partner



                                            By:      /s/ Craig M. Fleming
                                                -------------------------------
                                                     Craig M. Fleming
                                                     Vice President & Chief
                                                     Financial Officer


LENDER AND AGENT:                      BANK OF MONTREAL



                                       By:    /s/ Robert Roberts
                                              ---------------------------------
                                       Name:  Robert L. Roberts
                                       Title: Director, U.S. Corporate Banking



                                      -7-

<PAGE>   1
                                                                EXHIBIT 10.37.2



                     SECOND AMENDMENT TO GUARANTY AGREEMENT

         THIS SECOND AMENDMENT TO GUARANTY AGREEMENT (this "Amendment") dated
as of August 20,1998 is between BRIGHAM EXPLORATION COMPANY, a Delaware
corporation (the "Guarantor") and BANK OF MONTREAL, as agent ("Agent") for the
lenders (the "Lenders") that are or become parties to the Credit Agreement
defined below.

                                    RECITALS

         A. Brigham Oil & Gas, L.P., a Delaware limited partnership (the
"Borrower"), the Agent and the Lenders previously entered into that certain
Credit Agreement dated as of January 26, 1998 as amended by First Amendment to
Credit Agreement of even date herewith (as amended, the "Credit Agreement"),
pursuant to which the Lenders agreed to make certain loans and extensions of
credit to the Borrower.

         B. Pursuant to the terns and conditions stated in the Credit
Agreement, Guarantor executed that certain Guaranty Agreement of even date
therewith by Guarantor, as amended by First Amendment to Guaranty Agreement
dated as of March 30, 1998 (such Guaranty Agreement as amended called the
"Guaranty Agreement").

         C. Guarantor and the Agent now desire to amend certain provisions of
the Guaranty Agreement.

         NOW THEREFORE, in consideration of the mutual covenants and agreements
herein contained, the Guarantor, the Agent and the Lenders hereby agree that
the Guaranty Agreement shall be amended as follows:

         Section 1. Certain Definitions. As used in this Amendment, the terms
"Agent", "Amendment", "Borrower", "Credit Agreement", "Guarantor" and "Lenders"
shall have the meanings indicated above; and unless otherwise defined herein,
all terms beginning with a capital letter which are defined in the Guaranty
Agreement shall have the same meanings herein as therein unless the context
hereof otherwise requires.

         Section 2.    Amendments to Guaranty Agreement.

                (a) Additional Defined Terms. Section 1.02 of the Guaranty
          Agreement is hereby amended and supplemented by adding the following
          new definitions, which are read in their entirety as follows:

<PAGE>   2

          "Indenture" shall mean that certain Indenture dated as of August 20,
     1998, between the Guarantor, as issuer of the Subordinated Debt, and Chase
     Bank of Texas, National Association, as trustee.

          "Securities Purchase Agreement" shall mean that certain Securities
     Purchase Agreement dated as of August 20, 1998 among the Guarantor, Enron
     Capital & Trade Resources Corp., and Joint Energy Development Investments
     II Limited Partnership regarding $50,000,000 Senior Subordinated Secured
     Notes due 2003.

          "Subordination Agreement" shall mean that certain Intercreditor and
     Subordination Agreement dated August 20, 1998, as from time to time
     amended, among Enron Capital and Trade Resources Corp., Joint Energy
     Development Investments II Limited Partnership, and Bank of Montreal.

          "Subordinated Debt" shall mean the Debt in the principal amount not
     to exceed $40,000,000 (plus up to an additional $10,000,000 for interest
     paid in kind pursuant to Section 9.02 of the Indenture) of Guarantor
     incurred under the Indenture and expressly subordinated to the
     Indebtedness pursuant to the Subordination Agreement.

          "Subordinated Guarantees" shall mean the Guarantees permitted under
     Section 5.2(a)(7).

     (b) Section 3.1(m) is hereby amended by adding the following phrase at the
end thereof. ", except for liens and security interests securing the
Liabilities or as permitted under Section 5.2(b)(4)."

     (c) Section 5.2. Section 5.2 is hereby amended as follows:

         (i) Section 5.2(a) is amended by adding the following new clauses (6)
     and (7):

         "(6) the Subordinated Debt."

         "(7) Guarantees by Subsidiaries of the Guarantor (which also are
     obligated upon or otherwise guarantee the Liabilities pursuant to
     documents in form and substance satisfactory to the Agent) which guarantee
     the Subordinated Debt permitted under Section 5.2(a)(6) above, which
     Guarantees are subordinated consistent with the Subordination Agreement
     and otherwise are in form and substance satisfactory to the Agent
     consistent with the Subordination Agreement."

     (ii) Section 5.2(b) is amended by adding the following new clause (4):

          "(4) Liens securing the Subordinated Debt or the Subordinated
     Guarantees on Properties upon which prior Liens have been granted to
     secure the Liabilities pursuant to documents in form and substance
     satisfactory to the Agent, provided that such Liens (i) are subordinated
     and otherwise are in form and substance satisfactory to the Agent
     consistent with


                                      -2-
<PAGE>   3

     the Subordination Agreement and (ii) do not directly or indirectly secure
     any Hedging Agreements."

          (iii) Section 5.2(o) is hereby amended by deleting the parenthetical
     clause in the third line and inserting the following in lieu thereof:

          "(other than the Loan Documents, the Indenture and the documents
          described in Section 4.01(a) through (d) of the Indenture, and any
          other documents establishing Liens permitted under Section
          5.2(b)(4))"

          (iv) Section 5.2(s) is hereby deleted in its entirety, and the
     following is substituted therefor:

               "(s) Interest Coverage Ratio. The Guarantor will not permit its
          Interest Coverage Ratio as of the end of any fiscal quarter of the
          Guarantor (calculated quarterly at the end of each fiscal quarter) to
          be less than the following ratios during the following periods.
          Interest Coverage Ratio shall mean the ratio of (i) EBITDA to (ii)
          interest payments accruing (excluding amortizations of fee expense
          incurred in connection with this Agreement and the closing of the
          Indenture and Securities Purchase Agreement and any capitalized lease
          expense included in interest) during the following periods (for
          purposes hereof interest on the Subordinated Debt shall be deemed
          cash payments, calculated at the cash interest rate applicable to the
          Subordinated Debt, whether paid in cash or in kind, except that if a
          payment of interest is made in kind on any interest payment date
          applicable to the Subordinated Debt, an amount equal to the cash
          payment of interest that would have been due on such interest payment
          date if payment in kind had not been made shall be deemed subtracted
          from interest expense for the applicable test period ending on the
          last day of the fiscal quarter preceding such interest payment date
          (but not for any other test period):

               (i)   not less than 1.25 to 1 for the three (3) month period
                     ending December 31, 1998;

               (ii)  not less than 1.75 to I for the six (6) month period ending
                     March 31, 1999;

               (iii) not less than 2 to 1 for the nine (9) month period ending
                     June 30, 1999;

               (iv)  not less than 2.25 to 1 for the twelve (12) month period
                     ending September 30, 1999;

               (v)   not less than 2.75 to I for the twelve (12) month period
                     ending December 31, 1999; and


                                      -3-
<PAGE>   4

                    (vi)  thereafter, not less than 3 to 1 for the twelve (12)
                          month periods ending at the end of each fiscal quarter
                          of the Guarantor."

           (v) Section 5.2 is amended by adding the following new clauses (t)
     and (u):

                    "(t) Securities Purchase Agreement and Indenture. The
               Guarantor will not agree to any amendment or modification to the
               Securities Purchase Agreement or the Indenture without the
               express written consent of the Agent."

                    "(u) Payments on Subordinated Debt. No prepayments of
               principal will be made on the Subordinated Debt without prior
               written consent of the Lenders. No payments of interest will be
               made in cash on the Subordinated Debt if (i) an Event of Default
               or, with respect to Section 5.2(q), (r) or (s), Default, is in
               existence or would be created thereby; (ii) a Borrowing Base
               deficiency is in existence under the Credit Agreement; (iii)
               such payment will be in contravention of the Subordination
               Agreement or (iv) the Interest Coverage Ratio is less than the
               following ratios during the following periods:

                    (i)   1.5 to 1 for the twelve (12) month period ending
                          December 31, 1998;

                    (ii)  1.75 to 1 for the twelve (12) month periods ending
                          March 31, 1999 and June 30, 1999;

                    (iii) 2.5 to 1 for the twelve (12) month period ending
                          September 30, 1999;

                    (iv)  2.75 to 1 for the twelve month period ending December
                          30, 1999; and

                    (v)   thereafter, 3 to 1 for the twelve (12) month periods
                          ending at the end of each fiscal quarter of the
                          Guarantor."

         Section 4. Representations and Warranties. Guarantor hereby reaffirms
that as of the effective date of this Amendment, the representations and
warranties made by the Guarantor in Article III of the Guaranty Agreement will
be true and correct as though made on and as of the effective date of this
Amendment.

         Section 5. Ratification. Guarantor hereby expressly ratifies and
affirms its obligations under the Guaranty Agreement as amended by this
Amendment and agrees that the Guaranty Agreement as amended by this Amendment
remains in full force and effect.


                                      -4-
<PAGE>   5

         Section 6. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Credit Agreement shall be
construed in accordance with and be governed by the laws of the State of Texas
and the United States of America.

         Section 7. Descriptive Headings. etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 8. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.


                                      -5-
<PAGE>   6

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly
executed and delivered and effective as of the date first above written.


            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

         THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES
BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS
OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NOT UNWRITTEN ORAL
AGREEMENT BETWEEN THE PARTIES.


GUARANTOR:                       BRIGHAM EXPLORATION COMPANY



                                 By:            /s/ Craig M. Fleming
                                     -------------------------------------------
                                 Name:  Craig M. Fleming
                                 Title: Vice President & Chief Financial Officer


AGENT AND LENDER:                BANK OF MONTREAL



                                 By:           /s/ Robert Roberts
                                     -------------------------------------------
                                 Name:  Robert L. Roberts
                                 Title: Director, U.S. Corporate Banking



                                      -6-

<PAGE>   1
                                                                   EXHIBIT 10.38

 


===============================================================================


                         SECURITIES PURCHASE AGREEMENT

                                    BETWEEN

                          BRIGHAM EXPLORATION COMPANY

                                      AND

                     ENRON CAPITAL & TRADE RESOURCES CORP.
                                      AND
                    JOINT ENERGY DEVELOPMENT INVESTMENTS II
                              LIMITED PARTNERSHIP

                          DATED AS OF AUGUST 20, 1998



            $50,000,000 SENIOR SUBORDINATED SECURED NOTES DUE 2003,

            Warrants to Purchase 1,000,000 Shares of Common Stock;

                                      AND

                ACQUISITION OF 1,052,632 SHARES OF COMMON STOCK

===============================================================================
<PAGE>   2
 
                                 TABLE OF CONTENTS
<TABLE>
<S>                 <C>                                                     <C>
ARTICLE I
     DEFINITIONS..........................................................    1
     Section 1.01    Definitions..........................................    1
     Section 1.02    Accounting Procedures and Interpretation.............   10
 
ARTICLE II
     ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS.........................   10
     Section 2.01    Issuance of Securities...............................   10
     Section 2.02    The Closing; Funding Date............................   11
     Section 2.03    Delivery.............................................   11
     Section 2.04    Payment..............................................   11
     Section 2.05    Tax Matters..........................................   11
     Section 2.06    Rights of Purchasers.................................   12
 
ARTICLE III
     SECURITY FOR THE OBLIGATIONS.........................................   12
     Section 3.01    Security.............................................   12
 
ARTICLE IV
     REPRESENTATIONS AND WARRANTIES OF THE SELLER.........................   12
     Section 4.01    Corporate Existence..................................   12
     Section 4.02    Financial Condition..................................   13
     Section 4.03    Litigation...........................................   13
     Section 4.04    No Breach............................................   13
     Section 4.05    Authority............................................   14
     Section 4.06    Approvals............................................   14
     Section 4.07    Use of Loans.........................................   14
     Section 4.08    ERISA................................................   14
     Section 4.09    Taxes................................................   15
     Section 4.10    Titles, etc..........................................   15
     Section 4.11    No Material Misstatements............................   16
     Section 4.12    Investment Company Act...............................   17
     Section 4.13    Public Utility Holding Company Act...................   17
     Section 4.14    Subsidiaries.........................................   17
     Section 4.15    Location of Business and Offices.....................   17
     Section 4.16    Defaults.............................................   17
     Section 4.17    Environmental Matters................................   17
     Section 4.18    Compliance with the Law..............................   18
     Section 4.19    Insurance............................................   19
     Section 4.20    Hedging Agreements...................................   19
     Section 4.21    Restriction on Liens.................................   20
</TABLE> 

                                      -i-
<PAGE>   3
 
<TABLE>
<S>                  <C>                                                     <C>
     Section 4.22    Material Agreements..................................   20
     Section 4.23    Gas Imbalances.......................................   20
     Section 4.24    Capitalization.......................................   20
     Section 4.25    Acquired Shares......................................   20
     Section 4.26    Warrant Shares.......................................   21
     Section 4.27    No Restrictions......................................   21
     Section 4.28    Certain Fees.........................................   21
 
ARTICLE V
     REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS.....................   21
     Section 5.01    Investment...........................................   21
     Section 5.02    Nature of Purchasers.................................   22
     Section 5.03    Receipt of Information; Authorization................   22
 
ARTICLE VI
     CONDITIONS PRECEDENT TO FUNDING......................................   22
     Section 6.01    Conditions Precedent to Obligations of the Purchasers   22
     Section 6.02    Conditions Precedent to Obligations of the Seller....   25
     Section 6.03    Conditions Precedent to the Obligations of
                     Purchasers and Seller................................   26
 
ARTICLE VII
     AFFIRMATIVE COVENANTS................................................   26
     Section 7.01    Warrants.............................................   26
     Section 7.02    Hart-Scott -Rodino Compliance........................   26
     Section 7.03    Board Representation.................................   27
     Section 7.04    Common Stock; Dividends; Voting Rights...............   27
 
ARTICLE VIII
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE IX
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE X
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE XI
     [OMITTED BY THE PARTIES HERETO]......................................   27
 
ARTICLE XII
     MISCELLANEOUS........................................................   28
     Section 12.01   INTERPRETATION AND SURVIVAL OF PROVISIONS............   28
     Section 12.02   COSTS, EXPENSES AND TAXES............................   28
     Section 12.03   NO WAIVER; MODIFICATIONS IN WRITING..................   30
</TABLE>


                                      -ii-
<PAGE>   4


<TABLE>
<S>                  <C>                                                     <C>
     Section 12.04   BINDING EFFECT; ASSIGNMENT...........................   30
     Section 12.05   REPLACEMENT SECURITIES...............................   30
     Section 12.06   COMMUNICATIONS.......................................   31
     Section 12.07   GOVERNING LAW........................................   31
     Section 12.08   ARBITRATION..........................................   31
     Section 12.09   EXECUTION IN COUNTERPARTS............................   32 

Exhibits:

Exhibit A  -  Form of Warrants


Schedules:

Schedule 4.02  -  Liabilities
Schedule 4.03  -  Litigation
Schedule 4.09  -  Taxes
Schedule 4.10  -  Titles, Etc.
Schedule 4.14  -  Subsidiaries and Addresses
Schedule 4.19  -  Insurance
Schedule 4.20  -  Hedging Agreements
Schedule 4.22  -  Material Agreements
Schedule 4.23  -  Gas Imbalances
Schedule 4.24  -  Voting Agreements; Registration Rights
</TABLE>

                                     -iii-
<PAGE>   5
 
                         SECURITIES PURCHASE AGREEMENT


     SECURITIES PURCHASE AGREEMENT, dated as of August 20, 1998 (this
"Agreement"), among BRIGHAM EXPLORATION COMPANY, a Delaware corporation, ENRON
CAPITAL & TRADE RESOURCES CORP., a Delaware corporation ("ECT") and JOINT ENERGY
DEVELOPMENT INVESTMENTS II LIMITED PARTNERSHIP, a Delaware limited partnership
("JEDI-II").

     In consideration of the mutual covenants and agreements set forth herein
and for good and valuable consideration, the receipt of which is hereby
acknowledged, the parties agree as follows:

                                   ARTICLE I
                                  DEFINITIONS

     Section 1.01  DEFINITIONS.  As used in this Agreement, and unless the
context requires a different meaning, the following terms have the meanings
indicated:

     "Acquired Shares" means 1,052,632 shares of Common Stock acquired by the
Purchasers on the Funding Date in accordance with Section 2.01 and any
additional shares of Common Stock of the Seller issued to the Purchasers after
the Funding Date in accordance with Section 2.01(ii).

     "Affiliate" of any Person shall mean (i) any Person directly or indirectly
controlled by, controlling or under common control with such first Person, (ii)
any director or officer of such first Person or of any Person referred to in
clause (i) above and (iii) if any Person in clause (i) above is an individual,
any member of the immediate family (including parents, spouse and children) of
such individual and any trust whose principal beneficiary is such individual or
one or more members of such immediate family and any Person who is controlled by
any such member or trust.  For purposes of this definition, any Person which is
the sole general partner of a limited partnership, or which owns directly or
indirectly 20% or more of the securities having ordinary voting power for the
election of directors or other governing body of a corporation or 20% or more of
the partnership or other ownership interests of any other Person (other than as
a limited partner of such other Person) will be deemed to "control" (including,
with its correlative meanings, "CONTROLLED BY" and "UNDER COMMON CONTROL WITH")
such corporation or other Person.

     "Agent" is defined in the Indenture.

     "Average Share Price" means $9.50.

     "Basic Documents" means, collectively, this Agreement, the other Loan
Documents, the Structuring Fee Agreement and the Equity Documents.

     "Board of Directors" means the Board of Directors of the Seller.

     "BOG" means Brigham Oil & Gas, L.P., a Delaware limited partnership.

                                      -1-
<PAGE>   6
 
     "Business Day" means any day other than a Saturday, Sunday, or a legal
holiday for commercial banks in Houston, Texas, or New York, New York.

     "Business Opportunities Agreement" means the Corporate Opportunities
Shareholders' Agreement dated as of even date herewith between the Purchasers
and the Seller.

     "Capital Stock" of any Person means any and all shares, interests,
participations, or other equivalents (however designated) of, or rights,
warrants, or options to purchase, corporate stock, partnership interests, or any
other equity interest (however designated) of or in such Person.

     "Closing" has the meaning provided therefor in Section 2.02.

     "Closing Date" means the date upon which the Closing occurs as provided in
Section 2.02.

     "Code" means the Internal Revenue Code of 1986, as amended from time to
time, and any successor statute.

     "Collateral" is defined in the Indenture.

     "Collateral Documents" is defined in the Indenture.

     "Commission" means the United States Securities and Exchange Commission.

     "Common Stock" means the common stock, par value $0.01 per share, of the
Seller or such other class of securities as shall, after the date of this
Agreement, constitute the common equity of the Seller.

     "Consolidated Subsidiaries" shall mean each Subsidiary of the Seller
(whether now existing or hereafter created or acquired) the financial statements
of which shall be (or should have been) consolidated with the financial
statements of the Seller in accordance with GAAP.

     "Debt" means, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or evidenced
by bonds, debentures, notes or other similar instruments (including principal
and past due issuance fees); (ii) all obligations of such Person (whether
contingent or otherwise) in respect of bankers' acceptances, letters of credit,
surety or other bonds and similar instruments; (iii) all obligations of such
Person to pay the deferred purchase price of Property or services (other than
for borrowed money) excluding Trade Payables; (iv) all obligations under leases
which shall have been, or should have been, in accordance with GAAP, recorded as
capital leases in respect of which such Person is liable (whether contingent or
otherwise); (v) all obligations under leases (other than capital leases and oil
and gas leases) which require such Person or its Affiliate to make payments
exceeding $100,000 (or $500,000 in the aggregate) over the term of such lease,
including payments at termination, which are substantially equal to at least
eighty percent (80%) of the purchase price of the Property subject to such lease
plus interest at an imputed rate of interest; (vi) all Debt (as described in the
other clauses of this definition) of others secured by a Lien on any asset of
such Person, whether or not such Debt is assumed by such Person; (vii) all Debt
(as described in the other clauses of this

                                      -2-
<PAGE>   7
 
definition) of others guaranteed by such Person or in which such Person
otherwise assures a creditor against loss of the Debt of others; (viii) all
obligations or undertakings of such Person to maintain or cause to be maintained
the financial position or covenants of others including without limitation
agreements expressed as an agreement to purchase the Debt or Property of others
or otherwise; (ix) obligations to deliver Hydrocarbons in consideration of
advance payments; (x) obligations to pay for goods or services whether or not
such goods or services are actually received or utilized by such Person; (xi)
any capital stock of such Person in which such Person has a mandatory obligation
to redeem such stock; (xii) any Debt of a Special Entity for which such Person
is liable either by agreement or because of a Governmental Requirement; (xiii)
the undischarged balance of any production payment created by such Person or for
the creation of which such Person directly or indirectly received payment; and
(xiv) all obligations of such Person under Hedging Agreements, provided that
"Debt" shall not include (a) interest and fees (other than past due issuance
fees) on any of the foregoing, (b) obligations associated with bid, performance,
surety or appeal bonds (including those required by Governmental Requirements in
connection with Oil and Gas Properties), (c) gas balancing obligations (whether
volumetric or dollar denominated), (d) intercompany obligations among the Seller
and its Consolidated Subsidiaries, (e) indemnity obligations which have not
matured into fixed liabilities, and (f) purchase price adjustments and similar
post-closing obligations (but excluding the deferred payment of any purchase
price) incurred in connection with the permitted purchase and sale of Property
or stock, and which is to be determined and payable no later than 180 days
following the closing of such purchase and sale.

     "Designee" shall have the meaning set forth in Section 7.03.

     "Effective Date" means the date this Agreement is executed by all the
parties hereto.

     "Employee Plan" means any employee benefit plan, program or policy with
respect to which the Seller or any ERISA Affiliate may have any liability or any
obligation to contribute, other than a Plan or a Multiemployer Plan.

     "Environmental Laws" means any and all Governmental Requirements pertaining
to the environment in effect in any and all jurisdictions in which the Seller or
any Subsidiary is conducting or at any time has conducted business, or where any
Property of the Seller or any Subsidiary is located, including, without
limitation, the Oil Pollution Act of 1990 ("OPA"), as amended, the Clean Air
Act, as amended, the Comprehensive Environmental, Response, Compensation, and
Liability Act of 1980 ("CERCLA"), as amended, the Federal Water Pollution
Control Act, as amended, the Occupational Safety and Health Act of 1970, as
amended, the Resource Conservation and Recovery Act of 1976 ("RCRA"), as
amended, the Safe Drinking Water Act, as amended, the Toxic Substances Control
Act, as amended, the Superfund Amendments and Reauthorization Act of 1986, as
amended, the Hazardous Materials Transportation Act, as amended, and other
environmental conservation or protection laws.  As used in the provisions hereof
relating to Environmental Laws, the term "oil" has the meaning specified in OPA;
the terms "hazardous substance" and "release" (or "threatened release") have the
meanings specified in CERCLA, and the terms "solid waste" and

                                      -3-
<PAGE>   8
 
"disposal" (or "disposed") have the meanings specified in RCRA; provided,
however, that (i) in the event either OPA, CERCLA or RCRA is amended so as to
broaden the meaning of any term defined thereby, such broader meaning shall
apply subsequent to the effective date of such amendment, and (ii) to the extent
the laws of the state in which any Property of the Seller or any Subsidiary is
located establish a meaning for "oil," "hazardous substance," "release," "solid
waste" or "disposal" which is broader than that specified in either OPA, CERCLA
or RCRA, such broader meaning shall apply.

     "Equity Documents" means the Warrants, the stock certificates representing
the Acquired Shares, the Registration Rights Agreement and the Business
Opportunities Agreement.

     "ERISA" means the Employee Retirement Income Security Act of 1974, as
amended from time to time and any successor statute.

     "ERISA Affiliate" shall mean each trade or business (whether or not
incorporated) which together with the Seller or any Subsidiary of the Seller
would be deemed to be a "single employer" within the meaning of Section
4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section 414 of the
Code.

     "Excepted Liens" means (i) Liens for taxes, assessments or other
governmental charges or levies not yet due or which are being contested in good
faith by appropriate action and for which adequate reserves have been maintained
in accordance with GAAP; (ii) Liens in connection with workman's compensation,
unemployment insurance or other social security, old age pension or public
liability obligations not yet due or which are being contested in good faith by
appropriate action and for which adequate reserves have been maintained in
accordance with GAAP; (iii) operators', vendors', carriers', warehousemen's,
repairmen's, mechanics', workmen's, materialmen's, construction or other like
Liens arising by operation of law in the ordinary course of business or incident
to the exploration, development, operation and maintenance of Oil and Gas
Properties or customary landlord's liens, each of which is in respect of
obligations that have not been outstanding more than 90 days or which are being
contested in good faith by appropriate proceedings and for which adequate
reserves have been maintained in accordance with GAAP; (iv) any Liens reserved
in leases or farmout agreements for rent or royalties and for compliance with
the terms of the farmout agreements or leases in the case of leasehold estates,
to the extent that any such Lien referred to in this clause does not materially
impair the use of the Property covered by such Lien for the purposes for which
such Property is held or materially impair the value of the Property subject
thereto; (v) encumbrances (other than to secure the payment of borrowed money or
the deferred purchase price of Property or services), easements, restrictions,
servitudes, permits, conditions, covenants, exceptions or reservations in any
rights of way or other Property for the purpose of roads, pipelines,
transmission lines, transportation lines, distribution lines for the removal of
gas, oil, coal or other minerals or timber, and other like purposes, or for the
joint or common use of real estate, rights of way, facilities and equipment, and
defects, irregularities, zoning restrictions and deficiencies in title of any
rights of way or other Property which in the aggregate do not materially impair
the use of such rights of way or other Property for the purposes for which such
rights of way and other Property are held or materially impair the value of such
Property subject thereto; (vi) deposits of cash or securities to secure the
performance of bids, trade, contracts, leases, statutory

                                      -4-
<PAGE>   9
 
obligations and other obligations of a like nature incurred in the ordinary
course of business; and (vii) Liens permitted by the Loan Documents.

     "Financial Statements" means the financial statement or statements
described or referred to in Section 4.02.

     "Financing Agreement" means an agreement between the Seller and ECT
Securities Corp. pursuant to which the Seller grants to ECT Securities Corp. the
right and option to participate during the three years following the Closing
Date for up to 20% on any public or private (e.g. 144A) high yield debt offering
by the Seller with gross proceeds in excess of $50,000,000.

  "Funding Date" means the first Business Day following the date all of the
conditions precedent to funding in Article VI have been satisfied.

     "GAAP" means generally accepted accounting principles in the United States
of America in effect from time to time.

     "Governmental Authority" shall include the country, the state, county, city
and political subdivisions in which any Person or such Person's Property is
located or which exercises valid jurisdiction over any such Person or such
Person's Property, and any court, agency, department, commission, board, bureau
or instrumentality of any of them including monetary authorities which exercises
valid jurisdiction over any such Person or such Person's Property.  Unless
otherwise specified, all references to Governmental Authority herein shall mean
a Governmental Authority having jurisdiction over, where applicable, the Seller,
the Subsidiaries or any of their Property or any Purchaser.

     "Government Requirement" means any law, statute, code, ordinance, order,
determination, rule, regulation, judgment, decree, injunction, franchise,
permit, certificate, license, authorization or other directive or requirement
(in the case of banking regulatory authorities whether or not having the force
of law), including without limitation, Environmental Laws, energy regulations
and occupational, safety and health standards or controls of any Governmental
Authority.

     "Guarantors" means Brigham, Inc., Brigham Holdings I, LLC, Brigham Holdings
II, LLC, BOG and any other Person who becomes party to a Guaranty Agreement
pursuant to the terms of the Loan Documents.

     "Guaranty Agreements" means the agreements executed by the Guarantors in
form and substance satisfactory to the Trustee and the Purchasers guarantying,
unconditionally, payment of the Obligations, as the same may be amended,
modified or supplemented from time to time.

     "Hedging Agreements" means any commodity, interest rate or currency swap,
cap, floor, collar, forward agreement or other exchange or protection agreements
or any option with respect to any such transaction.

                                      -5-
<PAGE>   10
 
     "Hydrocarbon Interests" means all rights, titles, interests and estates now
or hereafter acquired in and to oil and gas leases, oil, gas and mineral leases,
or other liquid or gaseous hydrocarbon leases, mineral fee interests, overriding
royalty and royalty interests, net profit interests and production payment
interests, including any reserved or residual interests of whatever nature.

     "Hydrocarbons" means oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.

     "Indenture" means that certain Indenture dated as of August 20, 1998,
executed by Seller.

     "Investment Unit" has the meaning provided therefor in Section 2.05 of this
Agreement.

     "Lien" means any interest in Property securing an obligation owed to, or a
claim by, a Person other than the owner of the Property, whether such interest
is based on the common law, statute or contract, and whether such obligation or
claim is fixed or contingent, and including but not limited to (i) the lien or
security interest arising from a mortgage, encumbrance, pledge, security
agreement, conditional sale or trust receipt or a lease, consignment or bailment
for security purposes or (ii) production payments and the like payable out of
Oil and Gas Properties.  The term "Lien" shall include reservations, exceptions,
encroachments, easements, rights of way, covenants, conditions, restrictions,
leases and other title exceptions and encumbrances affecting Property.  For the
purpose of this Agreement, a Person shall be deemed to be the owner of any
Property which it has acquired or holds subject to a conditional sale agreement,
or leases under a financing lease or other arrangement pursuant to which title
to the Property has been retained by or vested in some other Person in a
transaction intended to create a financing.

     "Loan Documents" means this Agreement, the Indenture, the Notes, the
Structuring Fee Agreement, the Collateral Documents, and any and all other
agreements or instruments now or hereafter executed and delivered by the Seller
or any Subsidiary or Affiliate of the Seller (other than the Equity Documents
and any assignments, participation or similar agreements between any Purchaser
and any other lender or creditor with respect to any Obligations pursuant to
this Agreement) in connection with, or as security for the payment or
performance of, the Notes or this Agreement, as such agreements may be amended,
supplemented or restated from time to time.

     "Majority Purchasers" means, at any time, the Purchasers holding more than
50% of the  Warrants.

     "Material Adverse Effect" means any material and adverse effect on (i) the
assets, liabilities, financial condition, business, operations or affairs of the
Seller and its Subsidiaries taken as a whole, from those reflected in the
Financial Statements, or from the facts represented or warranted in any Loan
Document at the time made, or (ii) the ability of the Seller and its
Subsidiaries taken as a whole to carry out their business as of the Closing Date
or as proposed as of the Closing Date to be conducted or to meet their
obligations under the Loan Documents on a timely basis.

                                      -6-
<PAGE>   11
 
     "Mortgage" is defined in the Indenture.

     "Mortgaged Property" means the Property owned by the Seller and its
Subsidiaries which is subject to the Liens existing and to exist under the Loan
Documents.

     "Multiemployer Plan" means a Plan defined as such in Section 3(37) or
4001(a)(3) of ERISA.

     "NASDAQ" means  the National Association of Securities Dealers Automated
Quotation System.

     "Notes" means the Senior Subordinated Secured Notes issued pursuant to
Section 2.03 of this Agreement and the Indenture, in the aggregate face amount
of $50,000,000, dated as of the date hereof, made by the Seller and initially
payable to the order of the Purchasers in their respective Participations.

     "Noteholders" means, from time to time, the holders of the Notes.

     "Obligations" means any and all amounts, liabilities and obligations owing
from time to time by Seller to the Agent or the Noteholders, pursuant to any of
the Loan Documents and all renewals, extensions and/or rearrangements thereof,
whether such amounts, liabilities or obligations be liquidated or unliquidated,
now existing or hereafter arising, absolute or contingent.

     "Oil and Gas Properties" means Hydrocarbon Interests; the Properties now or
hereafter pooled or unitized with Hydrocarbon Interests; all presently existing
or future unitization, pooling agreements and declarations of pooled units and
the units created thereby (including without limitation all units created under
orders, regulations and rules of any Governmental Authority) which may affect
all or any portion of the Hydrocarbon Interests; all operating agreements,
contracts and other agreements which relate to any of the Hydrocarbon Interests
or the production, sale, purchase, exchange or processing of Hydrocarbons from
or attributable to such Hydrocarbon Interests; all Hydrocarbons in and under and
which may be produced and saved or attributable to the Hydrocarbon Interests,
including all oil in tanks, the lands covered thereby and all rents, issues,
profits, proceeds, products, revenues and other incomes from or attributable to
the Hydrocarbon Interests; all tenements, hereditaments, appurtenances and
Properties in any manner appertaining, belonging, affixed or incidental to the
Hydrocarbon Interests; and all Properties, rights, titles, interests and estates
described or referred to above, including any and all Property, real or
personal, now owned or hereafter acquired and situated upon, used, held for use
or useful in connection with the operating, working or development of any of
such Hydrocarbon Interests or Property (excluding drilling rights, automotive
equipment or other personal property which may be on such premises for the
purpose of drilling a well or other similar temporary use) and including any and
all oil wells, gas wells, injection wells or other wells, buildings, structures,
fuel separators, liquid extraction plants, plant compressors, pumps, pumping
units, field gathering systems, tanks and tank batteries, fixtures, valves,
fittings, machinery and parts, engines, boilers, meters, apparatus, appliances,
tools, implements, cables, wires, towers, casing, tubing and rods, similar
equipment, surface leases, rights-

                                      -7-
<PAGE>   12
 
of-way, easements and servitudes together with all additions, substitutions,
replacements, accessions and attachments to any and all of the foregoing.

     "Participation" means, for each Purchaser, such Purchaser's proportionate
share of the Obligations and the Warrants.  As of the Effective Date, ECT's
Participation shall be 25% and JEDI-II's Participation shall be 75%.

     "PBGC" means the Pension Benefit Guaranty Corporation or any entity
succeeding to any or all of its functions.

     "Person" means any individual, corporation, company, voluntary association,
partnership, joint venture, trust, limited liability company, unincorporated
organization or government or any agency, instrumentality or political
subdivision thereof, or any other form of entity.

     "Plan" means any employee pension benefit plan, as defined in Section 3(2)
of ERISA, which (i) is currently or hereafter sponsored, maintained or
contributed to by the Seller, any Subsidiary or an ERISA Affiliate or (ii) was
at any time during the preceding six calendar years sponsored, maintained or
contributed to, by the Seller, any Subsidiary or an ERISA Affiliate.

     "Property" means any interest in any kind of property or asset, whether
real, personal or mixed, or tangible or intangible.

     "Purchasers" means ECT and JEDI-II and/or, to the extent then applicable,
each assignee of ECT or JEDI-II or their respective successors or assigns
pursuant to Section 12.04.

     "Registration Rights Agreement" means the Registration Rights Agreement
dated as of the date hereof, made by the Seller in favor of the Purchasers
relating to the Warrants, the Warrant Shares and the Acquired Shares.

     "Reportable Event" means an event described in Section 4043(c) of ERISA
with respect to a Plan, other than an event described in paragraphs (1) through
(8) as to which the 30 day notice requirement has been waived by the PBGC.

     "Reserve Report" is defined in the Indenture.

     "Responsible Officer" means, as to any Person, the Chief Executive Officer,
the President or any Vice President of such Person and the Chief Financial
Officer of such Person.  Unless otherwise specified, all references to a
Responsible Officer herein shall mean a Responsible Officer of the Seller.

     "Securities" means the Notes, the Warrants and the Acquired Shares.

     "Securities Act" means the Securities Act of 1933, as amended from time to
time, and the rules and regulations of the Commission promulgated thereunder.

                                      -8-
<PAGE>   13
 
     "Seller" means Brigham Exploration Company, a Delaware corporation.

     "Senior Credit Agreement" means the Credit Agreement dated as of January
26, 1998, among BOG, the Senior Loan Agent, and the Senior Lenders, as it may
from time to time be amended, modified or supplemented from time to time, and
any Credit Agreement or similar agreement executed in connection with any
refinancing of the Senior Loan permitted hereunder and under the Subordination
Agreement.

     "Senior Loan Agent" means the agent or agents designated under the Senior
Credit Agreement.  Bank of Montreal is the Senior Loan Agent as of the date
hereof.

     "Senior Lenders" means each of the lenders from time to time under the
Senior Credit Agreement.

     "Senior Loan" shall mean, collectively, any advance or advances of
principal made by the Senior Lenders to BOG under the Senior Credit Agreement
and the other Senior Loan Documents.

     "Senior Loan Documents" means the Senior Credit Agreement and all
promissory notes, collateral documents and other agreements, documents and
instruments executed or delivered in connection therewith, as such agreements
may be amended, modified or supplemented from time to time.

     "Special Entity" means any joint venture, limited liability company or
partnership, general or limited partnership or any other type of partnership or
company other than a corporation, in which a Person or one or more of its other
Subsidiaries is a member, owner, partner or joint venturer and owns, directly or
indirectly, at least a majority of the equity of such entity or controls such
entity, but excluding any tax partnerships that are not classified as
partnerships under state law.  For purposes of this definition, any Person which
owns directly or indirectly an equity investment in another Person which allows
the first Person to manage or elect managers who manage the normal activities of
such second Person will be deemed to "control" such second Person (e.g.,a sole
general partner controls a limited partnership).

     "Structuring Fee Agreement" means the agreement between the Seller and ECT
Securities Corp. dated as of the date hereof.

     "Subordination Agreement" means the Intercreditor and Subordination
Agreement dated as of even date herewith, by and among the Senior Loan Agent,
the Agent, the Purchasers, the Seller and certain Subsidiaries, as the same may
be supplemented or amended from time to time.

     "Subsidiary" means (i) any corporation of which at least a majority of the
outstanding shares of stock having by the terms thereof ordinary voting power to
elect a majority of the board of directors of such corporation (irrespective of
whether or not at the time stock of any other class or classes of such
corporation shall have or might have voting power by reason of the happening of
any contingency) is at the time directly or indirectly owned or controlled by a
Person or one or more of 

                                      -9-
<PAGE>   14
 
its Subsidiaries or by a Person and one or more of its Subsidiaries and (ii) any
Special Entity. Unless otherwise indicated herein, each reference to the term
"Subsidiary" shall mean a Subsidiary of the Seller. Quest Resources L.L.C. and
Venture Acquisitions L.P. shall not be considered Subsidiaries of Seller.

     "Trade Payables" means customary trade payables incurred in the ordinary
course of business.

     "Trustee" means the Trustee as defined in the Indenture.

     "Warrant Shares" means the shares of Common Stock and other securities
receivable upon exercise of the Warrants.

     "Warrants" means the Warrants issued by the Seller to the Purchasers in
their respective Participations pursuant to Section 2.03, for the purchase of an
aggregate of 1,000,000 shares of Common Stock, and any Warrants issued upon the
transfer thereof or in substitution therefor, pursuant to the Warrant
Certificates to be issued to ECT and JEDI-II, forms of which are attached hereto
as Exhibit A.

     Section  1.02.  ACCOUNTING PROCEDURES AND INTERPRETATION.  Unless otherwise
specified herein, all accounting terms used herein shall be interpreted, all
determinations with respect to accounting matters hereunder shall be made, and
all financial statements and certificates and reports as to financial matters
required to be furnished by the Seller hereunder shall be prepared, in
accordance with GAAP, applied on a basis consistent with the Financial
Statements (except for changes concurred with by the Seller's independent public
accountants).

                                  ARTICLE II
                 ISSUANCE OF SECURITIES; RIGHTS OF PURCHASERS

     Section 2.01  ISSUANCE OF SECURITIES.  Subject to the terms and
conditions herein set forth, the Seller agrees that it will issue the Securities
to the Purchasers and the Purchasers agree that they shall each purchase the
Securities from the Seller for an aggregate 
cash consideration of $50,000,000,
as follows:

               (i)  The Notes and the Warrants will be purchased by the
          Purchasers in their respective participations and sold for an
          aggregate cash consideration of $40,000,000.

               (ii)  The Acquired Shares will be purchased by the Purchasers or
          their respective Affiliates for a total cash consideration of
          $10,000,000.  The number of Acquired Shares to be purchased and sold
          on the Funding Date shall be determined by dividing the $10,000,000
          purchase price by the Average Share Price.  If within 180 days
          following the Funding Date the Seller enters into an agreement to
          issue or issues new Common Stock for a price per share that is less
          than the Average Share

                                      -10-
<PAGE>   15
 
          Price (a "Post Funding Sale Price"), the Seller shall,
          contemporaneously with the issuance of such new Common Stock, issue
          and deliver to the Purchasers or their respective Affiliates
          additional shares of Common Stock (which shall be deemed additional
          Acquired Shares) such that, after issuance and delivery of such
          additional Acquired Shares, the total number of Acquired Shares
          received by the Purchasers or their respective Affiliates multiplied
          by the Post Funding Date Sale Price, shall aggregate $10,000,000.

     Section 2.02  THE CLOSING; FUNDING DATE.

          (a)  The execution of the Basic Documents and all other instruments
required pursuant to Section 6.01 will take place at a closing (the "Closing")
to be held at the offices of Bracewell & Patterson, L.L.P. on such date as the
Seller and the Purchasers shall agree.  The date and time at which the Closing
occurs is the "Closing Date".

          (b)  Delivery of the Securities by the Seller to the Purchasers, and
payment by the Purchasers to the Seller of the consideration therefor as set
forth in Section 2.01, shall occur on the Funding Date.

     Section 2.03  DELIVERY.   Delivery of the Securities pursuant to this
Agreement shall be made on the Funding Date by the Seller delivering to the
Purchasers, against payment of the purchase price therefor, as follows: (i) one
Note executed by the Seller in the face amount of $12,500,000.00, payable to the
order of ECT and one Note executed by the Seller in the face amount of
$37,500,000.00, payable to the order of JEDI-II, (ii) one certificate executed
by the Seller representing ECT's Participation in the Warrants and one
certificate executed by the Seller representing JEDI-II's Participation in the
Warrants, registered in the names of ECT and JEDI-II, respectively (or such
other Person as either Purchaser may have designated in writing to the Seller at
least three Business Days prior to the Funding Date) and (iii) a certificate or
certificates of Common Stock executed by the Seller representing the Purchasers
and/or their respective Affiliates share of the Acquired Shares registered in
the name(s) of the Purchasers and/or their respective Affiliates (or such other
Person as either Purchaser may have designated in writing to the Seller at least
three Business Days prior to the Funding Date).

     Section 2.04  PAYMENT.  Payment of the consideration for the Securities
shall be made on the Funding Date by wire transfer of immediately available
funds to such account of the Seller as shall have been designated to ECT at
least two Business Days prior to the Funding Date.

     Section 2.05 TAX MATTERS. The Seller and the Purchasers agree as follows:
(i) Purchasers' acquisition of the Securities constitutes the purchase of an
"investment unit" (the "Investment Unit") for purposes of Treas. Reg. (S)1.1273-
2(h)(1); (ii) the issue price of the Investment Unit is $50,000,000, as
determined in accordance with Treas. Reg. (S)1.1273-2(a)(1); (iii) the issue
price for the Investment Unit shall be allocated among the Notes, the Warrants,
and the Acquired Shares in accordance with their relative fair market values, as
required by Treas. Reg. (S)1.1273-2(h)(1); and 

                                      -11-
<PAGE>   16
 
(iv) the parties agree that the issue price shall be allocated among the Notes,
the Warrants, and the Acquired Shares as follows and the parties shall be bound
by such allocation for all tax-related purposes:

<TABLE>
<S>           <C>                   <C> 
               Notes:                $39,900,000
               Warrants:             $   100,000
               Acquired Shares:      $10,000,000
</TABLE>

     Section 2.06  RIGHTS OF PURCHASERS.  The Purchasers shall have such
rights with respect to the registration of the Warrant Shares and the Acquired
Shares under the Securities Act and state securities laws as are set forth in
the Registration Rights Agreement, which shall be executed by the Seller and the
Purchasers at the Closing.

                                  ARTICLE III
                         SECURITY FOR THE OBLIGATIONS

     Section 3.01  SECURITY.  The Obligations shall be secured by the
Collateral and the Collateral Documents in accordance with the Indenture.

                                  ARTICLE IV
                 REPRESENTATIONS AND WARRANTIES OF THE SELLER

     The Seller represents and warrants to the Purchasers, for the benefit of
each of the holders of the Notes, the holders of the Warrants and the holders of
the Acquired Shares, which representations and warranties shall survive the
execution of any Basic Document, that as of the date of this Agreement:

     Section 4.01  CORPORATE EXISTENCE.  The Seller: (i) is a corporation duly
organized, legally existing and in good standing under the laws of the State of
Delaware; (ii) has all requisite power, and has all material governmental
licenses, authorizations, consents and approvals necessary to own its assets and
carry on its business as now being or as proposed to be conducted; and (iii) is
qualified to do business in all jurisdictions in which the nature of the
business conducted by it makes such qualifications necessary and where failure
so to qualify would have a Material Adverse Effect.  Brigham, Inc.: (i) is a
corporation duly organized, legally existing and in good standing under the laws
of the State of Nevada; (ii) has all requisite power, and has all material
governmental licenses, authorizations, consents and approvals necessary to own
its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualifications necessary
and where failure so to qualify would have a Material Adverse Effect.  Each of
Brigham Holdings I, LLC and Brigham Holdings II, LLC:  (i) is a limited
liability company duly organized, legally existing and in good standing under
the laws of the State of Nevada; (ii) has all requisite power, and has all
material governmental licenses, authorizations, consents and approvals necessary
to own its assets and carry on its business as now being or as proposed to be
conducted; and (iii) is qualified to do business in all jurisdictions in which
the nature of the business conducted by it makes such qualifications 

                                      -12-
<PAGE>   17
 
necessary and where failure so to qualify would have a Material Adverse Effect.
Brigham Oil & Gas, L.P.: (i) is a limited partnership duly organized, legally
existing and in good standing under the laws of the State of Delaware; (ii) has
all requisite power, and has all material governmental licenses, authorizations,
consents and approvals necessary to own its assets and carry on its business as
now being or as proposed to be conducted; and (iii) is qualified to do business
in all jurisdictions in which the nature of the business conducted by it makes
such qualifications necessary and where failure so to qualify would have a
Material Adverse Effect.

     Section  4.02  FINANCIAL CONDITION.  The audited consolidated balance
sheet of the Seller and its Consolidated Subsidiaries as at December 31, 1997
and the related consolidated statement of income, stockholders' equity and cash
flow of the Seller and its Consolidated Subsidiaries for the fiscal year ended
on said date, with the opinion thereon of Price Waterhouse, heretofore furnished
to the Purchasers and the unaudited consolidated balance sheet of the Seller and
its Consolidated Subsidiaries as at June 30, 1998, and their related
consolidated statements of income, stockholders' equity and cash flow of the
Seller and its Consolidated Subsidiaries for the six-month period ended on such
date heretofore furnished to the Purchasers, are complete and correct and fairly
present the consolidated financial condition of the Seller and its Consolidated
Subsidiaries as at said dates and the results of its operations for the fiscal
year and the six-month period on said dates, all in accordance with GAAP, as
applied on a consistent basis (subject, in the case of the interim financial
statements, to normal year-end adjustments).  Neither the Seller nor any
Consolidated Subsidiary has on the Closing Date any material Debt, Trade
Payables, contingent liabilities, liabilities for taxes, unusual forward or
long-term commitments or unrealized or anticipated losses from any unfavorable
commitments, except as referred to or reflected or provided for in the Financial
Statements or in Schedule 4.02.  Since June 30, 1998, there has been no change
or event having a Material Adverse Effect.  Since the date of the Financial
Statements, neither the business nor the Properties of the Seller or any of the
Consolidated Subsidiaries, taken as a whole, have been materially and adversely
affected as a result of any fire, explosion, earthquake, flood, drought,
windstorm, accident, strike or other labor disturbance, embargo, requisition or
taking of Property or cancellation of contracts, permits or concessions by any
Governmental Authority, riot, activities of armed forces or acts of God or of
any public enemy.

     Section 4.03  LITIGATION.  Except as disclosed to the Purchasers in
Schedule 4.03, at the Closing Date there is no litigation, legal, administrative
or arbitral proceeding, investigation or other action of any nature pending or,
to the knowledge of the Seller, threatened against or affecting the Seller or
any Subsidiary which both (a) involves the possibility of any judgment or
liability against the Seller or any Subsidiary not fully covered by insurance
(except for normal deductibles), and (b) would be more likely than not to have a
Material Adverse Effect.

     Section 4.04  NO BREACH.  Neither the execution and delivery of the Basic
Documents, nor compliance with the terms and provisions thereof will conflict
with or result in a breach of, or require any consent which has not been
obtained as of the Closing Date under, the Articles of Incorporation or by-laws
of the Seller, the respective charter, by-laws, partnership agreements or
regulations of any Subsidiary or any Governmental Requirement or any material
agreement or instrument to which the Seller or any Subsidiary is a party or by
which it is bound or to which it or its Properties are subject, 

                                      -13-
<PAGE>   18
 
or constitute a default under any such agreement or instrument, or result in the
creation or imposition of any Lien upon any of the material revenues or assets
of the Seller or any Subsidiary pursuant to the terms of any such agreement or
instrument other than the Liens created by the Loan Documents and the
restrictions contained in the Senior Loan Documents (as amended concurrently
herewith) which limit the circumstances in which BOG can make dividends or
distributions to the Seller and in which the Seller can make cash payments of
interest on the Notes.

     Section 4.05  AUTHORITY.  The Seller and each Subsidiary has all
necessary power and authority to execute, deliver and perform its obligations
under the Basic Documents to which it is a party; and the execution, delivery
and performance by the Seller and each Subsidiary of the Basic Documents to
which it is a party, have been duly authorized by all necessary action on its
part; and the Basic Documents constitute the legal, valid and binding
obligations of the Seller and each Subsidiary, enforceable in accordance with
their terms, except as such enforceability may be limited by bankruptcy,
insolvency, fraudulent transfer and similar laws affecting creditors' rights
generally or by general principles of equity.

     Section 4.06  APPROVALS.  Except for registration of the Securities under
the Securities Act, no authorizations, approvals or consents of, and no filings
or registrations with, any Governmental Authority are necessary for the
execution, delivery or performance by the Seller or any Subsidiary of the Basic
Documents or for the validity or enforceability thereof.

     Section   4.07  USE OF LOANS.  The purchase price of the Notes, the
Warrants and the Acquired Shares shall be used solely to pay principal and
interest outstanding on the Senior Loan.  In no event shall the purchase price
of the Notes, the Warrants or the Acquired Shares be used to finance in whole or
in part any hostile acquisition.  The Seller is not engaged principally, or as
one of its important activities, in the business of extending credit for the
purpose, whether immediate, incidental or ultimate, or buying or carrying margin
stock (within the meaning of Regulation G, U or X of the Board of Governors of
the Federal Reserve System) and no part of the purchase price of the Notes, the
Warrants or the Acquired Shares will be used to buy or carry any margin stock.

     Section 4.08  ERISA.

          (a)  The Seller and each ERISA Affiliate have complied in all material
respects with ERISA and, where applicable, the Code regarding such Plan.

          (b)  Each Plan is, and has been, maintained in substantial compliance
with ERISA and, where applicable, the Code.

          (c)  No act, omission or transaction has occurred which could  result
in imposition on the Seller or any ERISA Affiliate (whether directly or
indirectly) of an amount of $100,000 or more as (i) either a civil penalty
assessed pursuant to section 502(c), (i) or (1) of ERISA or a tax imposed
pursuant to Chapter 43 of Subtitle D of the Code or (ii) breach of fiduciary
duty liability damages under section 409 of ERISA.

          (d)  No Plan (other than a defined contribution plan) or any trust
created under any such Plan has been terminated since September 2, 1974.  No
liability to the PBGC in excess of $100,000 (other than for the payment of
current premiums which are not past due) by the Seller or any ERISA Affiliate
has been or is expected by the Seller or 

                                      -14-
<PAGE>   19
 
any ERISA Affiliate to be incurred with respect to any Plan. No ERISA Event with
respect to any Plan has occurred which could reasonably expected to result in
liabilities of $100,000 or more.

          (e)  Full payment when due has been made of all amounts which the
Seller or any ERISA Affiliate is required under the terms of each Plan or
applicable law to have paid as contributions to such Plan, and no accumulated
funding deficiency in an amount of $100,000 or more (as defined in section 302
of ERISA and section 412 of the Code), whether or not waived, exists with
respect to any Plan.

          (f)  The actuarial present value of the benefit liabilities under each
Plan which is subject to Title IV of ERISA does not, as of the end of the
Seller's most recently ended fiscal year, exceed the current value of the assets
(computed on a plan termination basis in accordance with Title IV of ERISA) of
such Plan allocable to such benefit liabilities by $100,000 or more.  The term
"actuarial present value of the benefit liabilities" shall have the meaning
specified in section 4041 of ERISA.

          (g)  None of the Seller or any ERISA Affiliate sponsors, maintains, or
contributes to an employee welfare benefit plan, as defined in section 3(1) of
ERISA, including, without limitation, any such plan maintained to provide
benefits to former employees of such entities, that may not be terminated by the
Seller or any ERISA Affiliate in its sole discretion at any time without any
material liability.

          (h)  None of the Seller or any ERISA Affiliate sponsors, maintains or
contributes to, or has at any time in the preceding six calendar years,
sponsored, maintained or contributed to, any Multiemployer Plan.

          (i)  None of the Seller or any ERISA Affiliate is required to provide
security under section 401(a)(29) of the Code due to a Plan amendment that
results in an increase in current liability for the Plan.

     Section 4.09  TAXES.   Except as set out in Schedule 4.09, the Seller and
each Subsidiary has filed all United States Federal income tax returns and all
other tax returns which are required to be filed by it and has paid all material
taxes due pursuant to such returns or pursuant to any assessment received by the
Seller or any such Subsidiary, except for any taxes which are being contested in
good faith and by proper proceedings and against which adequate reserves are
being maintained.  The charges, accruals and reserves on the books of the Seller
and its Subsidiaries in respect of taxes and other governmental charges are, in
the opinion of the Seller, adequate.  No tax lien has been filed and, to the
knowledge of the Seller, no claim is being asserted with respect to any such
tax, fee or other charge, except for any taxes, fees or other charges which are
being contested in good faith and by proper proceedings and against which
adequate reserves are being maintained.


                                      -15-
<PAGE>   20

     Section 4.10  TITLES, ETC.
 
          (a)  Subject to the matters set out in Schedule 4.10, each of the
Seller and the Subsidiaries has good and defensible title to (i) the Oil and Gas
Properties that are both (A) evaluated in the most recently delivered Reserve
Report and (B) described in Part One of Exhibit A to the Mortgage, free and
clear of all Liens except Liens permitted by Section 8.02 of the Indenture, and
(ii) to the best of Seller's knowledge, the balance of Seller's material
(individually or in the aggregate) Oil and Gas Properties (and/or those of the
Subsidiaries) that are described in the Mortgage or that are otherwise evaluated
in the most recently delivered Reserve Report, are free and clear (to the best
of Seller's knowledge) of all Liens except Liens permitted by Section 8.02 of
the Indenture.  Except for immaterial divergences, after giving full effect to
the Excepted Liens and the matters set forth in Schedule 4.10, the Seller or its
Subsidiaries own the net interests in production attributable to the Hydrocarbon
Interests that are both (A) evaluated in the most recently delivered Reserve
Report and (B) reflected in the Mortgage, and the ownership of such Hydrocarbon
Interests shall not in any material respect obligate the Seller or its
Subsidiaries to bear the costs and expenses relating to the maintenance,
development and operations of each such Hydrocarbon Interest in an amount in
excess of the working interest of such Hydrocarbon Interest set forth in the
Mortgage (without a corresponding increase in net revenue interest).  The Seller
does not believe, based upon information in its possession, that its most
recently delivered Reserve Report materially overstates its (or any
Subsidiaries) oil and gas reserves, bearing in mind that reserves are evaluated
based upon estimates and assumptions with respect to which reasonable minds of
competent reserve engineers may differ and that reserve estimates are affected
by the oil and gas prices used in the preparation thereof.

          (b)  All leases and agreements necessary for the conduct of the
business of the Seller and the Subsidiaries are valid and subsisting, in full
force and effect and there exists no default or event or circumstance which with
the giving of notice or the passage of time or both would give rise to a default
under any such lease or leases, which would affect in any material respect the
conduct of the business of the Seller and the Subsidiaries.

          (c)  The Properties presently owned, leased or licensed by the Seller
and the Subsidiaries, including, without limitation, all easements and rights of
way, include all Properties necessary to permit the Seller and the Subsidiaries
to conduct their business in all material respects in the same manner as its
business has been conducted prior to the Closing Date.

          (d)  All of the Properties of the Seller and the Subsidiaries which
are reasonably necessary for the operation of their business are in good working
condition in all material respects and are maintained in accordance with prudent
business standards.

     Section 4.11  NO MATERIAL MISSTATEMENTS.  Taken as a whole, the written
information, statements, exhibits, certificates, documents and reports furnished
to the Purchasers by the Seller or any Guarantor in connection with the
negotiation of this Agreement do not contain any material misstatement of fact
or omit to state a material fact or any fact necessary to make the statements
contained therein not materially misleading in the light of the circumstances in
which made and with respect to the Seller or any Guarantor.  As of the Closing
Date, there is no fact peculiar to the Seller or any Guarantor which has a
Material Adverse Effect or in the future is reasonably likely to have 

                                      -16-
<PAGE>   21
 
(so far as the Seller can now foresee) a Material Adverse Effect and which has
not been set forth in this Agreement or the other documents, certificates and
statements furnished to the Purchasers by or on behalf of the Seller or any
Guarantor prior to, or on, the Closing Date in connection with the transactions
contemplated hereby.

     Section 4.12  INVESTMENT COMPANY ACT.  Neither the Seller nor any
Subsidiary is an "investment company" or a company "controlled" by an
"investment company," within the meaning of the Investment Company Act of 1940,
as amended.

     Section 4.13  PUBLIC UTILITY HOLDING COMPANY ACT.  Neither the Seller
nor any Subsidiary is a "holding company," or a "subsidiary company" of a
"holding company," or an "affiliate" of a "holding company" or of a "subsidiary
company" of a "holding company," or a "public utility" within the meaning of the
Public Utility Holding Company Act of 1935, as amended.

     Section 4.14  SUBSIDIARIES.  Except as set forth on Schedule 4.14, the
Seller has no Subsidiaries or any direct or indirect ownership interest in any
other Persons.  Schedule 4.14 sets forth the ownership interest of the Seller
(direct or indirect) in and to all such Persons.

     Section 4.15  LOCATION OF BUSINESS AND OFFICES.  As of the Closing Date,
the Seller's principal place of business and chief executive offices are located
at the address stated in Section 12.06.  The principal place of business and
chief executive office of each Subsidiary are located at the addresses stated on
Schedule 4.14.

     Section 4.16  DEFAULTS.  Neither the Seller nor any Subsidiary is in
default nor has any event or circumstance occurred which, but for the expiration
of any applicable grace period or the giving of notice, or both, would
constitute a default under any material agreement or instrument to which the
Seller or any Subsidiary is a party or by which the Seller or any Subsidiary is
bound which default would have a Material Adverse Effect.  No Default hereunder
has occurred and is continuing.  No "Event of Default" under the Senior Loan
Documents has occurred and is continuing nor has Seller or any of its
Subsidiaries received any notice of a "Default" under the Senior Loan Documents
that has triggered a cure period.

     Section 4.17  ENVIRONMENTAL MATTERS.  Except as provided in Schedule
4.17 or  for matters which are more likely than not to not to have a Material
Adverse Effect (or with respect to (c), (d) and (e) below, where the failure to
take such actions is more likely than not to not have a Material Adverse
Effect):

          (a)  Neither any Property of the Seller or any of its Subsidiaries nor
the operations conducted thereon violate any order or requirement of any court
or Governmental Authority or any Environmental Laws;

          (b)  Without limitation of clause (a) above, no Property of the Seller
or any of its Subsidiaries nor the operations currently conducted thereon or, to
the best knowledge of the Seller, by any prior owner or operator of such
Property or operation, are in violation of or subject to any 

                                      -17-
<PAGE>   22
 
existing, pending or threatened action, suit, investigation, inquiry or
proceeding by or before any court or Governmental Authority or to any remedial
obligations under Environmental Laws;

          (c)  All notices, permits, licenses or similar authorizations, if any,
required to be obtained or filed by the Seller or any of its Subsidiaries in
connection with the operation or use of any and all Property of the Seller and
each of its Subsidiaries, including without limitation present, or to the best
of Seller's knowledge, past treatment, storage, disposal or release of a
hazardous substance or solid waste into the environment, have been duly obtained
or filed, and the Seller and each Subsidiary thereof are in compliance with the
terms and conditions of all such notices, permits, licenses and similar
authorizations;

          (d)  All hazardous substances, solid waste, and oil and gas
exploration and production wastes, if any, generated at any and all Property of
the Seller and each of its Subsidiaries have in the past, during Seller's or its
Subsidiaries' tenure of ownership and to the best of Seller's knowledge, prior
thereto, been transported, treated and disposed of in accordance with
Environmental Laws and so as not to pose an imminent and substantial
endangerment to public health or welfare or the environment, and, to the best
knowledge of the Seller, all such transport carriers and treatment and disposal
facilities have been and are operating in compliance with Environmental Laws and
so as not to pose an imminent and substantial endangerment to public health or
welfare or the environment, and are not the subject of any existing, pending or
threatened action, investigation or inquiry by any Governmental Authority in
connection with any Environmental Laws;

          (e)  The Seller has taken all steps reasonably necessary to determine
and has determined that no hazardous substances, solid waste, or oil and gas
exploration and production wastes, have been disposed of or otherwise released
and there has been no threatened release of any hazardous substances on or to
any Property of the Seller or any of its Subsidiaries except in compliance with
Environmental Laws and so as not to pose an imminent and substantial
endangerment to public health or welfare or the environment;

          (f)  To the extent applicable, all Property of the Seller and each of
its Subsidiaries currently satisfies all design, operation, and equipment
requirements imposed by the OPA or scheduled as of the Closing Date to be
imposed by OPA during the term of this Agreement, and the Seller does not have
any reason to believe that such Property, to the extent subject to OPA, will not
be able to maintain compliance with the OPA requirements during the term of this
Agreement; and

          (g)  Neither the Seller nor any of its Subsidiaries has any known
contingent liability in connection with any release or threatened release of any
oil, hazardous substance or solid waste into the environment.

     Section 4.18  COMPLIANCE WITH THE LAW.  Neither the Seller nor any
Subsidiary has violated any Governmental Requirement or failed to obtain any
license, permit, franchise or other governmental authorization necessary for the
ownership of any of its Properties or the conduct of its business, which
violation or failure would have (in the event such violation or failure were

                                      -18-
<PAGE>   23
 
asserted by any Person through appropriate action) a Material Adverse Effect.
Except for such acts or failures to act as would not have a Material Adverse
Effect, the Oil and Gas Properties (and properties unitized therewith) of the
Seller and its subsidiaries have been maintained, operated and developed in a
good and workmanlike manner and in conformity with all applicable laws and all
rules, regulations and orders of all duly constituted authorities having
jurisdiction and in conformity with the provisions of all leases, subleases or
other contracts comprising a part of the Hydrocarbon Interests and other
contracts and agreements forming a part of such Oil and Gas Properties;
specifically in this connection, but subject to the Material Adverse Effect
qualification set forth above, (i) after the Closing Date, no such Oil and Gas
Property is subject to having allowable production reduced below the full and
regular allowable (including the maximum permissible tolerance) because of any
overproduction (whether or not the same was permissible at the time) prior to
the Closing Date and (ii) none of the wells comprising a part of such Oil and
Gas Properties (or properties unitized therewith) are deviated from the vertical
more than the maximum permitted by applicable laws, regulations, rules and
orders, and such wells are, in fact, bottomed under and are producing from, and
the well bores are wholly within, such Oil and Gas Properties (or in the case of
wells located on properties unitized therewith, such unitized properties).

     Section 4.19  INSURANCE.  Schedule 4.19 attached hereto contains an
accurate and complete description of all material policies of fire, liability,
workmen's compensation and other forms of insurance owned or held by the Seller
and each Subsidiary as of the Closing Date.  All such policies are in full force
and effect, all premiums with respect thereto covering all periods up to and
including the Closing Date have been paid, and no notice of cancellation or
termination has been received with respect to any such policy.  Such policies
are sufficient for compliance with all requirements of law and of all agreements
to which the Seller or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at lease such
amounts and against at least such risks (but including in any event public
liability) as are usually insured against in the same general area by companies
engaged in the same or a similar business for the assets and operations of the
Seller and each Subsidiary; will remain in full force and effect through the
respective dates set forth on Schedule 4.19 without the payment of additional
premiums; and will not in any way be affected by, or terminate or lapse by
reason of, the transactions contemplated by this Agreement.  Schedule 4.19
identifies all material risks, if any, which the Seller, the Subsidiaries and
their respective board of directors or officers have designated as being self
insured.  Neither the Seller nor any Subsidiary has been refused any insurance
with respect to its assets or operations, nor has its coverage been limited
below usual and customary policy limits, by an insurance carrier to which it has
applied for any such insurance or with which is has carried insurance during the
last three years.

     Section 4.20  HEDGING AGREEMENTS.   Schedule 4.20 sets forth, as of the
Closing Date, a true and complete list of all Hedging Agreements (including
commodity price swap agreements, forward agreements or contracts of sale which
provide for prepayment for deferred shipment or delivery of oil, gas or other
commodities) of the Seller and each Subsidiary, the material terms thereof
(including the type, term, effective date, termination date and notional amounts
of volumes), the net mark to market value thereof, all credit support agreements
relating thereto (including any margin required or supplied), and the
counterparty to each such agreement.

                                      -19-
<PAGE>   24
 
     Section 4.21  RESTRICTION ON LIENS.  Neither the Seller nor any
Subsidiary is a party to any agreement or arrangement (other than the Loan
Documents and the Senior Loan Documents), or subject to any order, judgment,
writ or decree, which either restricts or purports to restrict ability to grant
Liens to other Persons on or in respect of their respective assets or
Properties.

     Section 4.22  MATERIAL AGREEMENTS.  Set forth on Schedule 4.22 hereto is
a complete and correct list of all material agreements, leases, indentures,
purchase agreements, obligations in respect of letters of credit, guarantees,
joint venture agreements, and other instruments in effect or to be in effect as
of the Closing Date (other than the Senior Loan Documents and Hedging
Agreements) providing for, evidencing, securing or otherwise relating to any
material Debt of the Seller or any Subsidiary, and all obligations of the Seller
or any Subsidiary to issuers of surety or appeal bonds (excluding operator's
bonds, plugging and abandonment bonds, and similar surety obligations obtained
in the ordinary course of business) issued for account of the Seller or any such
Subsidiary, and such list correctly set forth the names of the debtor or lessee
and creditor or lessor with respect to the Debt or lease obligations outstanding
or to be outstanding and the property subject to any Lien securing such Debt or
lease obligations.

     Section 4.23  GAS IMBALANCES.  As of the Closing Date, except as set
forth in the most recent Reserve Report furnished to the Purchasers or on
Schedule 4.23, on a net basis there are no gas imbalances, take or pay or other
prepayments with respect to the Seller's or any Subsidiary's Hydrocarbon
Interests which would require the Seller or such Subsidiary to deliver five
percent (5%) or more of the monthly production from the Seller's and its
Subsidiaries' Hydrocarbons produced on a monthly basis from the Hydrocarbon
Interests, at some future time without then or thereafter receiving full payment
therefor.

     Section 4.24  CAPITALIZATION.  The authorized Capital Stock of the
Seller consists of: (a) 30,000,000 shares of Common Stock, par value $.01 per
share and (b) 10,000,000 shares of Preferred Stock, par value $.01 per share, of
which there are issued and outstanding 12,253,574 shares of Common Stock and no
other shares of Capital Stock.  All outstanding shares of Common Stock are
validly issued, fully paid and nonassessable and were issued free of preemptive
rights.  Except as set forth on Schedule 4.24, the Seller is not a party to any
voting trust or other agreement with respect to the voting of its Capital Stock.
Except for the Warrants, there are no (i) outstanding securities convertible or
exchangeable into Capital Stock of the Seller or (ii) warrants, contracts,
commitments, agreements, understandings, or arrangements of any kind to which
the Seller is a party relating to the repurchase or issuance of any Capital
Stock.  Except as set forth on Schedule 4.24 and except as contemplated in the
Equity Documents, the Seller is not a party to or bound by any agreement with
respect to any of its securities which grants registration rights to any Person.

     Section 4.25  ACQUIRED SHARES.  When issued and delivered against
payment therefor in accordance with the terms of this Agreement, the Acquired
Shares will be duly and validly issued, fully paid, nonassessable, free of
preemptive rights and free from all taxes payable by the Seller and Liens
(except any Liens created or suffered to be created by the Purchasers) and will
not be subject to any restriction on the voting or transfer thereof created by
the Seller other than in the Equity Documents and the applicable provisions of
federal and state securities laws.

                                      -20-
<PAGE>   25
 
     Section 4.26  WARRANT SHARES.  When issued and delivered against
payment therefor in accordance with the terms of the Warrants, the Warrant
Shares issuable upon exercise of the Warrants will be duly and validly issued,
fully paid, nonassessable, free of preemptive rights and free from all taxes
payable by the Seller and Liens (except any Liens created or suffered to be
created by the Purchasers) and will not be subject to any restriction on the
voting or transfer thereof created by the Seller other than in the Equity
Documents and the applicable provisions of federal and state securities laws.
The Seller has duly and validly reserved the Warrant Shares, as of the Closing
Date, for issuance upon conversion of the Warrants.

     Section 4.27  NO RESTRICTIONS.  The Seller currently is not, and in the
future will not, be subject to any agreements that purport to impose
restrictions or limitations on the Purchasers, as affiliates of the Seller or
otherwise, without the prior written consent and authorization of each of the
Purchasers.

     Section 4.28  CERTAIN FEES.  Except for the fees payable to ECT
Securities Corp. and JEDI-II pursuant to the Structuring Fee Agreement, no fees
or commissions will be payable by the Seller to brokers, finders, investment
bankers, or Purchasers with respect to the issuance and sale of any of the
Securities or the consummation of the transaction contemplated by this
Agreement.  The Seller agrees that it will indemnify and hold harmless the
Purchasers from and against any and all claims, demands, or liabilities for
broker's, finders, placement, or other similar fees or commissions incurred by
the Seller or alleged to have been incurred by the Seller in connection with the
issuance or sale of the Securities or the consummation of the transaction
contemplated by this Agreement.

                                   ARTICLE V
               REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS

     The Purchasers each represent and warrant to the Seller, which
representations and warranties shall survive the execution of any Basic
Document, that as of the date of this Agreement:

     Section 5.01  INVESTMENT.  Each Purchaser represents and warrants to, and
covenants and agrees with, the Seller that the Securities are being acquired for
its own account and with no intention of distributing or reselling the Notes,
the Warrants, the Warrant Shares or the Acquired Shares in any transaction which
would be in violation of the securities laws of the United States of America or
any State, without prejudice, however, to Purchaser's right at all times to sell
or otherwise dispose of all or any part of the Notes, the Warrants, the Warrant
Shares or the Acquired Shares under a registration statement under the
Securities Act and applicable state securities laws or under an exemption from
such registration available thereunder (including, without limitation, if
available, Rule 144A promulgated thereunder).  If either Purchaser should in the
future decide to dispose of any of the Notes, the Warrants, the Warrant Shares
or the Acquired Shares, the Purchasers understand and agree (i) that it may do
so only (A) in compliance with the Securities Act and applicable state
securities law, as then in effect, and (B) in the manner contemplated by any
registration statement pursuant to which such securities are being offered, and
(ii) that stop-transfer instructions to that effect will be in effect with
respect to such securities.  The Purchasers agree to 

                                      -21-
<PAGE>   26
 
the imprinting, so long as appropriate, of a legend on each Note and on each
certificate representing Warrants, Warrant Shares or the Acquired Shares, to the
effect as set forth above.

     Section 5.02  NATURE OF PURCHASERS.  Each Purchaser represents and
warrants to, and covenants and agrees with, the Seller that, (i) it is an
"accredited investor" within the meaning of paragraphs (a)(3) or (8) of Rule 501
under the Securities Act and (ii) by reason of its business and financial
experience it has such knowledge, sophistication and experience in business and
financial matters so as to be capable of evaluating the merits and risks of the
prospective investment in the Securities, is able to bear the economic risk of
such investment and, at the present time, would be able to afford a complete
loss of such investment.

     Section 5.03  RECEIPT OF INFORMATION; AUTHORIZATION.  Each Purchaser
acknowledges that it has been furnished all information that it deems necessary
or desirable to the making of an informed investment decision concerning the
Securities.  Each Purchaser acknowledges that it has had an opportunity to ask
questions of and receive satisfactory answers from designated representatives of
the Seller concerning the terms and conditions pursuant to which the purchase of
the Securities are made.  Each Purchaser acknowledges that it has been afforded
an opportunity to examine such documents and other information which it has
requested for the purpose of verifying the information provided to it and for
the purpose of answering any questions it may have concerning the business
affairs and financial condition of the Seller.  Each Purchaser represents that
it alone or with its advisors has knowledge and experience in the business of
the Seller and the Seller so as to be capable of evaluating the merits and risks
of an investment in the Seller based upon the information furnished to it, its
knowledge of the business and affairs of the Seller, the records, files, and
plans of the Seller (which have been made available to it), such additional
information as it has requested and has received from the Seller, and the
independent inquiries and investigations undertaken by it.  Each Purchaser
represents and warrants that the purchase of the Securities by it has been duly
and properly authorized and this Agreement and each Basic Document to which the
Purchasers are a signatory has been duly executed and delivered by it or on its
behalf.

                                  ARTICLE VI
                        CONDITIONS PRECEDENT TO FUNDING

     Section 6.01  CONDITIONS PRECEDENT TO OBLIGATIONS OF THE PURCHASERS.  The
obligation of the Purchasers to acquire the Securities on the Funding Date is
subject to each of the following:

          (a)  The accuracy as of the Closing Date of each and every
representation and warranty of the Seller, each Guarantor, and the Senior Loan
Agent made in this Agreement or any other Basic Document, or in any certificate
delivered to the Purchasers pursuant to or in connection with this Agreement,
and receipt by the Purchasers of a Certificate executed by a duly Responsible
Officer, dated as of the Funding Date, certifying that each of the
representations and warranties of the Seller and each Guarantor made in this
Agreement or any other Basic Document are true and correct as of the Funding
Date, and that the Seller and each Guarantor has performed to date all of its
respective covenants and agreements under the Basic Documents.

                                      -22-
<PAGE>   27
 
          (b)  The absence as of the Closing Date and the Funding Date of a
Default or Event of Default hereunder or an "Event of Default" under the Senior
Credit Agreement or any Default hereunder the Senior Loan Documents that has
triggered a cure period.

          (c)  The performance by the Seller of its respective obligations to be
performed hereunder on or before the Funding Date.

          (d)  The satisfaction of each of the following conditions as of or
prior to the Closing Date:

               (i)   The Purchasers (or the Trustee, where appropriate) shall
     have received the following, each in form and substance satisfactory to the
     Purchasers and in sufficient counterparts:

                     (A)   Duly executed counterparts of this Agreement and the
          Indenture signed by all the parties hereto and thereto.

                     (B)   The duly executed Financing Agreement, Structuring
          Fee Agreement, Guaranty Agreements, Subordination Agreement and
          Registration Rights Agreement, dated as of the Closing Date in form
          and substance satisfactory to Purchasers.

                     (C)   Duly executed counterparts of the Collateral
          Documents (including without limitation UCC-1 Financing Statements).

                     (D)   Certificates of good standing as to the Seller and
          each Guarantor issued by the Secretary of State of their respective
          states of incorporation or formation.

                     (E)   The duly executed certificate of the Secretary of the
          Seller setting forth (i) resolutions of its directors in form and
          substance satisfactory to the Purchasers with respect to the
          authorization of this Agreement and the other Basic Documents to which
          it is a party and the transactions contemplated hereby and thereby;
          (ii) the names and true signatures of the officers authorized to sign
          such instruments; and (iii) copies of the articles or certificate of
          incorporation and the bylaws of the Seller.

                     (F)   The duly executed certificate of the Secretary of
          each Guarantor which is a corporation setting forth (i) resolutions of
          its directors in form and substance satisfactory to the Purchasers
          with respect to the authorization of the Guaranty Agreements executed
          by such Guarantors and the transactions contemplated hereby and
          thereby; (ii) the names and true signatures of the officers authorized
          to sign such instruments; and (iii) copies of the articles or
          certificate of incorporation and the bylaws of each Guarantor.

                                      -23-
<PAGE>   28
 
                     (G)   The duly executed certificate of all the partners of
          each Guarantor that is a Partnership and each member of each Guarantor
          that is a limited liability company, setting forth (i) the
          authorization of the Guaranty Agreements and the transactions
          contemplated hereby and thereby; (ii) the names and title of all
          persons authorized to sign such instruments; and (iii) copies of the
          applicable partnership agreement or other regulating documents of each
          such Guarantor.

                     (H)   Evidence that the insurance required hereunder and
          under the other Basic Documents has been obtained and is in full force
          and effect.

                     (I)   Copies of the Senior Loan Documents.

                     (J)   Any other document which the Purchasers may
          reasonably request, including opinions addressed to Purchasers, dated
          as of the Closing Date, from the counsel for the Seller and each of
          the Guarantors acceptable to each of the Purchasers addressing the
          existence and good standing of the Seller, the authorization of the
          Basic Documents, the enforceability of the Basic Documents, the
          absence of conflicts with law, other material agreements, and court
          orders, the absence of litigation, and such other matters as the
          Purchasers may reasonably request.

               (ii)  The Seller shall have executed (but not delivered) the
     Notes, Warrants and Acquired Shares, each in form and substance
     satisfactory to the Purchasers.

               (iii) The Seller shall have received consents to the Basic
     Documents by the Senior Lenders; and the Senior Loan Documents shall have
     been amended in form and substance reasonably satisfactory to Purchasers to
     permit the transactions contemplated by the Loan Documents, including the
     payment of dividends or other distributions by Subsidiaries to the Seller
     in order for the Seller to meet its debt service obligations to the
     Purchasers under the Notes.

               (iv)  The Purchasers shall have completed a due diligence review
     of the Seller and the Subsidiaries to the satisfaction of the Purchasers in
     their sole discretion.

               (v)   The Purchasers shall have received the latest internally
     prepared consolidated financial statements of the Seller and its
     Subsidiaries which shall be at least through June 30, 1998.  Since June 30,
     1998, there shall have occurred no event which could have a Material
     Adverse Effect.

               (vi)  The Board of Directors of each of the Seller, the
     Guarantors, the Purchasers and Enron Corp. must have approved the
     transactions contemplated under this Agreement and the other Basic
     Documents.

               (vii) All other consents, including without limitation any
     required shareholder approval, and waivers necessary to complete the
     transactions under this 

                                      -24-
<PAGE>   29
 
     Agreement and the other Basic Documents shall have been obtained by the
     Seller, the Guarantors and the Purchasers.

          (e)  The Warrants Shares and the Acquired Shares shall have been
approved for listing on NASDAQ and the registration statement on Form S-1
registering the Notes, the Warrants, and the Acquired Shares shall have been
declared effective by the Commission and no stop order with respect thereto
shall have been issued.

          (f)  The Seller shall have delivered to the Purchasers the executed
Notes, Warrants and Acquired Shares.

          (g)  The Mortgages shall have been filed in two counties of 
Purchasers's choice.

          (h)  The Seller shall have paid to ECT Securities Corp. and JEDI-II
all payments required under the terms of the Structuring Fee Agreement.

          (i)  If requested in writing by either of the Purchasers, a Designee
of the Purchasers shall have been appointed to the Board of Directors of the
Seller pursuant to Section 7.03.

          (j)  The Seller shall have duly and validly reserved the Warrant
Shares for issuance upon conversion of the Warrants.

          (k)  The issuance of the Securities by the Seller shall not as of the
Funding Date be enjoined (temporarily or permanently) under the laws of any
jurisdiction to which the Seller is subject.

          (l)  Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

     Section 6.02  CONDITIONS PRECEDENT TO OBLIGATIONS OF THE SELLER.  The
obligations of the Seller to issue and sell Securities hereunder is subject, on
the Funding Date, to the prior or simultaneous satisfaction or waiver of the
following conditions:

          (a)  The representations and warranties made by the Purchasers herein
shall be true and correct in all respects on and as of the Funding Date with the
same effect as though such representations and warranties had been made on and
as of the Funding Date.

          (b)  The Purchasers shall have accepted delivery of and made payment
for the Securities.

          (c)  The issuance of the Securities by the Seller shall not as of the
Funding Date be enjoined (temporarily or permanently) under the laws of any
jurisdiction to which the Seller is subject.

                                      -25-
<PAGE>   30
 
          (d)  Each of the Basic Documents shall have been executed and
delivered by all the respective parties thereto and shall be in full force and
effect.

     Section 6.03  CONDITIONS PRECEDENT TO THE OBLIGATIONS OF PURCHASERS AND 
SELLER.  The obligations of the Purchasers and Seller hereunder are contingent
upon the Funding Date  occurring on or before 5:00 p.m., Houston, Texas time on
September 1, 1998.

                                  ARTICLE VII
                             AFFIRMATIVE COVENANTS

     Unless the prior written consent to the contrary is obtained from (i) the
holders of the majority of the Warrants (as to Sections 7.01 and 7.02) and (ii)
ECT (as to Sections 7.03 and 7.04) the Seller will, for the benefit of each of
the holders of the Warrants or Warrant Shares and the holders of the Acquired
Shares, comply with the covenants contained in this Article VII (or cause each
Subsidiary's compliance with the applicable covenants).

     Section 7.01  WARRANTS.  Seller shall at all times during the term of
the Warrants maintain a sufficient number of shares of Common Stock of the
Seller to be issued as Warrant Shares upon the exercise of all or part of the
Warrants.  Seller shall (i) notify the holders of the Warrants promptly after
the exercise of any of the Warrants by a holder or holders thereof, of the
exercise thereof, (ii) provide to the holders of the Warrants such information
or materials in connection therewith as may be reasonably requested by the
holders of the Warrants, and (iii) otherwise provide to all the holders of the
Warrants copies of all notices provided to or from the Seller in connection with
the Warrants.  Seller's obligations under this Section 7.01 shall expire upon
expiration of the term of the Warrants.

     Section 7.02  HART-SCOTT-RODINO COMPLIANCE.  As soon as practicable
after the receipt from any holder of the Warrants or any Seller (the "Notice
Giver") of notice of the exercise of a number of Warrants sufficient to require
a filing under the Hart-Scott-Rodino Antitrust Improvements Act of 1976 and the
rules, regulations and formal interpretations thereunder, as amended from time
to time (the "HSR Act"), but in any event no later than the 10th Business Day
after receipt of such notice, the Seller will (i) prepare and file with the
Antitrust Division of the Department of Justice (the "DOJ") and the Federal
Trade Commission (the "FTC") the Notification and Report Form (accompanied by
all documentary attachments contemplated thereby) required by the HSR Act, (ii)
upon the request of any holder of the Warrants (the "Notice Giver"), request
early termination of the waiting period imposed by the HSR Act, (iii) coordinate
and cooperate with the Notice Giver in responding to formal and informal
requests for additional information and documentary material from the DOJ and
the FTC in connection with such filing, and (iv) use its best efforts to take,
or cause to be taken, all reasonable action and to do, or cause to be done, all
things reasonably necessary and appropriate to permit the issuance to the Notice
Giver of the shares of common stock issuance upon the exercise of the warrants
with respect to which any filing is required under the HSR Act, and (v)
reimburse the holders of the Warrants for the entire amount of any filing fee or
any other costs and expenses incurred by holders of the Warrants in connection
therewith (including legal fees), or as required to be paid under the HSR Act.
Seller's obligations under this Section 7.02 shall expire one (1) year following
the expiration of the term of the Warrants.

                                      -26-
<PAGE>   31
 
     Section 7.03  BOARD REPRESENTATION.  ECT or its designated Affiliate
(the "Acting Party") shall have the right (a) to designate one member of the
Board of Directors of the Seller or (b) (i) to receive (and Seller covenants and
agrees to deliver to the Acting Party) prior notice of any proposed board action
and to receive (and Seller covenants and agrees to deliver to the Acting Party)
reasonable notice of and a right to attend any meeting of the Seller's Board of
Directors, (ii) to receive (and Seller covenants and agrees to deliver to the
Acting Party), promptly after they are produced, all management reports and
accounts relating to the Seller that are provided to Seller's Board of Directors
or any committee of the Board of Directors and (iii) upon reasonable notice, to
have reasonable access to the books and records of the Seller, including
statutory books, minute books and customer lists.  In the event the Acting Party
elects to designate a person to serve as a member of the Board of Directors of
the Seller (the "Designee"), the Seller shall (x) expand as required the number
of directors constituting the entire board, (y) fill the vacancy created by such
expansion with such Designee and (z) submit the name of such Designee to the
stockholders of the Seller (together with a recommendation of his or her
election) at each meeting of stockholders at which directors are elected, until
requested otherwise by the Acting Party. The obligations of the Seller pursuant
to this Section 7.03 shall continue in full force and effect for so long as the
ECT and JEDI-II and/or their respective Affiliates beneficially own 5% or more
of the outstanding Common Stock of the Seller (including the Warrant Shares
represented by the Warrants, whether exercised or not).  Any Designee shall
agree to resign at the request of the Seller, at any time after the expiration
of the rights of the ECT and any Acting Party pursuant to this Section 7.03.
The rights of ECT under this Section 7.03 shall not be assignable other than to
an Affiliate of ECT.

     Section 7.04  COMMON STOCK; DIVIDENDS; VOTING RIGHTS.  The declaration
of dividends by the Seller shall be solely at the discretion of the Board of
Directors of the Seller.  Except for holders of Common Stock, no other class of
Capital Stock of the Seller shall have any voting rights whatsoever, either
separately or in conjunction with the Common Stock.  Seller's obligations under
this Section 7.04 shall expire upon payment of the Notes in full.


                                 ARTICLE VIII
                        [OMITTED BY THE PARTIES HERETO]


                                  ARTICLE IX
                        [OMITTED BY THE PARTIES HERETO]


                                   ARTICLE X
                        [OMITTED BY THE PARTIES HERETO]


                                  ARTICLE XI
                        [OMITTED BY THE PARTIES HERETO]

                                      -27-
<PAGE>   32
 
                                  ARTICLE XII
                                 MISCELLANEOUS

     Section 12.01.  INTERPRETATION AND SURVIVAL OF PROVISIONS.  Article,
Section, Schedule, and Exhibit references are to this Agreement, unless
otherwise specified.  All references to instruments, documents, contracts, and
agreements are references to such instruments, documents, contracts, and
agreements as the same may be amended, supplemented, and otherwise modified from
time to time, unless otherwise specified.  The word "including" shall mean
"including but not limited to."  Whenever the Seller has an obligation under the
Basic Documents, the expense of complying with that obligation shall be an
expense of the Seller unless otherwise specified.  Whenever any determination,
consent, or approval is to be made or given by the Purchasers, any holder of the
Warrants or the Acquired Shares, such action shall be in such Person's sole
discretion unless otherwise specified in this Agreement.  If any provision in
the Basic Documents is held to be illegal, invalid, not binding, or
unenforceable, such provision shall be fully severable and the Basic Documents
shall be construed and enforced as if such illegal, invalid, not binding, or
unenforceable provision had never comprised a part of the Basic Documents, and
the remaining provisions shall remain in full force and effect.  The Basic
Documents have been reviewed and negotiated by sophisticated parties with access
to legal counsel and shall not be construed against the drafter.  The
representations, warranties, and covenants made in this Agreement, the Notes or
any other Basic Document shall remain operative and in full force and effect
regardless of (a) any investigation made by or on behalf of the Seller or the
Purchasers or (b) acceptance of any of the Securities and payment therefor and
repayment or repurchase thereof.  All indemnification obligations of the Seller
and the provisions of Section 12.02 shall remain operative and in full force and
effect unless such obligations are expressly terminated in a writing referencing
those individual Sections, regardless of any purported general termination of
this Agreement.

     Section 12.02  COSTS, EXPENSES AND TAXES. 

          (a)   Intentionally Deleted.

          (b)   The Seller agrees to indemnify the Purchasers, and their
respective officers, directors, employees, representatives, agents, attorneys,
and Affiliates (collectively, "Related Parties") from, hold each of them
harmless against and promptly upon demand pay or reimburse each of them for, any
and all actions, suits, proceedings (including any investigations, litigation,
or inquiries), claims, demands, and causes of action by third parties, and, in
connection therewith, all reasonable costs, losses, liabilities, damages, or
expenses of any kind or nature whatsoever (collectively the "INDEMNITY MATTERS")
which may be incurred by or asserted against or involve any of them (whether or
not any of them is designated a party thereto) as a result of, arising out of,
or in any way related to (i) any actual or proposed use by the Seller of the
proceeds of any sale of the Securities, (ii) the operations of the business of
the Seller or any Subsidiary, (iii) any bodily injury or death or property
damage occurring in or upon or in the vicinity of any Collateral, (iv) any claim
by any third Person against any Collateral assigned to or paid to any Noteholder
pursuant to any Collateral Document, (v) the failure of the Seller or any
Subsidiary to comply with any Governmental Requirement, or (vi) any other aspect
of this Agreement and the other Basic 

                                      -28-
<PAGE>   33
 
Documents, including, without limitation, the reasonable fees and disbursements
of counsel and all other reasonable expenses incurred in connection with
investigating, defending or preparing to defend any such action, suit,
proceeding (including any investigations, litigation, or inquiries), or claim
and INCLUDING ALL INDEMNITY MATTERS ARISING BY REASON OF THE ORDINARY NEGLIGENCE
OF ANY INDEMNITEE (but excluding all Indemnity Matters arising solely by reason
of claims between the Purchasers or any Purchaser's shareholders against any
Purchaser or by reason of the gross negligence or wilful misconduct of any
Indemnitee).

          (c)  The Seller agrees to pay and hold the Purchasers harmless from
and against any and all present and future stamp and other similar taxes with
respect to this Agreement and the  Equity Documents and save the Purchasers
harmless from and against any and all liabilities with respect to or resulting
from any delay or omission to pay such taxes, and will indemnify the Purchasers
for the full amount of taxes paid by the Purchasers in respect of payments made
or to be made under this Agreement, any other Equity Document and any liability
(including penalties, interest, and expenses) arising therefrom or with respect
thereto, whether or not such taxes were correctly or legally asserted.

          (d)  In the case of any indemnification hereunder, the Purchaser or
other Person indemnified hereunder shall give notice to the Seller within a
reasonable period of time of any such claim or demand being made against the
Purchaser or other indemnified Person and the Seller, at its sole cost and
expense, shall provide a defense of such claim, provided, however, that, (i) if
the Seller has failed to assume the defense and employ counsel or (ii) if the
defendants in any such action include both the indemnified party and the Seller
or any Subsidiary and counsel to the indemnified party shall have concluded that
there may be reasonable defenses available to the indemnified party that are
different from or additional to those available to the Seller or such Subsidiary
or if the interests of the indemnified party reasonably may be deemed to
conflict with the interest of the Seller or such Subsidiary, then the
indemnified party shall have the right to select a separate counsel and to
assume such legal defense and otherwise to participate in the defense of such
action, with the expenses and fees of such separate counsel and other expenses
related to such participation to be reimbursed by the Seller as incurred.

          (e)  No indemnitee may settle any claim to be indemnified without the
consent of the indemnitor, such consent not to be unreasonably withheld;
provided, that the indemnitor may not reasonably withhold consent to any
settlement that an indemnitee proposes if the indemnitor does not have the
financial ability to pay all its obligations outstanding and asserted against
the indemnitee at that time, including the maximum potential claims against the
indemnitee to be indemnified pursuant to this Section 12.02.

          (f)  This Section 12.02 shall not apply to actions, suits,
proceedings, investigations, demands, losses, liabilities, claims, damages,
deficiencies, interest, judgements, costs, or expenses relating to any Property
to the extent arising from the acts or omissions of the Agent or any Noteholder
during the period after which such Person, its successors or assigns shall have
acquired possession of such Property (whether through foreclosure or deed in
lieu of foreclosure, as mortgagee in possession or otherwise).

                                      -29-
<PAGE>   34
 
          (g)  The Seller's obligations under this Section 12.02 shall survive
any termination of this Agreement and the payment of the Obligations.

     Section 12.03  NO WAIVER; MODIFICATIONS IN WRITING. 

          (a)  No failure or delay on the part of the Seller or the Purchasers
in exercising any right, power, or remedy hereunder shall operate as a waiver
thereof, nor shall any single or partial exercise of any such right, power, or
remedy preclude any other or further exercise thereof or the exercise of any
right, power, or remedy.  The remedies provided for herein are cumulative and
are not exclusive of any remedies that may be available to the Seller or the
Purchasers at law or in equity or otherwise.

          (b)  Except as otherwise provided herein, no amendment, waiver,
consent, modification, or termination of any provision of this Agreement, shall
be effective unless signed by the Seller and the holders of more than 50% of the
outstanding principal balance of the Notes and the holders of more than 50% of
the Warrants.  Any amendment, supplement or modification of or to any provision
of this Agreement or any other Equity Document, any waiver of any provision of
this Agreement or any other Equity Document, and any consent to any departure by
the Seller from the terms of any provision of this Agreement or any other Equity
Document, shall be effective only in the specific instance and for the specific
purpose for which made or given.  Except where notice is specifically required
by this Agreement, no notice to or demand on the Seller in any case shall
entitle the Seller to any other or further notice or demand in similar or other
circumstances.

     Section 12.04  BINDING EFFECT; ASSIGNMENT.  This Agreement shall be
binding upon the Seller and the Purchasers, and their respective successors and
permitted assigns. Except as expressly provided in this Agreement, this
Agreement shall not be construed so as to confer any right or benefit upon any
Person other than the parties to this Agreement, and their respective successors
and permitted assigns.  Subject to applicable federal and state securities laws
the rights and obligations of the Purchasers under this Agreement with respect
to the Warrants and the Equity Documents may be sold, assigned or pledged by any
Purchaser, in whole or in part, in accordance with the provisions of the
Warrants, and upon any such assignment, the holders of the Warrants shall
succeed to all of the selling Purchaser's rights and obligations under this
Agreement with respect to the Warrants and the Equity Documents to the extent
assigned and the selling Purchaser shall be automatically released from any
obligations thereunder with respect to the Warrants and the Equity Documents to
the extent assigned.  Subject to applicable federal and state securities laws
the Acquired Shares may be sold, assigned or pledged subject only to the
Registration Rights Agreement and upon any such assignment the holders of the
Acquired Shares shall succeed to the Purchaser's rights and obligations under
the Registration Rights Agreement.  Upon request of any Purchaser in connection
with any transfer of the Warrants or Acquired Shares, the Seller shall execute
and deliver any amendment to this Agreement, the Warrants, and the other Equity
Documents reasonably requested by the Purchaser to reflect the transfer and
delineate the rights of the transferor and the transferee.

     Section 12.05  REPLACEMENT SECURITIES.  Upon receipt of evidence
satisfactory to the Seller of the loss, theft, destruction, or mutilation of any
Warrants, Warrant Shares or Acquired Shares and, 

                                      -30-
<PAGE>   35
 
in the case of any such loss, theft, or destruction, upon delivery of any
unsecured letter of indemnity reasonably satisfactory to the Seller or, in the
case of any such mutilation, upon surrender or cancellation thereof, the Seller
will issue a new Warrants, Warrant Shares or Acquired Shares, as applicable.

     Section 12.06  COMMUNICATIONS.  All notices and demands provided for
hereunder shall be in writing and shall be given by registered or certified
mail, return receipt requested, telecopy, air courier guaranteeing overnight
delivery or personal delivery to the following addresses:

     If to the Purchasers:

     Enron Capital Management II Limited Partnership
     c/o Enron Capital II Corp.
     1400 Smith Street
     Houston, Texas 77002
     Attention: Shirley Hudler
     Telecopier: (713) 646-8008

     and

     Enron Capital & Trade Resources Corp.
     1400 Smith Street
     Houston, Texas 77002
     Attention: Donna Lowry
     Telecopier: (713) 646-4039

     If to the Seller:

     6300 Bridge Point Parkway
     Building 2, Suite 500
     Austin, Texas 78730
     Attention: Craig M. Fleming
     Telecopier: (512) 472-3400

or to such other address as the Seller or any Purchaser may designate in
writing.  All other communications may be by regular mail.  All notices and
communications shall be deemed to have been duly given:  at the time delivered
by hand, if personally delivered; four days after being sent by certified mail,
return receipt requested, if mailed; when receipt acknowledged, if telecopied;
and on the next Business Day if timely delivered to an air courier guaranteeing
overnight delivery.

     Section 12.07  GOVERNING LAW.  This Agreement will be construed in
accordance with and governed by the laws of the State of Texas without regard to
principles of conflicts of laws.


                                      -31-
<PAGE>   36

     Section 12.08  ARBITRATION.
 
          (a)  BINDING ARBITRATION.  Subject to the provisions of subparagraph
(e), on the request of either the Seller or any Purchaser, whether made before
or after the institution of any legal proceeding, any action, dispute, claim or
controversy of any kind now existing or hereafter arising between any of the
parties hereto in any way arising out of, pertaining to or in connection with
this Agreement (a "Dispute") shall be resolved by binding arbitration in
accordance with the terms hereof.  Either the Seller or any Purchaser may, by
summary proceedings, bring an action in court to compel arbitration of any
Dispute.

          (b)  GOVERNING RULES.  Any arbitration shall be administered by the
American Arbitration Association (the "AAA") in accordance with the terms of
this Section, the Commercial Arbitration Rules of the AAA, and, to the maximum
extent applicable, the Federal Arbitration Act.  Judgment on any award rendered
by an arbitrator may be entered in any court having jurisdiction.

          (c)  ARBITRATORS.  Any arbitration shall be conducted before a three
person panel of neutral arbitrators. Such panel shall consist of one person from
each of the following categories: (1) an attorney who has practiced in the area
of commercial law for at least 10 years or a retired judge at the Texas or
United States District Court or an appellate court level; (2) a person with at
least 10 years experience in commercial lending; and (3) a person with at least
10 years experience in the energy service industry. The AAA shall submit a list
of persons meeting the criteria outlined above for each category of arbitrator,
and the parties shall select one person from each category in the manner
established by the AAA. If the parties cannot agree on an arbitrator within 30
days after the request for an arbitration, then any party may request the AAA to
select an arbitrator. The arbitrator may engage engineers, accountants or other
consultants that the arbitrator deems necessary to render a conclusion in the
arbitration proceeding.

          (d)  CONDUCT OF ARBITRATION.  To the maximum extent practicable, an
arbitration proceeding hereunder shall be concluded within 180 days of the
filing of the Dispute with the AAA.  Arbitration proceedings shall be conducted
in Houston, Texas.  At the conclusion of any arbitration proceeding, the
arbitrator shall make specific written findings of fact and conclusions of law.
The arbitrator shall have the power to award recovery of all costs and fees to
the prevailing party.  The Seller and the Purchasers each agree to keep all
Disputes and arbitration proceedings strictly confidential except for disclosure
of information required by applicable law.

          (e)  COSTS OF ARBITRATION.  All fees of the arbitrator and any
engineer, accountant or other consultant engaged by the arbitrator, shall be
paid by the Seller (as to 50%) and the Purchasers (as to 50%) unless otherwise
awarded by the arbitrator.

     Section 12.09  EXECUTION IN COUNTERPARTS.  This Agreement may be executed
in any number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together, shall
constitute but one and the same Agreement.

                                      -32-
<PAGE>   37
 
          IN WITNESS WHEREOF, the parties hereto execute this Agreement,
effective as of the date first above written.

                              BRIGHAM EXPLORATION COMPANY,
                              a Delaware corporation



                              By:  /s/ CRAIG M. FLEMING
                                  ---------------------------------------------
                                    Craig M. Fleming
                                    Chief Financial Officer

                                      -33-
<PAGE>   38
 
                              JOINT ENERGY DEVELOPMENT
                              INVESTMENTS II LIMITED PARTNERSHIP,
                              a Delaware limited partnership, as Purchaser


                              By:  Enron Capital Management II Limited
                                   Partnership, its General Partner

                                  By:  Enron Capital II Corp., its
                                       General Partner


                                         By: /s/ MARK J. WARNER
                                             ----------------------------------
                                         Name:   Mark J. Warner
                                               --------------------------------
                                         Title:  Agent and Attorney-in-Fact
                                                -------------------------------


                              ENRON CAPITAL & TRADE RESOURCES
                              CORP., a Delaware corporation



                              By: /s/ MARK J. WARNER
                                  --------------------------------------------
                              Name:   Mark J. Warner
                                    ------------------------------------------
                              Title:  Agent and Attorney-in-Fact
                                     -----------------------------------------

                                      -34-

<PAGE>   1
                                                                   EXHIBIT 10.39


                         REGISTRATION RIGHTS AGREEMENT

     This Registration Rights Agreement (this "Agreement") is made and entered
into as of August 20, 1998, by and among Brigham Exploration Company, a Delaware
corporation (the "Company"), Joint Energy Development Investments II Limited
Partnership, a Delaware limited partnership ("JEDI"), and Enron Capital & Trade
Resources Corp., a Delaware corporation ("ECT").

     This Agreement is made pursuant to the Securities Purchase Agreement.  In
order to induce ECT and JEDI to enter into the Securities Purchase Agreement,
the Company has agreed to provide the registration and other rights set forth in
this Agreement.  Pursuant to the Securities Purchase Agreement, ECT and JEDI
will purchase the Acquired Shares and Warrants.  The execution and delivery of
this Agreement is a condition to the Closing (as defined in the Securities
Purchase Agreement).

     The parties agree as follows:

                                 ARTICLE I

     Section 1.01.  Definitions.  Capitalized terms used herein without
definition shall have the meanings given to them in the Securities Purchase
Agreement.  The terms set forth below are used herein as so defined:

          "Commission" has the meaning specified therefor in Section 1.02 of
this Agreement.

          "Common Stock" means the common stock, par value $0.01 per share, of
the Company.

          "Exchange Act" shall mean the Securities Exchange Act of 1934, as
amended, and the rules and regulations promulgated thereunder.

          "Holder" means the record holder of any Registrable Securities.

          "Inspector" has the meaning specified therefor in Section 2.03 this
Agreement.

          "Losses" has the meaning specified therefor in Section 2.07 of this
Agreement.

          "Other Holders" has the meaning specified therefor in Section 2.01 of
this Agreement.

          "Person" means any individual, corporation, limited liability company,
partnership, joint venture, association, joint-stock company, business trust,
trust or unincorporated entity.

          "Records" has the meaning specified therefor in Section 2.03 of this
Agreement.

<PAGE>   2
 
          "Registrable Securities" means the Acquired Shares, the Warrants, the
Warrant Shares and any other securities issued upon the exercise of the
Warrants, until such time as such securities cease to be Registrable Securities
pursuant to Section 1.02 hereof.

          "Requesting Holder(s)" has the meaning specified therefor in Section
2.01 of this Agreement.

          "Request Notice" has the meaning specified therefor in Section 2.01 of
this Agreement.

          "Registration Statement" has the meaning specified therefor in Section
2.01 of this Agreement.

          "Securities Act" has the meaning specified therefor in Section 1.02 of
this Agreement.

          "Securities Purchase Agreement" means the Securities Purchase
Agreement, dated as of August 20, 1998, among the Company, ECT and JEDI,
individually and as agent.

          "Selling Holder" means a Holder who is selling Registrable Securities
pursuant to a Registration Statement.

     Section 1.02.  Registrable Securities.  Any Registrable Security will cease
to be a Registrable Security when (i) a Registration Statement covering such
Registrable Security has been declared effective by the Securities and Exchange
Commission (the "Commission") and such Registrable Security has been sold or
disposed of pursuant to such effective Registration Statement; (ii) such
Registrable Security is disposed of pursuant to Rule 144 (or any similar
provision then in force) under the Securities Act of 1933, as amended (the
"Securities Act");  (iii) such Registrable Security is eligible to be, and at
the time of determination can be, disposed of pursuant to paragraph (k) of Rule
144 (or any similar provision then in force) under the Securities Act; or (iv)
such Registrable Security is held by the Company or one of its subsidiaries.

                                 ARTICLE II

     Section 2.01.  Demand Registration. (a) Any time after the Funding Date, as
defined in the Securities Purchase Agreement, (i) any Holder or Holders who
collectively beneficially own at least 25% (twenty-five percent) of the
Registrable Securities may request (a "Request Notice") the Company to register
under the Securities Act (other than pursuant to a shelf registration on Form S-
3) all or any portion of the Registrable Securities that are held by such Holder
or Holders (collectively, the "Requesting Holder") for sale in the manner
specified in the Request Notice and (ii) in the event that the Company is
eligible to file a Registration Statement on Form S-3, any Holders who
collectively beneficially own at least a majority of the Registrable Securities
may submit a Request Notice to the Company to register under Form S-3 all or any
portion of the Registrable Securities that are held by such Requesting Holder(s)
for sale in the manner specified in the Request Notice.

                                       2
<PAGE>   3
 
          (b) Promptly following receipt of a Request Notice, the Company shall
immediately notify each Holder (except the Requesting Holder) of the receipt of
a Request Notice and shall use its best efforts to file a registration statement
under the Securities Act (each such registration statement is hereinafter
referred to as a "Registration Statement") effecting the registration under the
Securities Act, for public sale in accordance with the method of disposition
specified in such Request Notice, of the Registrable Securities specified in the
Request Notice (and in any notices that the Company receives from other Holders
no later than the 15th day after receipt of the notice sent by the Company)
(such other Holders and the Requesting Holder are hereinafter referred to as the
"Requesting Holders").  If such method of disposition shall be an underwritten
public offering, the Requesting Holders holding a majority of the Registerable
Securities to be registered may designate the managing underwriter of such
offering, subject to the approval of the Company, which approval shall not be
withheld unreasonably.  The Company shall be obligated to register Registrable
Securities pursuant to this Section 2.01 on two occasions only.  A request
pursuant to this Section 2.01 shall be counted ("Counted") only when (i) all the
Registrable Securities requested to be included in any such registration have
been so included, (ii) the corresponding Registration Statement has become
effective under the Securities Act, and (iii) the public offering has been
consummated and the Registrable Securities have been sold on the terms and
conditions specified therein; provided, however, that in the event of a shelf
registration if the Company is then eligible to file a Registration Statement on
Form S-3, the Company shall keep such Registration Statement effective for two
years from the effective date of the Registration Statement.

          (c) The Company may delay the filing or effectiveness of a
Registration Statement after receipt of a Request Notice (i) for up to 90 days
if at the time of such request, the Company is engaged in a firm commitment
underwritten public offering of its securities in which Holders may include
Registrable Securities and for which the Company has delivered the notice to the
Holders required by Section 2.02 or (ii) for up to 60 days if at the time of
such request the Board of Directors of the Company determines in its reasonable
judgment and in good faith that the filing of such a Registration Statement or
the making of any required disclosure in connection therewith would have a
material adverse effect on the Company or substantially interfere with a
significant transaction in which the Company is then engaged; provided that the
Company may not delay the filing of a Registration Statement in reliance on this
clause (ii) more than once during any period of twelve consecutive calendar
months.

          (d) The Company and the parties to the Registration Rights Agreement
with the Company dated February 26, 1997, who are entitled to piggy-back
registration rights as of the Closing Date ("Other Holders") with respect to a
Registration Statement filed pursuant to Section 2.01 may include securities of
the Company in such Registration Statement, but only to the extent that, in the
good faith opinion of the managing underwriter (if such method of disposition
shall be an underwritten public offering) supported by written reasons therefor,
the inclusion of such shares would not raise a substantial doubt as to whether
the proposed offering could successfully be consummated.  Subject to Section
2.01(c) above, except as provided in this subsection (d), the Company will not
effect any other registration of its equity securities (except with respect to
Registration Statements on Form S-4 or S-8 or for purposes permissible under
such forms as of the date hereof), whether for its own account or that of any
Other Holder, from the date of receipt of a 

                                       3
<PAGE>   4
 
Request Notice related to an underwritten public offering until the completion
of the distribution by the underwriters of all securities thereunder.

          (e) Exercise of the right to convert the Warrants to Warrant Shares
shall at the Holder's sole election and discretion be contingent upon the
registration of the Warrant Shares in accordance with this Agreement and should
such registration not be completed pursuant to the terms hereof, Holder shall
have the right, at its sole discretion, to rescind its election to convert the
Warrants.

          (f) From and after the date of this Agreement and until no Registrable
Securities remain outstanding, the Company shall not grant registration rights
to any Person if such rights would conflict with the provisions of this
Agreement.

          Section 2.02.  Piggy-Back Registration.  If the Company proposes to
register any of its equity securities under the Securities Act for sale to the
public, whether for its own account or for the account of Other Holders or both
(except with respect to Registration Statements on Forms S-4 or S-8 or for
purposes permissible under such forms as of the date hereof), each such time it
will give written notice to all Holders of its intention to do so no less than
20 days prior to the anticipated filing date.  Upon the written request received
by the Company from any Holder no later than the 15th day after receipt by such
Holder of the notice sent by the Company (which request shall state the intended
method of disposition thereof),  the Company will use best efforts to cause the
Registrable Securities as to which registration shall have been so requested to
be included in the securities to be covered by such Registration Statement, all
to the extent requisite to permit the sale or other disposition by each Holder
(in accordance with its written request) of such Registrable Securities so
registered; provided, however, that the Company may at any time prior to the
effectiveness of any such Registration Statement, in its sole discretion and
without the consent of any Holder, abandon any proposed offering by the Company
in which any Holder had requested to participate.  The number of Registrable
Securities to be included in such a registration may be reduced or eliminated if
and to the extent, in the case of an underwritten offering, the managing
underwriter shall advise the Company that such inclusion would materially
jeopardize the successful marketing of the securities (including the Registrable
Securities) proposed to be sold therein; provided, however, that such number of
shares of Registrable Securities shall not be reduced if any securities included
in such registration are included other than for the account of the Company
unless the shares included in the Registration for the account of such Persons
are also reduced on a pro rata basis, provided, in the case of a Registration
Statement filed pursuant to the exercise of demand registration rights of any
Other Holders, priority shall be given first to the Other Holders demanding such
registration.

          Section 2.03.  Registration Procedures.  If and whenever the Company
is required pursuant to this Agreement to effect the registration of any of the
Registrable Securities under the Securities Act, the Company will, as
expeditiously as possible:

          (a) prepare and file with the Commission a Registration Statement, on
a form available to the Company, with respect to such securities (which filing
shall be made (i) as promptly 

                                       4
<PAGE>   5
 
as possible (but in no event later than 30 days after the receipt by the Company
of a Request Notice) in the case of a shelf registration if the Company is then
eligible to file a Registration Statement on Form S-3 or (ii) as promptly as
possible (but in no event later than 60 days after the receipt by the Company of
a Request Notice) in the case of any underwritten offering or if the Company is
not eligible to file a Registration Statement on Form S-3, provided that in no
event will the Company be obligated to file a Registration Statement pursuant to
(i) or (ii) prior to the Funding Date pursuant to the Securities Purchase
Agreement. The Company shall thereafter use best efforts to cause such
Registration Statement to become and remain effective for the period of the
distribution in order for it to be Counted;

          (b) prepare and file with the Commission such amendments and
supplements to such Registration Statement and the prospectus used in connection
therewith as may be necessary to keep such Registration Statement effective for
the distribution period to be Counted and as may be necessary to comply with the
provisions of the Securities Act with respect to the disposition of all
securities covered by such Registration Statement in accordance with the Holders
intended method of disposition;

          (c) furnish to each Selling Holder and to each underwriter such number
of copies of the Registration Statement and the prospectus included therein
(including each preliminary prospectus and each document incorporated by
reference therein to the extent then required by the rules and regulations of
the Commission) as such Persons may reasonably request in order to facilitate
the public sale or other disposition of the Registrable Securities covered by
such Registration Statement;

          (d) if applicable, use best efforts to register or qualify the
Registrable Securities covered by such Registration Statement under the
securities or blue sky laws of such jurisdictions as the Selling Holders or, in
the case of an underwritten public offering, the managing underwriter, shall
reasonably request, provided that the Company will not be required to qualify
generally to transact business in any jurisdiction where it is not then required
to so qualify or to take any action that would subject it to general service of
process in any such jurisdiction where it is not then so subject;

          (e) immediately notify each Selling Holder and each underwriter, at
any time when a prospectus relating thereto is required to be delivered under
the Securities Act, of the happening of any event as a result of which the
prospectus contained in such Registration Statement, as then in effect, includes
an untrue statement of a material fact or omits to state any material fact
required to be stated therein or necessary to make the statements therein not
misleading in the light of the circumstances then existing and as promptly as
practicable amend or supplement the prospectus or take other appropriate action
so that the prospectus does not include an untrue statement of a material fact
or omit to state a material fact required to be stated therein or necessary to
make the statements therein not misleading in the light of the circumstances
then existing;

          (f) in the case of an underwritten public offering, furnish upon
request, (i) on the date that Registrable Securities are delivered to the
underwriters for sale pursuant to such 

                                       5
<PAGE>   6
 
Registration Statement, an opinion of counsel for the Company dated as of such
date and addressed to the underwriters and to the Selling Holders, stating that
such Registration Statement has become effective under the Securities Act and
that (A) to the best knowledge of such counsel, no stop order suspending the
effectiveness thereof has been issued and no proceedings for that purpose have
been instituted or are pending or contemplated under the Securities Act, (B) the
Registration Statement, the related prospectus, and each amendment or supplement
thereof, comply as to form in all material respects with the requirements of the
Securities Act and the applicable rules and regulations thereunder of the
Commission (except that such counsel need express no opinion as to the financial
statements, or any expertized schedule, report or information contained or
incorporated therein) and (C) to such other effects as may reasonably be
requested by counsel for the underwriters, and (ii) on the effective date of the
Registration Statement and on the date that Registrable Securities are delivered
to the underwriters for sale pursuant to such Registration Statement, a letter
dated such dates from the independent accountants retained by the Company,
addressed to the underwriters and, if available, to the Selling Holders, stating
that they are independent public accountants within the meaning of the
Securities Act and that, in the opinion of such accountants, the financial
statements of the Company and the schedules thereto that are included or
incorporated by reference in the Registration Statement or the prospectus, or
any amendment or supplement thereof, comply as to form in all material respects
with the applicable requirements of the Securities Act and the published rules
and regulations thereunder, and such letter shall additionally address such
other financial matters (including information as to the period ending no more
than five business days prior to the date of such letter) included in the
Registration Statement in respect of which such letter is being given as the
underwriters may reasonably request;

          (g) make available for inspection by the Selling Holders designated by
a majority thereof, any underwriter participating in any distribution pursuant
to such Registration Statement, and any attorney, accountant or other agent
retained by such representative of the Selling Holders or underwriter (the
"Inspectors"),  all financial and other records, pertinent corporate documents
and properties of the Company (collectively, the "Records"), and cause the
Company's officers, directors and employees to supply all information reasonably
requested by any such Inspector in connection with such Registration Statement.

          (h) cause the Registerable Securities to be listed on New York Stock
Exchange, American Stock Exchange or on the NASDAQ National Market if the Common
Stock is or becomes so listed;

          (i) use best efforts to keep effective and maintain for the period of
distribution to be Counted, qualification, approval or listing obtained to cover
the Registrable Securities as may be necessary for the Selling Holders to
dispose thereof and shall from time to time amend or supplement any prospectus
used in connection therewith to the extent necessary in order to comply with
applicable law;

          (j) use best efforts to cause the Registrable Securities to be
registered with or approved by such other governmental agencies or authorities
as may be necessary by virtue of the 

                                       6
<PAGE>   7
 
business and operations of the Company to enable the Selling Holders to
consummate the disposition of such Registrable Securities; and

          (k) take such other actions as are reasonably requested by the Selling
Holders or the underwriters, if any, in order to expedite, facilitate or
consummate the disposition of such Registrable Securities.

     In connection with each registration hereunder with respect to an
underwritten public offering, the Company and each Selling Holder agrees to
enter into a written agreement with the managing underwriter or underwriters
selected in the manner herein provided in such form and containing such
provisions as are customary in the securities business for such an arrangement
between underwriters and companies of the Company's size and investment stature,
provided that such agreement shall not contain any such provision applicable to
the Company or the Selling Holders that is inconsistent with the provisions
hereof; and further provided, that the time and place of the closing under said
agreement shall be as mutually agreed upon among the Company, the Selling
Holders and such managing underwriter.  In connection with each registration
hereunder, each Selling Holder will furnish promptly to the Company in writing
such information with respect to itself and the proposed distribution by it as
shall be necessary in order to ensure compliance with federal and applicable
state securities laws.

     Section 2.04.  Restrictions on Public Sale by Selling Holders of
Registrable Securities.   To the extent not inconsistent with applicable law,
including insurance codes, each Selling Holder whose Registrable Securities are
included in a Registration Statement pursuant to this Agreement agrees not to
effect any public sale or distribution of the issue being registered (or any
securities of the Company convertible into or exchangeable or exercisable for
securities of the same type as the issue being registered) during the 14 days
before, and during the 90-day period beginning on, the effective date of such
Registration Statement (except as part of such registration), but only if and to
the extent requested in writing (with reasonable prior notice) by the managing
underwriter or underwriters in the case of an underwritten public offering by
the Company of securities of the same type as the Registrable Securities,
provided that the duration of the foregoing restrictions shall be no longer than
the duration of the shortest restriction imposed by the underwriters on the
officers or directors or any other stockholder of the Company; and provided
further, that the period of time for which the Company is required to keep such
registration statement which includes Registrable Securities continuously
effective shall be increased by a period equal to such requested holdback
period.

     Section 2.05.  Restrictions on Public Sale by the Company.  To the extent
required by an underwriter in an underwritten public offering, the Company
agrees not to effect on its own behalf any public sale or distribution of any
securities similar to those being registered, or any securities convertible into
or exchangeable or exercisable for such securities, during the 14 days before,
and during the 90-day period beginning on, the effective date of any
registration statement in which the Selling Holders of Registrable Securities
are participating, other than pursuant to such registration statement or a
Registration Statement on Form S-8 or Form S-4.

                                       7
<PAGE>   8
 
     Section 2.06.  Expenses.

          (a)  "Registration Expenses" means all expenses incident to the
Company's performance under or compliance with this Agreement, including without
limitation, all registration and filing fees, blue sky fees and expenses,
printing expenses, listing fees, fees and disbursements of counsel and
independent public accountants for the Company, fees of the National Association
of Securities Dealers, Inc., transfer taxes, fees of transfer agents and
registrars, costs of insurance and reasonable out-of-pocket expenses (including
without limitation, reasonable legal fees of one counsel for all Selling
Holders), but excluding any Selling Expenses.  "Selling Expenses" means all
underwriting fees, discounts and selling commissions allocable to the sale of
the Registrable Securities.

          (b) The Company will pay all Registration Expenses in connection with
each Registration Statement filed pursuant to this Agreement, whether or not the
Registration Statement becomes effective, and the Selling Holders shall pay all
Selling Expenses in connection with any Registrable Securities registered
pursuant to this Agreement.

     Section 2.07.  Indemnification.  (a)   In the event of a registration of
any Registrable Securities under the Securities Act pursuant to this Agreement,
the Company will indemnify and hold harmless each Selling Holder thereunder and
each underwriter, pursuant to the applicable underwriting agreement with such
underwriter, of Registrable Securities thereunder and each Person, if any, who
controls such Selling Holder or underwriter within the meaning of the Securities
Act and the Exchange Act, against any losses, claims, damages or liabilities
(including reasonable attorneys' fees) ("Losses"), joint or several, to which
such Selling Holder or underwriter or controlling Person may become subject
under the Securities Act, the Exchange Act or otherwise, insofar as such Losses,
(or actions in respect thereof) arise out of or are based upon any untrue
statement or alleged untrue statement of any material fact contained in any
Registration Statement under which such Registrable Securities were registered
under the Securities Act pursuant to this Agreement, any preliminary prospectus
or final prospectus contained therein, or any amendment or supplement thereof,
or arise out of or are based upon the omission or alleged omission to state
therein a material fact required to be stated therein or necessary to make the
statements therein not misleading, and will reimburse each such Selling Holder,
each such underwriter and each such controlling Person for any legal or other
expenses reasonably incurred by them in connection with investigating or
defending any such Loss or actions; provided, however, that the Company will
not be liable in any such case if and to the extent that any such loss, claim,
damage or liability arises out of or is based upon an untrue statement or
alleged untrue statement or omission or alleged omission so made in conformity
with information furnished by such Selling Holder, such underwriter or such
controlling Person in writing specifically for use in such Registration
Statement or prospectus.

          (b) Each Selling Holder agrees to indemnify and hold harmless the
Company, its directors, officers, employees and agents and each Person, if any,
who controls the Company within the meaning of the Securities Act or of the
Exchange Act to the same extent as the foregoing indemnity from the Company to
such Selling Holder, but only with respect to information regarding such Selling
Holder furnished in writing by or on behalf of such Selling Holder expressly for

                                       8
<PAGE>   9
 
inclusion in any Registration Statement or prospectus relating to the
Registrable Securities, or any amendment or supplement thereto; provided,
however, that the liability of such Selling Holder shall not be greater in
amount than the dollar amount of the proceeds (net of any Selling Expenses)
received by such Selling Holder from the sale of the Registrable Securities
giving rise to such indemnification.

          (c) Promptly after receipt by an indemnified party hereunder of notice
of the commencement of any action, such indemnified party shall, if a claim in
respect thereof is to be made against the indemnifying party hereunder, notify
the indemnifying party in writing thereof, but the omission so to notify the
indemnifying party shall not relieve it from any liability which it may have to
any indemnified party.  In case any such action shall be brought against any
indemnified party and it shall notify the indemnifying party of the commencement
thereof, the indemnifying party shall be entitled to participate in and, to the
extent it shall wish, to assume and undertake the defense thereof with counsel
reasonably satisfactory to such indemnified party and, after notice from the
indemnifying party to such indemnified party of its election so to assume and
undertake the defense thereof, the indemnifying party shall not be liable to
such indemnified party under this Section 2.07 for any legal expenses
subsequently incurred by such indemnified party in connection with the defense
thereof other than reasonable costs of investigation and of liaison with counsel
as so elected; provided, however, that, (i) if the indemnifying party has failed
to assume the defense and employ counsel or (ii) if the defendants in any such
action include both the indemnified party and the indemnifying party and counsel
to the indemnified party shall have concluded that there may be reasonable
defenses available to the indemnified party that are different from or
additional to those available to the indemnifying party or that the interests of
the indemnified party reasonably may be deemed to conflict with the interests of
the indemnifying party, then the indemnified party shall have the right to
select a separate counsel and to assume such legal defense and otherwise to
participate in the defense of such action, with the expenses and fees of such
separate counsel and other expenses related to such participation to be
reimbursed by the indemnifying party as incurred.

          (d) If the indemnification provided for in this Section 2.07 is
unavailable to the Company or the Selling Holders or is insufficient to hold
them harmless in respect of any Losses, then each such indemnifying party, in
lieu of indemnifying such indemnified party, shall contribute to the amount paid
or payable by such indemnified party as a result of such Losses as between the
Company on the one hand and each Selling Holder on the other, in such proportion
as is appropriate to reflect the relative fault of the Company on the one hand
and of each Selling Holder on the other in connection with the statements or
omissions which resulted in such Losses, as well as any other relevant equitable
considerations.  The relative fault of the Company on the one hand and each
Selling Holder on the other shall be determined by reference to, among other
things, whether the untrue or alleged untrue statements of a material fact or
the omission or alleged omission to state a material fact has been made by, or
relates to, information supplied by such party, and the parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission.

                                       9
<PAGE>   10
 
          No person guilty of fraudulent misrepresentation (within the meaning
of Section 11(f) of the Securities Act) shall be entitled to contribution from
any Person who is not guilty of such fraudulent misrepresentation.

                                 ARTICLE III


     Section 3.01  Communications.  All notices and other communications
provided for or permitted hereunder shall be made in writing by telecopy,
courier service or personal delivery:

          (a) if to a Holder, at the most current address given by such Holder
to the Company in accordance with the provisions of this Section 3.01, which
address initially is, with respect to JEDI or ECT, the address set forth in the
Securities Purchase Agreement, and

          (b) if to the Company, initially at its address set forth in the
Securities Purchase Agreement, and

          (c) for each, thereafter at such other address, notice of which is
given in accordance with the provisions of this Section 3.01.

          All such notices and communications shall be deemed to have been
received at the time delivered by hand, if personally delivered; when receipt
acknowledged, if telecopied; and on the next business day if timely delivered to
an air courier guaranteeing overnight delivery.

     Section 3.02.  Successor and Assigns.  This Agreement shall inure to the
benefit of and be binding upon the successors and assigns of each of the
parties, including subsequent holders of Registrable Securities.

     Section 3.03.  Counterparts.  This Agreement may be executed in any number
of counterparts and by different parties hereto in separate counterparts, each
of which counterparts, when so executed and delivered, shall be deemed to be an
original and all of which counterparts, taken together, shall constitute but one
and the same Agreement.

     Section 3.04.  Headings.  The headings in this Agreement are for
convenience of reference only and shall not limit or otherwise affect the
meaning hereof.

     Section 3.05.  Governing Law.  THE LAWS OF THE STATE OF TEXAS SHALL GOVERN
THIS AGREEMENT WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS.

     Section 3.06.  Severability of Provisions.  Any provision of this Agreement
which is prohibited or unenforceable in any jurisdiction shall, as to such
jurisdiction, be ineffective to the extent of such prohibition or
unenforceability without invalidating the remaining provisions hereof or
affecting or impairing the validity or enforceability of such provision in any
other jurisdiction.

                                       10
<PAGE>   11
 
     Section 3.07.  Entire Agreement.  This Agreement, together with the
Securities Purchase Agreement and the other Basic Documents (as defined in the
Securities Purchase Agreement) are  intended by the parties as a final
expression of their agreement and intended to be a complete and exclusive
statement of the agreement and understanding of the parties hereto in respect of
the subject matter contained herein.  There are no restrictions, promises,
warranties or undertakings, other than those set forth or referred to herein
with respect to the registration rights granted by the Company with respect to
the securities sold pursuant to the Securities Purchase Agreement.  This
Agreement, the Securities Purchase Agreement and the other Basic Documents
supersede all prior agreements and understandings between the parties with
respect to such subject matter.

     Section 3.08.  Attorneys' Fees.  In any action or proceeding brought to
enforce any provision of this Agreement, the successful party shall be entitled
to recover reasonable attorneys' fees in addition to its costs and expenses and
any other available remedy.

     Section 3.09.  Amendment.  This Agreement may be amended only by means of a
written amendment signed by the Company and by the Holders of a majority of the
Registrable Securities.

     Section 3.10.  Registrable Securities Held by the Company or Its
Affiliates.  In determining whether the Holders of the required amount of
Registrable Securities have concurred in any direction, amendment, supplement,
waiver or consent, Registrable Securities owned by the Company or one of its
Affiliates shall be disregarded.

     Section 3.11.  Assignment of Rights.   The rights of any Holder under this
Agreement may be assigned to any Person who acquires any Registrable Securities.
Any assignment of registration rights pursuant to this Section 3.11 shall be
effective only upon receipt by the Company of written notice from such assigning
Holder stating the name and address of any assignee.  The rights of an assignee
under this Section 3.11 shall be the same rights granted to the assigning Holder
under this Agreement.  In connection with any such assignment, the term "Holder"
as used herein shall, where appropriate to assign the rights and obligations of
the assigning Holder hereunder to such assignee, be deemed to refer to the
assignee.

                                       11
<PAGE>   12
 
          IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first written above.

      
                             BRIGHAM EXPLORATION COMPANY
      
      
      
                             By: /s/ CRAIG M. FLEMING
                                ------------------------------------
                                  Craig M. Fleming
                                  Chief Financial Officer
      
      
      
                             JOINT ENERGY DEVELOPMENT
                             INVESTMENTS II LIMITED PARTNERSHIP
      
                             By:  Enron Capital Management II Limited
                                  Partnership, its General Partner
      
                                  By Enron Capital II Corp., its General Partner
      
      
                                  By: /s/ MARK J. WARNER
                                     -------------------------------
                                  Name:   Mark J. Warner
                                       -----------------------------
                                  Title:  Agent and Attorney-in-Fact
                                        ----------------------------
      
      
      
                             ENRON CAPITAL & TRADE RESOURCES CORP.
      
      
                                  By: /s/ MARK J. WARNER
                                     -------------------------------
                                  Name:   Mark J. Warner
                                       -----------------------------
                                  Title:  Agent and Attorney-in-Fact
                                        ----------------------------

                                       12

<PAGE>   1
                                                                  EXHIBIT 10.40



                               GUARANTY AGREEMENT


                                       BY


                            [SEE SCHEDULE I HERETO]


                                  IN FAVOR OF


                   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
                                   AS TRUSTEE



                                AUGUST 20, 1998


<PAGE>   2

                               TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                                                Page
                                                                                                ----
<S>                                                                                             <C>
ARTICLE 1
         GENERAL TERMS
         Section 1.1   Terms Defined Above or in the Indenture.....................................2
         Section 1.2   Certain Definitions.........................................................2

ARTICLE 2
         THE GUARANTY
         Section 2.1   Liabilities Guaranteed......................................................4
         Section 2.2   Nature of Guaranty..........................................................4
         Section 2.3   Trustee's Rights............................................................4
         Section 2.4   Guarantor's Waivers.........................................................5
         Section 2.5   Maturity of Liabilities; Payment............................................5
         Section 2.6   Trustee's, Agent's and Noteholders' Expenses................................5
         Section 2.7   Liability...................................................................5
         Section 2.8   Events and Circumstances Not Reducing or Discharging 
                       Guarantor's Obligations.....................................................6
         Section 2.9   Right of Subrogation and Contribution.......................................7

ARTICLE 3
         REPRESENTATIONS AND WARRANTIES
         Section 3.1   By Guarantor................................................................8
         Section 3.2   No Representation by Noteholders............................................9

ARTICLE 4
         SUBORDINATION OF INDEBTEDNESS
         Section 4.1   Subordination of All Guarantor Claims.......................................9
         Section 4.2   Claims in Bankruptcy.......................................................10
         Section 4.3   Payments Held in Trust.....................................................10
         Section 4.4   Liens Subordinate..........................................................10

ARTICLE 5
         MISCELLANEOUS
         Section 5.1   Successors and Assigns.....................................................11
         Section 5.2   Notices....................................................................11
         Section 5.3   Business and Financial Information.........................................11
         Section 5.4   Construction...............................................................11
         Section 5.5   Invalidity.................................................................11
         Section 5.6   Subordination Agreement....................................................11
         Section 5.7   ENTIRE AGREEMENT...........................................................12
</TABLE>


                                      -i-
<PAGE>   3

                               GUARANTY AGREEMENT


         THIS GUARANTY AGREEMENT by [see Schedule I hereto] (hereinafter called
"Guarantor"), is in favor of CHASE BANK OF TEXAS, NATIONAL ASSOCIATION in its
capacity as trustee under the Indenture (as hereinafter defined), and each and
every successor trustee under the Indenture (the "Trustee"), for the ratable
benefit of Agent and the Noteholders (each as hereinafter defined).

                              W I T N E S S E T H:

     A. Brigham Exploration Company, a Delaware corporation ("Borrower") has
executed an Indenture, dated as of August 20, 1998, by and among the Borrower
and Chase Bank of Texas, National Association (the "Indenture"), pursuant to
which the Borrower has issued and will issue its Senior Subordinated Secured
Notes in the aggregate face amount of $50,000,000, with final maturity on
August 20, 2003 (such notes, as from time to time supplemented, amended or
modified and all other notes given in substitution therefor or in modification,
renewal or extension thereof, in whole or in part, being hereinafter called the
"Notes"), to Joint Energy Development Investments II Limited Partnership, a
Delaware limited partnership ("JEDI-II") and Enron Capital & Trade Resources
Corp., a Delaware corporation ("ECT").

     B. Brigham Oil & Gas, L.P., a Delaware limited partnership ("BOG") and
Bank of Montreal, as Agent ("B-MO"; B-MO, together with any other parties from
time to time constituting lenders under the Senior Credit Agreement (as
hereinafter defined) are herein called the "Senior Lenders") have entered into
that certain Credit Agreement dated as of January 28, 1998 as heretofore and
hereafter amended (such agreement, as the same may from time to time be
modified, extended, renewed, restated, replaced, amended or supplemented, being
herein called the "Senior Credit Agreement") pursuant to which the Senior
Lenders made and continue to make loans to BOG as evidenced by and to be
evidenced by the notes in the aggregate original principal amount of
$75,000,000 (such notes, as the same may from time to time be modified,
extended, renewed, restated, amended, replaced or supplemented, being herein
called the "BMO Notes").

     C. The BMO Notes and all other obligations now or hereafter existing or to
exist under the Senior Credit Agreement are guaranteed by various guaranties
(such instruments, together with any others as may now exist or hereafter be
executed pursuant to the Senior Credit Agreement, as any of the same may from
time to time be amended, renewed, restated, modified or supplemented, being
referred to herein collectively as the "Senior Guaranties").

     D. In connection with the execution and delivery of the Indenture,
JEDI-II, as agent (the "Agent"), JEDI-II, individually, ECT and B-MO, as agent
for the Senior Lenders (the "Senior Loan Agent"), have executed an
Intercreditor and Subordination Agreement dated as of August 20, 1998 (the
"Subordination Agreement") in order to evidence the relative priorities and
rights of the Senior


                                      -1-
<PAGE>   4

Loan Agent and the Senior Lenders under the Senior Credit Agreement to the
rights and obligations of the Agent and the Noteholders under the Indenture.

     E. The Guarantor will derive substantial benefit, both directly and
indirectly, from the making of the loans under the Indenture and the Notes and
has agreed to execute and deliver this Guaranty Agreement to the Trustee for
the benefit of the Agent and the Noteholders.

     NOW, THEREFORE, (i) in order to comply with the terms and conditions of
the Indenture, (ii) to induce the Noteholders to loan monies, with or without
security to or for the account of Borrower in accordance with the terms of the
Indenture, (iii) at the special insistence and request of the Noteholders, and
(iv) for other good and valuable consideration, the receipt and sufficiency of
which is hereby acknowledged, Guarantor hereby agrees as follows:

                                   ARTICLE 1
                                 GENERAL TERMS

     Section 1.1 Terms Defined Above or in the Indenture. As used in this
Guaranty Agreement, the terms defined above shall have the meanings
respectively assigned to them. Other capitalized terms which are defined in the
Indenture but which are not defined herein shall have the same meanings as
defined in the Indenture.

     Section 1.2 Certain Definitions. As used in this Guaranty Agreement, the
following terms shall have the following meanings, unless the context otherwise
requires:

     "Contribution Obligation" shall mean an amount equal, at any time and from
     time to time and for each respective Subsidiary Guarantor, to the product
     of (a) its Contribution Percentage times (b) the sum of all payments made
     previous to or at the time of calculation by all Subsidiary Guarantors in
     respect of the Liabilities, as a Subsidiary Guarantor (less the amount of
     any such payments previously returned to any Subsidiary Guarantor by
     operation of law or otherwise, but not including payments received by any
     Subsidiary Guarantor by way of its rights of subrogation and contribution
     under Section 2.9 of the other Guaranty Agreements), provided, however,
     such Contribution Obligation for any Subsidiary Guarantor shall in no
     event exceed such Subsidiary Guarantor's Maximum Guaranteed Amount, as
     defined in the respective Guaranty Agreement of such Subsidiary Guarantor.

     "Contribution Percentage" shall mean for any Subsidiary Guarantor for any
     applicable date as of which such percentage is being determined, an amount
     equal to the quotient of (a) the Net Worth of such Subsidiary Guarantor as
     of such date, divided by (b) the sum of the Net Worth of all the
     Subsidiary Guarantors as of such date.

     "Guarantor Claims" shall have the meaning indicated in Section 4.1 hereof.


                                      -2-
<PAGE>   5

     "Guaranty Agreement" shall mean this Guaranty Agreement, and where the
     context indicates, the Guaranty Agreement of any other Subsidiary
     Guarantor, as the same may from time to time be amended or supplemented.

     "Liabilities" shall mean:

          (a) any and all indebtedness, obligations and liabilities of the
     Borrower to the Agent and the Noteholders pursuant to the Indenture,
     including without limitation, the unpaid principal of and interest on the
     Notes;

          (b) any additional Obligations (as defined in the Indenture) owing to
     the Agent and the Noteholders; and

          (c) all renewals, rearrangements, increases, extensions for any
     period, amendments or supplements in whole or in part of the Notes or any
     documents evidencing the above.

     "Maximum Guaranteed Amount" shall mean, for the Guarantor, the greater of
     (a) the "reasonably equivalent value" or "fair consideration" (or
     equivalent concept) received by the Guarantor in exchange for the
     obligation incurred hereunder, within the meaning of any applicable state
     or federal fraudulent conveyance or transfer laws; or (b) the lesser of
     (i) the maximum amount that will not render the Guarantor insolvent, or
     (ii) the maximum amount that will not leave the Guarantor with any
     property deemed an unreasonably small capital. Clauses (i) and (ii) are
     and shall be determined pursuant to and as of the appropriate date
     mandated by such applicable state or federal fraudulent conveyance or
     transfer laws and to the extent allowed by law take into account the
     rights to contribution and subrogation under Section 2.9 in each Guaranty
     Agreement so as to provide for the largest Maximum Guaranteed Amount
     possible.

     "Net Payments" shall mean an amount equal, at any time and from time to
     time and for each respective Subsidiary Guarantor, to the difference of
     (a) the sum of all payments made previous to or at the time of calculation
     by such Subsidiary Guarantor in respect to the Liabilities, as a
     Subsidiary Guarantor, and in respect of its obligations contained in this
     Guaranty Agreement, less (b) the sum of all such payments previously
     returned to such Subsidiary Guarantor by operation of law or otherwise and
     including payments received by such Subsidiary Guarantor by way of its
     rights of subrogation and contribution under Section 2.9 of the other
     Guaranty Agreements.

     "Net Worth" shall mean for any Subsidiary Guarantor, calculated on and as
     of any applicable date on which such amount is being determined, the
     difference between (a) the sum of all such Subsidiary Guarantor's
     property, at a fair valuation and as of


                                      -3-
<PAGE>   6

     such date, minus (b) the sum of all such Subsidiary Guarantor's debts, at
     a fair valuation and as of such date, excluding the Liabilities.

     "Noteholders" shall mean the holders of the Notes from time to time, and
     the holders of any promissory note or notes given in substitution or
     replacement thereof, including, without limitation, pursuant to Section
     2.06 of the Indenture.

     "Subsidiary Guarantors" shall mean the Guarantors as defined in the
     Indenture, including the Guarantor.

                                   ARTICLE 2
                                  THE GUARANTY

     Section 2.1 Liabilities Guaranteed. Guarantor hereby irrevocably and
unconditionally guarantees the prompt payment of the Liabilities when due,
whether at maturity or otherwise, provided, however, that, notwithstanding
anything herein or in any other Basic Document to the contrary, the maximum
liability of Guarantor hereunder shall in no event exceed the Maximum
Guaranteed Amount.

     Section 2.2 Nature of Guaranty. This Guaranty Agreement is an absolute,
irrevocable, completed and continuing guaranty of payment and not a guaranty of
collection, and no notice of the Liabilities or any extension of credit already
or hereafter contracted by or extended to Borrower need be given to Guarantor.
This Guaranty Agreement may not be revoked by Guarantor and shall continue to
be effective with respect to debt under the Liabilities arising or created
after any attempted revocation by Guarantor and shall remain in full force and
effect until the Liabilities are paid in full. Borrower and the Noteholders may
modify, alter, rearrange, extend for any period and/or renew from time to time,
the Liabilities, and the Noteholders may waive any Default or Events of Default
without notice to the Guarantor and in such event Guarantor will remain fully
bound hereunder on the Liabilities. This Guaranty Agreement shall continue to
be effective or be reinstated, as the case may be, if at any time any payment
of the Liabilities is rescinded or must otherwise be returned by any of the
Noteholders upon the insolvency, bankruptcy or reorganization of Borrower or
otherwise, all as though such payment had not been made. This Guaranty
Agreement may be enforced by the Trustee, Agent and any holder of any of the
Liabilities and shall not be discharged by the assignment or negotiation of all
or part of the Liabilities. Guarantor hereby expressly waives presentment,
demand, notice of non-payment, protest and notice of protest and dishonor,
notice of Default or Event of Default, and also notice of acceptance of this
Guaranty Agreement, acceptance on the part of the Noteholders being
conclusively presumed by the Noteholders' request for this Guaranty Agreement
and delivery of the same to the Trustee.

     Section 2.3 Trustee's Rights. Guarantor authorizes the Trustee, without
notice or demand and without affecting Guarantor's liability hereunder, to take
and hold security for the payment of this Guaranty Agreement and/or the
Liabilities, and exchange, enforce, waive and release any such security; and to
apply such security and direct the order or manner of sale thereof as the
Trustee in


                                      -4-
<PAGE>   7

its discretion may determine; and to obtain a guaranty of the Liabilities from
any one or more Persons and at any time or times to enforce, waive, rearrange,
modify, limit or release any of such other Persons from their obligations under
such guaranties.

     Section 2.4 Guarantor's Waivers. Guarantor waives any right to require the
Trustee, Agent or any of the Noteholders to (i) proceed against Borrower or any
other person liable on the Liabilities, (ii) enforce any of their rights
against any other guarantor of the Liabilities (iii) proceed or enforce any of
their rights against or exhaust any security given to secure the Liabilities
(iv) have Borrower joined with Guarantor in any suit arising out of this
Guaranty Agreement and/or the Liabilities, or (v) pursue any other remedy in
the Trustee's, the Agent's or the Noteholders' powers whatsoever. Neither the
Trustee, Agent, nor the Noteholders shall be required to mitigate damages or
take any action to reduce, collect or enforce the Liabilities. Guarantor waives
any defense arising by reason of any disability, lack of corporate authority or
power, or other defense of Borrower or any other guarantor of the Liabilities,
and shall remain liable hereon regardless of whether Borrower or any other
guarantor be found not liable thereon for any reason. Whether and when to
exercise any of the remedies of the Trustee, Agent or the Noteholders under any
of the Basic Documents shall be in the sole and absolute discretion of the
Trustee, acting on behalf of itself, the Agent and the Noteholders, and no
delay by the Trustee in enforcing any remedy, including delay in conducting a
foreclosure sale, shall be a defense to the Guarantor's liability under this
Guaranty Agreement.

     Section 2.5 Maturity of Liabilities; Payment. Guarantor agrees that if the
maturity of any of the Liabilities is accelerated by bankruptcy or otherwise,
such maturity shall also be deemed accelerated for the purpose of this Guaranty
Agreement without demand or notice to Guarantor. Guarantor will, forthwith upon
notice from the Trustee, pay to the Trustee the amount due and unpaid by
Borrower and guaranteed hereby. The failure of the Trustee to give this notice
shall not in any way release Guarantor hereunder.

     Section 2.6 Trustee's, Agent's and Noteholders' Expenses. If Guarantor
fails to pay the Liabilities after notice from Trustee of Borrower's failure to
pay any Liabilities at maturity, and if the Trustee, Agent or any Noteholder
obtains the services of an attorney for collection of amounts owing by
Guarantor hereunder, or obtaining advice of counsel in respect of any of their
rights under this Guaranty Agreement, or if suit is filed to enforce this
Guaranty Agreement, or if proceedings are had in any bankruptcy, probate,
receivership or other judicial proceedings for the establishment or collection
of any amount owing by Guarantor hereunder, or if any amount owing by Guarantor
hereunder is collected through such proceedings, Guarantor agrees to pay to the
Trustee, Agent and Noteholder, the Trustee's, Agent's and Noteholder's
respective reasonable attorneys' fees.

     Section 2.7 Liability. It is expressly agreed that the liability of the
Guarantor for the payment of the Liabilities guaranteed hereby shall be primary
and not secondary.

     Section 2.8 Events and Circumstances Not Reducing or Discharging
Guarantor's Obligations. Guarantor hereby consents and agrees to each of the
following to the fullest extent permitted by law, and agrees that Guarantor's
obligations under this Guaranty Agreement shall not


                                      -5-
<PAGE>   8

be released, diminished, impaired, reduced or adversely affected by any of the
following, and waives any rights (including without limitation rights to
notice) which Guarantor might otherwise have as a result of or in connection
with any of the following:

         (a) Modifications, etc. Any renewal, extension, modification,
increase, decrease, alteration or rearrangement of all or any part of the
Liabilities, the Notes, the Indenture or the Basic Documents or any instrument
executed in connection therewith, or any contract or understanding between
Borrower and the Trustee, the Agent or any of the Noteholders, or any other
Person, pertaining to the Liabilities;

         (b) Adjustment, etc. Any adjustment, indulgence, forbearance or
compromise that might be granted or given by any Trustee, Agent or any
Noteholder to Borrower or Guarantor or any Person liable on the Liabilities;

         (c) Condition of Borrower or Guarantor. The insolvency, bankruptcy
arrangement, adjustment, composition, liquidation, disability, dissolution,
death or lack of power of Borrower or Guarantor or any other Person at any time
liable for the payment of all or part of the Liabilities; or any dissolution of
Borrower or Guarantor, or any sale, lease or transfer of any or all of the
assets of Borrower or Guarantor, or any changes in the shareholders, partners,
or members of Borrower or Guarantor; or any reorganization of Borrower or
Guarantor;

         (d) Invalidity of Liabilities. The invalidity, illegality or
unenforceability of all or any part of the Liabilities, or any document or
agreement executed in connection with the Liabilities, for any reason
whatsoever, including without limitation the fact that the Liabilities, or any
part thereof, exceed the amount permitted by law, the act of creating the
Liabilities or any part thereof is ultra vires, the officers or representatives
executing the documents or otherwise creating the Liabilities acted in excess
of their authority, the Liabilities violate applicable usury laws, the Borrower
has valid defenses, claims or offsets (whether at law, in equity or by
agreement) which render the Liabilities wholly or partially uncollectible from
Borrower, the creation, performance or repayment of the Liabilities (or the
execution, delivery and performance of any document or instrument representing
part of the Liabilities or executed in connection with the Liabilities, or
given to secure the repayment of the Liabilities) is illegal, uncollectible,
legally impossible or unenforceable, or the Indenture, the Basic Documents or
other documents or instruments pertaining to the Liabilities have been forged
or otherwise are irregular or not genuine or authentic;

         (e) Release of Obligors. Any full or partial release of the liability
of Borrower on the Liabilities or any part thereof, of any co-guarantors, or
any other Person now or hereafter liable, whether directly or indirectly,
jointly, severally, or jointly and severally, to pay, perform, guarantee or
assure the payment of the Liabilities or any part thereof, it being recognized,
acknowledged and agreed by Guarantor that Guarantor may be required to pay the
Liabilities in full without assistance or support of any other Person, and
Guarantor has not been induced to enter into this Guaranty Agreement on the
basis of a contemplation, belief, understanding or agreement that other parties


                                      -6-
<PAGE>   9

other than the Borrower will be liable to perform the Liabilities, or the
Trustee, Agent or any of the Noteholders will look to other parties to perform
the Liabilities.

         (f) Other Security. The taking or accepting of any other security,
collateral or guaranty, or other assurance of payment, for all or any part of
the Liabilities;

         (g) Release of Collateral, etc. Any release, surrender, exchange,
subordination, deterioration, waste, loss or impairment (including without
limitation negligent, willful, unreasonable or unjustifiable impairment) of any
collateral, property or security, at any time existing in connection with, or
assuring or securing payment of, all or any part of the Liabilities;

         (h) Care and Diligence. The failure of the Trustee, Agent, Noteholders
or any other Person to exercise diligence or reasonable care in the
preservation, protection, enforcement, sale or other handling or treatment of
all or any part of such collateral, property or security;

         (i) Status of Liens. The fact that any collateral, security, security
interest or lien contemplated or intended to be given, created or granted as
security for the repayment of the Liabilities shall not be properly perfected
or created, or shall prove to be unenforceable or subordinate to any other
security interest or lien, it being recognized and agreed by Guarantor that
Guarantor is not entering into this Guaranty Agreement in reliance on, or in
contemplation of the benefits of, the validity, enforceability, collectibility
or value of any of the collateral for the Liabilities;

         (j) Payments Rescinded. Any payment by Borrower to the Trustee, Agent
or the Noteholders is held to constitute a preference under the bankruptcy
laws, or for any reason the Trustee, Agent or the Noteholders are required to
refund such payment or pay such amount to Borrower or someone else; or

         (k) Other Actions Taken or Omitted. Any other action taken or omitted
to be taken with respect to the Basic Documents, the Liabilities, or the
security and collateral therefor, whether or not such action or omission
prejudices Guarantor or increases the likelihood that Guarantor will be
required to pay the Liabilities pursuant to the terms hereof; it being the
unambiguous and unequivocal intention of Guarantor that Guarantor shall be
obligated to pay the Liabilities when due, notwithstanding any occurrence,
circumstance, event, action, or omission whatsoever, whether contemplated or
uncontemplated, and whether or not otherwise or particularly described herein,
except for the full and final payment and satisfaction of the Liabilities.

     Section 2.9 Right of Subrogation and Contribution. If Guarantor makes a
payment in respect of the Liabilities, it shall be subrogated to the rights of
the Trustee against the Borrower with respect to such payment and shall have
the rights of contribution against the other Subsidiary Guarantors set forth in
Section 2.9 of the Subsidiary Guarantors' Guaranty Agreements; provided that
Guarantor shall not enforce its rights to any payment by way of subrogation or
by exercising its rights of contribution or reimbursement or the right to
participate in any security now or hereafter held by or for the benefit of the
Trustee, Agent or any of the Noteholders until the Liabilities have been paid


                                      -7-
<PAGE>   10

in full. The Guarantor agrees that after all the Liabilities have been paid in
full that if its then current Net Payments are less than the amount of its then
current Contribution Obligation, Guarantor shall pay to the other Subsidiary
Guarantors an amount (together with any payments required of the other
Subsidiary Guarantors by Section 2.9 of each other Guaranty Agreement) such
that the Net Payments made by all Subsidiary Guarantors in respect of the
Liabilities shall be shared among all of the Subsidiary Guarantors in
proportion to their respective Contribution Percentage.

                                   ARTICLE 3
                         REPRESENTATIONS AND WARRANTIES

     Section 3.1 By Guarantor. In order to induce the Trustee, Agent and the
Noteholders to accept this Guaranty Agreement, Guarantor represents and
warrants to the Trustee, Agent and the Noteholders (which representations and
warranties will survive the creation of the Liabilities and any extension of
credit thereunder) that:

         (a) Benefit to Guarantor. Guarantor's guaranty pursuant to this
Guaranty Agreement reasonably may be expected to benefit, directly or
indirectly, Guarantor.

         (b) Existence. Guarantor is duly organized, legally existing and in
good standing under the laws of the state of its formation and is duly
qualified as a foreign entity in all jurisdictions wherein the property owned
or the business transacted by it makes such qualification necessary.

         (c) Power and Authorization. Guarantor is duly authorized and
empowered to execute, deliver and perform this Guaranty Agreement and all
corporate or other organizational action on Guarantor's part requisite for the
due execution, delivery and performance of this Guaranty Agreement has been
duly and effectively taken.

         (d) Binding Obligations. This Guaranty Agreement constitutes valid and
binding obligations of Guarantor, enforceable in accordance with its terms
(except that enforcement may be subject to any applicable bankruptcy,
insolvency or similar laws generally affecting the enforcement of creditors'
rights or by general principles of equity).

         (e) No Consent. Guarantor's execution, delivery and performance of
this Guaranty Agreement does not require the consent or approval of any other
Person, including without limitation any regulatory authority or governmental
body of the United States or any state thereof or any political subdivision of
the United States or any state thereof.

         (f) Solvency. The Guarantor hereby represents that (i) it is not
insolvent as of the date hereof and will not be rendered insolvent as a result
of this Guaranty Agreement, (ii) it is not engaged in business or a
transaction, or about to engage in a business or a transaction, for which any
property or assets remaining with such Guarantor is unreasonably small capital,
and (iii) it does not intend to incur, or believe it will incur, debts that
will be beyond its ability to pay as such debts mature.


                                      -8-
<PAGE>   11

         (g) Litigation. Except as disclosed to the Noteholders in Schedule
4.03 of the Securities Purchase Agreement, at the Closing Date there is no
litigation, legal, administrative or arbitral proceeding, investigation or
other action of any nature pending or, to the knowledge of the Guarantor
threatened against the Guarantor or any of its Subsidiaries which involves the
possibility of any judgment or liability against the Guarantor or any of its
Subsidiaries not fully covered by insurance (except for normal deductibles),
and which would be more likely than not to have a Material Adverse Effect.

         (h) No Breach. Neither the execution and delivery of this Guaranty
Agreement, nor compliance with the terms and provisions hereof will conflict
with or result in a breach of, or require any consent which has not been
obtained as of the Closing Date under, the respective charter or by-laws or
other constituent documents of the Guarantor or any of its Subsidiaries or any
Governmental Requirement or any material agreement or instrument to which the
Guarantor or any of its Subsidiaries is a party or by which it is bound or to
which it or its Properties are subject, or constitute a default under any such
agreement or instrument, or result in the creation or imposition of any Lien
upon any of the material revenues or assets of the Guarantor or any of its
Subsidiaries pursuant to the terms of any such agreement or instrument other
than the Liens created by the Basic Documents.

     Section 3.2 No Representation by Noteholders. Neither the Trustee, the
Agent or the Noteholders nor any other Person has made any representation,
warranty or statement to the Guarantor in order to induce the Guarantor to
execute this Guaranty Agreement.

                                   ARTICLE 4
                         SUBORDINATION OF INDEBTEDNESS

     Section 4.1 Subordination of All Guarantor Claims. As used herein, the
term "Guarantor Claims" shall mean all debts and liabilities of Borrower to
Guarantor, whether such debts and liabilities now exist or are hereafter
incurred or arise, or whether the obligation of Borrower thereon be direct,
contingent, primary, secondary, several, joint and several, or otherwise, and
irrespective of whether such debts or liabilities be evidenced by note,
contract, open account, or otherwise, and irrespective of the person or persons
in whose favor such debts or liabilities may, at their inception, have been, or
may hereafter be created, or the manner in which they have been or may
hereafter be acquired by Guarantor. The Guarantor Claims shall include without
limitation all rights and claims of Guarantor against Borrower arising as a
result of subrogation or otherwise as a result of Guarantor's payment of all or
a portion of the Liabilities. If any Default exists and is continuing, and if
the Trustee gives notice thereof to the Guarantor requiring the Guarantor
Claims not be paid, then, for so long as any Default continues to exist,
Guarantor shall not receive or collect, directly or indirectly, from Borrower
or any other party any amount upon the Guarantor Claims.

     Section 4.2 Claims in Bankruptcy. In the event of receivership,
bankruptcy, reorganization, arrangement, debtor's relief, or other insolvency
proceedings involving Borrower as debtor, the Trustee, Agent and/or the
Noteholders shall have the right to prove their claim in any


                                      -9-
<PAGE>   12

proceeding, so as to establish its rights hereunder and receive directly from
the receiver, trustee or other court custodian, dividends and payments which
would otherwise be payable upon Guarantor Claims. Guarantor hereby assigns such
dividends and payments to the Trustee, as trustee under the Indenture. Should
the Trustee, Agent or any Noteholder receive, for application upon the
Liabilities, any such dividend or payment which is otherwise payable to
Guarantor, and which, as between Borrower and Guarantor, shall constitute a
credit upon the Guarantor Claims, then upon payment in full of the Liabilities,
Guarantor shall become subrogated to the rights of the Trustee, Agent or the
Noteholders, as applicable, to the extent that such payments to the Trustee,
Agent or the Noteholders, as applicable, on the Guarantor Claims have
contributed toward the liquidation of the Liabilities, and such subrogation
shall be with respect to that proportion of the Liabilities which would have
been unpaid if the Trustee, Agent or Noteholders, as applicable, had not
received dividends or payments upon the Guarantor Claims.

     Section 4.3 Payments Held in Trust. In the event that notwithstanding
Sections 4.1 and 4.2 above, Guarantor should receive any funds, payments,
claims or distributions which are prohibited by such Sections, Guarantor agrees
to hold in trust for the Trustee, as trustee under the Indenture, an amount
equal to the amount of all funds, payments, claims or distributions so
received, and agrees that it shall have absolutely no dominion over the amount
of such funds, payments, claims or distributions except to pay them promptly to
the Trustee, and Guarantor covenants promptly to pay the same to the Trustee.

     Section 4.4 Liens Subordinate. Guarantor agrees that any liens, security
interests, judgment liens, charges or other encumbrances upon Borrower's assets
securing payment of the Guarantor Claims shall be and remain inferior and
subordinate to any liens, security interests, judgment liens, charges or other
encumbrances upon Borrower's assets securing payment of the Liabilities,
regardless of whether such encumbrances in favor of Guarantor, the Trustee,
Agent or the Noteholders presently exist or are hereafter created or attach.
Without the prior written consent of the Trustee, Guarantor shall not (a)
exercise or enforce any creditor's right it may have against the Borrower, or
(b) foreclose, repossess, sequester or otherwise take steps or institute any
action or proceeding (judicial or otherwise, including without limitation the
commencement of or joinder in any liquidation, bankruptcy, rearrangement,
debtor's relief or insolvency proceeding) to enforce any lien, mortgages, deeds
of trust, security interest, collateral rights, judgments or other encumbrances
on assets of Borrower held by Guarantor.

                                   ARTICLE 5
                                 MISCELLANEOUS

     Section 5.1 Successors and Assigns. This Guaranty Agreement is and shall
be in every particular available to the successors and assigns of Trustee,
Agent and the Noteholders and is and shall always be fully binding upon the
legal representatives, heirs, successors and assigns of Guarantor,
notwithstanding that some or all of the monies, the repayment of which this
Guaranty Agreement applies, may be actually advanced after any bankruptcy,
receivership, reorganization, death, disability or other event affecting
Guarantor. The Trustee may resign, withdraw or be replaced


                                     -10-
<PAGE>   13

as trustee under the Indenture, and upon any such event a new trustee may be
appointed under the Indenture. In such event, Trustee shall be fully discharged
thereafter from all liability therefor, and any new trustee under the Indenture
shall be vested with all rights, powers and remedies of Trustee hereunder. In
connection therewith, Guarantor will take whatever action is reasonably
required in order to reaffirm its obligations under this Guaranty Agreement

     Section 5.2 Notices. Any notice or demand to Guarantor under or in
connection with this Guaranty Agreement may be given and shall conclusively be
deemed and considered to have been given and received in accordance with
Section 13.05 of the Indenture, addressed to Guarantor at the address on the
signature page hereof or at such other address provided to Trustee and Agent in
writing.

     Section 5.3 Business and Financial Information. Subject to any applicable
confidentiality agreements, the Guarantor will promptly furnish to Trustee,
Agent and the Noteholders from time to time upon request such information
regarding the business and affairs and financial condition of the Guarantor and
its subsidiaries as the Trustee, Agent or the Noteholders may reasonably
request.

     Section 5.4 Construction. This Guaranty Agreement is a contract made under
and shall be construed in accordance with and governed by the laws of the State
of Texas.

     Section 5.5 Invalidity. In the event that any one or more of the
provisions contained in this Guaranty Agreement shall, for any reason, be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality
or unenforceability shall not affect any other provision of this Guaranty
Agreement.

     Section 5.6 Subordination Agreement. This Guaranty Agreement and the
rights and remedies of Agent and the Noteholders under this Guaranty Agreement
are subject to the terms and conditions of the Subordination Agreement.

     Section 5.7 ENTIRE AGREEMENT. THIS WRITTEN GUARANTY AGREEMENT EMBODIES THE
ENTIRE AGREEMENT AND UNDERSTANDING AMONG THE AGENT, THE NOTEHOLDERS AND THE
GUARANTOR AND SUPERSEDES ALL OTHER AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH
PARTIES RELATING TO THE SUBJECT MATTER HEREOF AND THEREOF. THIS WRITTEN
GUARANTY AGREEMENT REPRESENTS THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY
NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.


                                     -11-

<PAGE>   14

     WITNESS THE EXECUTION HEREOF, as of this the 20th day of August, 1998.

                                        [See Schedule I hereto]



                                        By:
                                           ------------------------------------
                                        Name:
                                        Title:

                                        Address:
                                                -------------------------------

                                                -------------------------------

                                                -------------------------------

                                        Telecopier No.:
                                                       ------------------------
                                        Telephone No.:
                                                      -------------------------
                                        Attention:
                                                  -----------------------------


                                     -12-
<PAGE>   15

                                   Schedule I

Subsidiary Guarantors

Brigham Oil & Gas, L.P.
Brigham, Inc.
Brigham Holdings I, LLC
Brigham Holdings II, LLC
Sooner Production, LLC
DND Oil & Gas, L.P.



                                     -13-

<PAGE>   1
                                                                      EXHIBIT 21


                                  Subsidiaries

Brigham Oil & Gas, L.P., a Delaware limited partnership
Brigham, Inc., a Nevada corporation
Brigham Holdings I, LLC, a Nevada limited liability company
Brigham Holdings II, LLC, a Nevada limited liability company

<PAGE>   1
                                                                    Exhibit 23.1


                       CONSENT OF INDEPENDENT ACCOUNTANTS



         We hereby consent to the incorporation by reference in the Registration
Statement on Form S-8 (No. 333- 56961) of Brigham Exploration Company and in the
Registration Statement on Form S-8 (No. 333-70137) of Brigham Exploration
Company of our report dated March 30, 1999, which appears on page F-1 of this
Form 10-K of Brigham Exploration Company.


/s/ PricewaterhouseCoopers LLP

PRICEWATERHOUSECOOPERS LLP


Houston, Texas
March 30, 1999

<PAGE>   1
                                                                    Exhibit 23.2

                  CONSENT OF INDEPENDENT PETROLEUM CONSULTANTS


         As independent petroleum consultants, we hereby consent to the
incorporation by reference in the Registration Statement on Form S-8 (No.
333-56961) of Brigham Exploration Company and in the Registration Statement on
Form S-8 (No. 333-70137) of Brigham Exploration Company of our estimates of
reserves, included in this Annual Report on Form 10-K, and to all references to
our firm included in this Annual Report.



/s/ Cawley, Gillespie & Associates, Inc.

CAWLEY, GILLESPIE & ASSOCIATES, INC.


Fort Worth, Texas
March 26, 1999

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<ARTICLE> 5
<MULTIPLIER> 1,000
       
<S>                             <C>
<PERIOD-TYPE>                   YEAR
<FISCAL-YEAR-END>                          DEC-31-1998
<PERIOD-START>                             JAN-01-1998
<PERIOD-END>                               DEC-31-1998
<CASH>                                           2,569
<SECURITIES>                                         0
<RECEIVABLES>                                    7,938
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<CURRENT-ASSETS>                                10,797
<PP&E>                                       1,336,331
<DEPRECIATION>                                       0
<TOTAL-ASSETS>                                 150,516
<CURRENT-LIABILITIES>                           23,513
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                                0
                                          0
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<OTHER-SE>                                      24,548
<TOTAL-LIABILITY-AND-EQUITY>                   150,516
<SALES>                                         13,799
<TOTAL-REVENUES>                                14,189
<CGS>                                                0
<TOTAL-COSTS>                                    3,022
<OTHER-EXPENSES>                                38,714
<LOSS-PROVISION>                                     0
<INTEREST-EXPENSE>                               6,984
<INCOME-PRETAX>                               (34,531)
<INCOME-TAX>                                   (1,186)
<INCOME-CONTINUING>                           (33,345)
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<CHANGES>                                            0
<NET-INCOME>                                  (33,345)
<EPS-PRIMARY>                                     2.64
<EPS-DILUTED>                                     2.64
        

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