BRIGHAM EXPLORATION CO
10-Q, 1999-11-15
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>   1

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

                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

             [X] QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF THE
                         SECURITIES EXCHANGE ACT OF 1934


                For the quarterly period ended September 30, 1999

                                       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 000-22433

                           BRIGHAM EXPLORATION COMPANY
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                         <C>                                      <C>
               DELAWARE                                 1311                               75-2692967
     (State of other jurisdiction           (Primary Standard Industrial                (I.R.S. Employer
   of incorporation or organization)         Classification Code Number)             Identification Number)
</TABLE>

                            6300 BRIDGE POINT PARKWAY
                               BLDG. 2, SUITE 500
                               AUSTIN, TEXAS 78730
                                 (512) 427-3300

 (Name, address, including zip code, and telephone number, including area code,
                  of Registrant's principal executive offices)


   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 twelve months (or 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    .
    ---      ---

As of November 1, 1999, 14,517,786 shares of Common Stock, $.01 per share, were
outstanding.

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


<PAGE>   2



                           BRIGHAM EXPLORATION COMPANY

                                      INDEX


<TABLE>
<CAPTION>
                                                                                                          PAGE
PART I.   FINANCIAL INFORMATION:                                                                         NUMBER
                                                                                                         ------
<S>               <C>                                                                                    <C>
Item 1.   Unaudited Financial Statements

              Condensed Consolidated Financial Statements of Brigham Exploration Company
                  Balance Sheets - December 31, 1998 and September 30, 1999.........................        1
                  Statements of Operations - Three and nine months ended
                    September 30, 1998 and 1999.....................................................        2
                  Statements of Cash Flows - Nine months ended September 30, 1998 and 1999..........        3
                  Statement of Changes in Stockholders' Equity - Nine months ended
                     September 30, 1999.............................................................        4
                  Notes to Condensed Consolidated Financial Statements..............................      5 - 7

              Condensed Financial Statements of Brigham Exploration Company Subsidiaries
                  Balance Sheets - September 30, 1999...............................................        8
                  Balance Sheets - December 31, 1998................................................        9
                  Statements of Operations - Three months ended September 30, 1999..................       10
                  Statements of Operations - Three months ended September 30, 1998..................       11
                  Statements of Operations - Nine months ended September 30, 1999...................       12
                  Statements of Operations - Nine months ended September 30, 1998...................       13
                  Statements of Cash Flows - Nine months ended September 30, 1999...................       14
                  Statements of Cash Flows - Nine months ended September 30, 1998...................       15
                  Statements of Changes in Equity - Nine months ended September 30, 1999............       16
                  Notes to Condensed Financial Statements...........................................      17-19

          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.

Item 2.   Management's Discussion and Analysis of Results of
              Operations and Financial Condition....................................................      20-29


PART II.  OTHER INFORMATION:

Item 2.   Changes in Securities.....................................................................       30

Item 6.   Exhibits and Reports on Form 8-K..........................................................       30
</TABLE>


<PAGE>   3


PART I.   FINANCIAL INFORMATION:

Item 1.   Financial Statements

                           BRIGHAM EXPLORATION COMPANY

                             CONDENSED CONSOLIDATED
                                 BALANCE SHEETS
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                                December 31,       September 30,
                                                                                   1998                1999
                                                                                ------------       -------------
                                                                                                    (unaudited)
<S>                                                                             <C>                <C>
                                     ASSETS
Current assets:
     Cash and cash equivalents                                                  $      2,569       $       3,381
     Accounts receivable                                                               7,938               5,627
     Prepaid expenses                                                                    290                 480
                                                                                ------------       -------------
        Total current assets                                                          10,797               9,488
                                                                                ------------       -------------

Natural gas and oil properties, at cost, net                                         134,317             106,498
Other property and equipment, at cost, net                                             2,014               1,813
Drilling advances paid                                                                   230                 532
Deferred loan fees                                                                     3,146               4,052
Other noncurrent assets                                                                   12                 101
                                                                                ------------       -------------
                                                                                $    150,516       $     122,484
                                                                                ============       =============

                      LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Accounts payable                                                           $     19,883       $      13,621
     Accrued drilling costs                                                            1,219                  70
     Participant advances received                                                       764               1,804
     Other current liabilities                                                         1,647               1,498
                                                                                ------------       -------------
        Total current liabilities                                                     23,513              16,993
                                                                                ------------       -------------

Notes payable                                                                         59,000              55,000
Senior subordinated notes, net                                                        35,786              39,729
Other noncurrent liabilities                                                           7,536               1,449

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 14,517,786 issued and outstanding at
        December 31, 1998 and September 30, 1999, respectively                           133                 145
     Additional paid-in capital                                                       58,838              64,218
     Unearned stock compensation                                                        (890)               (358)
     Accumulated deficit                                                             (33,400)            (54,692)
                                                                                ------------       -------------
        Total stockholders' equity                                                    24,681               9,313
                                                                                ------------       -------------
                                                                                $    150,516       $     122,484
                                                                                ============       =============
</TABLE>

  Natural gas and oil properties are accounted for using the full cost method.
   See accompanying notes to the condensed consolidated financial statements.


                                        1
<PAGE>   4


                           BRIGHAM EXPLORATION COMPANY

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

<TABLE>
<CAPTION>
                                                                Three Months                      Nine Months
                                                            Ended September 30,               Ended September 30,
                                                       --------------------------------------------------------------------
                                                            1998             1999               1998              1999
                                                       --------------   --------------     --------------    --------------
<S>                                                    <C>              <C>                 <C>              <C>
Revenues:
     Natural gas and oil sales                         $        4,162   $        4,109      $      11,292    $       10,855
     Workstation revenue                                           75               86                322               247
                                                       --------------   --------------     --------------    --------------
                                                                4,237            4,195             11,614            11,102
                                                       --------------   --------------     --------------    --------------
Costs and expenses:
     Lease operating                                              564              525              1,542             1,679
     Production taxes                                             255              300                705               685
     General and administrative                                 1,069              901              3,362             2,710
     Depletion of natural gas and oil properties                1,690            2,839              4,480             5,650
     Depreciation and amortization                                113              132                288               398
     Amortization of stock compensation                            65             (123)               298               (10)
                                                       --------------   --------------     --------------    --------------
                                                                3,756            4,574             10,675            11,112
                                                       --------------   --------------     --------------    --------------
        Operating income                                          481             (379)               939               (10)
                                                       --------------   --------------     --------------    --------------

Other income (expense):
     Interest income                                               37               40                114               134
     Interest expense                                          (1,979)          (3,250)            (4,411)           (9,221)
     Loss on sale of natural gas and oil properties                --               --                 --           (12,195)
                                                       --------------   --------------     --------------    --------------
                                                               (1,942)          (3,210)            (4,297)          (21,282)
                                                       --------------   --------------     --------------    --------------

Net loss before income taxes                                   (1,461)          (3,589)            (3,358)          (21,292)
Income tax benefit                                                497               --              1,135                --
                                                       --------------   --------------     --------------    --------------
     Net loss                                          $         (964)  $       (3,589)    $       (2,223)   $      (21,292)
                                                       ==============   ==============     ==============    ==============

Net loss per share:
     Basic / Diluted                                   $        (0.08)  $        (0.25)     $       (0.18)   $        (1.52)

Weighted average common shares outstanding:
     Basic / Diluted                                           12,677           14,447             12,396            14,028
</TABLE>



   See accompanying notes to the condensed consolidated financial statements.



                                       2
<PAGE>   5


                          BRIGHAM EXPLORATION COMPANY

                             CONDENSED CONSOLIDATED
                            STATEMENTS OF CASH FLOWS
                                 (in thousands)
                                  (unaudited)

<TABLE>
<CAPTION>
                                                                                         Nine               Nine
                                                                                     Months Ended       Months Ended
                                                                                    September 30,       September 30,
                                                                                         1998                1999
                                                                                   -----------------    -------------
<S>                                                                                <C>                  <C>
Cash flows from operating activities:
     Net loss                                                                      $          (2,223)   $     (21,292)
     Adjustments to reconcile net loss to cash provided (used)
     by operating activities:
         Depletion of natural gas and oil properties                                           4,480             5,650
         Depreciation and amortization                                                           288               398
         Amortization of stock compensation                                                      298               (10)
         Interest paid through issuance of senior subordinated notes                              --             4,028
         Amortization of deferred loan fees                                                      463             1,160
         Amortization of discount on senior subordinated notes                                    74               394
         Loss on sale of natural gas and oil properties                                           --            12,195
         Changes in deferred income tax liability                                             (1,135)               --
         Changes in working capital and other items:
            (Increase) decrease in accounts receivable                                        (3,198)            2,311
            Increase in prepaid expenses                                                         (74)             (190)
            Increase (decrease) in accounts payable                                            1,759            (2,466)
            Decrease in participant advances received                                            437             1,040
            Increase (decrease) in other current liabilities                                   1,612              (137)
            Other noncurrent assets                                                                6               (89)
            Other noncurrent liabilities                                                         (94)           (5,663)
                                                                                   -----------------     -------------
            Net cash provided (used) by operating activities                                   2,693            (2,671)
                                                                                   -----------------     -------------

Cash flows from investing activities:
     Additions to natural gas and oil properties                                             (52,782)          (18,310)
     Proceeds from sale of natural gas and oil properties                                         --            27,122
     Additions to other property and equipment                                                  (511)             (146)
     Increase in drilling advances paid                                                         (326)             (302)
                                                                                   -----------------     -------------
            Net cash provided (used) by investing activities                                 (53,619)            8,364
                                                                                   -----------------     -------------

Cash flows from financing activities:
     Proceeds from issuance of common stock                                                    9,448                --
     Proceeds from issuance of senior subordinated notes                                      40,000                --
     Increase in notes payable                                                                83,800            12,750
     Repayment of notes payable                                                              (78,800)          (16,750)
     Principal payments on capital lease obligations                                            (176)             (193)
     Deferred loan fees paid                                                                  (3,796)             (688)
                                                                                   -----------------     -------------
            Net cash (used) provided by financing activities                                  50,476            (4,881)
                                                                                   -----------------     -------------

Net increase (decrease) in cash and cash equivalents                                            (450)              812

Cash and cash equivalents, beginning of period                                                 1,701             2,569
                                                                                   -----------------     -------------
Cash and cash equivalents, end of period                                           $           1,251     $       3,381
                                                                                   =================     =============

Supplemental disclosure of cash flow information:
     Cash paid during the period for interest                                      $           3,182     $       3,739
                                                                                   =================     =============

Supplemental disclosure of noncash investing and financing activities:
     Capital lease asset additions                                                 $             320     $          51
                                                                                   =================     =============
     Decrease in accounts payable and other noncurrent liabilities in exchange
         for issuance of common stock                                              $              --     $       4,240
                                                                                   =================     =============
     Increase in accounts payable for deferred loan fees to be
         paid in future periods                                                    $              --     $         150
                                                                                   =================     =============
     Increase in deferred loan fees for issuance of warrants                       $              --     $       1,228
                                                                                   =================     =============
</TABLE>

   See accompanying notes to the condensed consolidated financial statements.



                                       3
<PAGE>   6


                           BRIGHAM EXPLORATION COMPANY

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


<TABLE>
<CAPTION>
                                          Common Stock          Additional     Unearned
                                   ---------------------------   Paid-in        Stock          Accum.
                                      Shares          Amounts    Capital     Compensation      Deficit          Total
                                   --------------    --------- ------------- --------------  --------------  --------------
<S>                                    <C>           <C>       <C>           <C>             <C>             <C>
Balance, December 31, 1998             13,306,206    $     133 $      58,838 $         (890) $      (33,400) $       24,681

     Net loss for the period
        ended Sept. 30, 1999                   --           --            --             --         (21,292)        (21,292)
     Issuance of common stock           1,211,580           12         4,228             --              --           4,240
     Forfeiture of stock options               --           --          (555)           555              --              --
     Revision in terms
                       of warrants             --           --           479             --              --             479
     Issuance of warrants                      --           --         1,228             --              --           1,228
     Amortization of unearned
                stock compensation             --           --            --            (23)             --             (23)

                                   --------------  ----------- ------------- --------------  --------------  --------------
Balance, September 30, 1999            14,517,786  $       145 $      64,218 $         (358) $      (54,692) $        9,313
                                   ==============  =========== ============= ==============  ==============  ==============
</TABLE>


   See accompanying notes to the condensed consolidated financial statements.



                                        4
<PAGE>   7


                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (unaudited)


1.     ORGANIZATION AND NATURE OF OPERATIONS

       Brigham Exploration Company (the "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"). 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.

2.     BASIS OF PRESENTATION

       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.

       The accompanying condensed consolidated financial statements are
       unaudited, and in the opinion of management, reflect all adjustments that
       are necessary for a fair presentation of the financial position and
       results of operations for the periods presented. All such adjustments are
       of a normal and recurring nature. The results of operations for the
       periods presented are not necessarily indicative of the results to be
       expected for the entire year. The unaudited condensed consolidated
       financial statements should be read in conjunction with the Company's
       1998 Annual Report on Form 10-K pursuant to Section 13 or 15(d) of the
       Securities Exchange Act of 1934.

3.     SALE OF NATURAL GAS AND OIL PROPERTIES

       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.

       In June 1999, the Company sold all of its interests in certain producing
       and non-producing natural gas and oil properties for a total sales price
       of $17.1 million. Due to the magnitude of the reserve volumes that were
       attributable to these properties relative to the Company's remaining net
       reserve volumes, the Company recognized as a loss the difference between
       the sales price received, after adjustment for transaction costs, and the
       $28.9 million basis allocated to the divested properties in accordance
       with the full-cost method of accounting for oil and gas properties.


                                       5
<PAGE>   8
                           BRIGHAM EXPLORATION COMPANY

                             NOTES TO THE CONDENSED
                        CONSOLIDATED FINANCIAL STATEMENTS
                                   (unaudited)


4.     ISSUANCE OF COMMON STOCK

       In March 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
       through December 31, 1999, 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 seismic
       processing services has been determined on a quarterly basis. Subsequent
       to March 30, 1999, Brigham issued an additional 208,715 shares of common
       stock valued at $3.50 per share to Veritas pursuant to its election to
       settle certain seismic processing service obligations incurred during
       the second and third quarters of 1999 in common stock instead of cash.

5.     AMENDMENT TO REVOLVING CREDIT FACILITY

       In July 1999, the Company and its senior lenders entered into an
       amendment to the Company's revolving credit facility (the "Credit
       Facility"). This amendment provides the Company with borrowing
       availability of $56 million principally to fund its planned drilling
       activities and anticipated working capital requirements through the end
       of 1999. The Company's senior lenders have indicated that the borrowing
       availability provided under the amended Credit Facility exceeds that
       which would otherwise be made available under a more traditional
       conforming borrowing base calculation based on the estimated value of
       the Company's current net proved reserves and its cash flow. As
       consideration for this amendment to the Credit Facility, in July 1999
       the Company issued to its senior lenders one million warrants to
       purchase the Company's common stock at an exercise price of $2.25 per
       share. The warrants have a seven-year term from the date of issuance and
       are exercisable at the holders' option at any time. An estimated value
       of $1.2 million was attributed to these warrants by the Company and was
       recognized as additional deferred loan fees which will be amortized over
       the remaining period to maturity of the Credit Facility borrowings at
       January 26, 2001.

6.     HEDGING ACTIVITIES

       In September 1999, the Company entered into five call options with a
       counterparty for certain future oil and natural gas production. Under the
       terms of the contracts, for any month where the average index price (WTI
       or ANR Pipeline Company - Oklahoma) is greater than the strike price per
       the contract, the Company is required to pay to the counterparty the
       absolute value of that difference times the production volumes covered
       under the contract. If the average index price is less than the strike
       price for a given month, no settlement is required. These contracts are


                                       6
<PAGE>   9

       summarized as follows:

<TABLE>
<CAPTION>
                      Daily                             Total Volumes Hedged            Average
          Call       Volumes                       -------------------------------       Fixed
         Options     Hedged     Monthly Term         2000       2001        2000     Contract Price
       -----------   -------   --------------      ------    ---------   ---------   --------------
<S>                  <C>       <C>                 <C>       <C>         <C>         <C>
       Contract #1       600   October 1999 -      55,200       54,000          --           $24.00
                        Bbls   March 2000            Bbls         Bbls                      per Bbl

       Contract #2       600   April 2000 -        54,600           --          --           $22.00
                        Bbls   June 2000             Bbls                                   per Bbl

       Contract #3    10,000   May 2001 -              --    1,840,000          --           $2,665
                       MMBtu   October 2001                      MMBtu                    per MMBtu

       Contract #4    10,000   November 2000 -         --      610,000   1,200,000           $2,670
                       MMBtu   April 2002                        MMBtu       MMBtu        per MMBtu

       Contract #5    10,000   May 2002 -              --           --     610,000           $2,670
                       MMBtu   June 2002                                     MMBtu        per MMBtu
</TABLE>

7.     ACCOUNTING FOR DERIVATIVE INSTRUMENTS AND HEDGING ACTIVITIES

       In June 1998, the Financial Accounting Standards Board (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, as amended by SFAS No. 137, effective January 1, 2001. The Company
       is in the process of analyzing the potential impact of this standard on
       its financial statement presentations.


                                       7
<PAGE>   10

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                            CONDENSED BALANCE SHEETS
                            AS OF SEPTEMBER 30, 1999
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                              BRIGHAM                     BRIGHAM       BRIGHAM
                                                               OIL &        BRIGHAM,      HOLDINGS      HOLDINGS
                                                             GAS, L.P.        INC.         I, LLC        II, LLC
<S>                                                          <C>           <C>            <C>           <C>
                                                         ASSETS
Current assets:
     Cash and cash equivalents                               $   3,175     $   3,376      $       5     $       6
     Accounts receivable                                         5,627         5,627             --            --
     Prepaid expenses                                              480           480             --            --
                                                             ---------     ---------      ---------     ---------
        Total current assets                                     9,282         9,483              5             6
                                                             ---------     ---------      ---------     ---------

Natural gas and oil properties, at cost, net                   106,498       106,498             --            --
Other property and equipment, at cost, net                       1,813         1,813             --            --
Investment in subsidiaries
     and intercompany advances                                     329            --          1,339        46,372
Drilling advances paid                                             532           532             --            --
Deferred loan fees                                               2,586         2,586             --            --
Other noncurrent assets                                            101           101             --            --
                                                             ---------     ---------      ---------     ---------
                                                             $ 121,141     $ 121,013      $   1,344     $  46,378
                                                             =========     =========      =========     =========

                                                    LIABILITIES AND EQUITY
Current liabilities:
     Accounts payable                                        $  13,621     $  13,621      $      --     $      --
     Accrued drilling costs                                         70            70             --            --
     Participant advances received                               1,804         1,804             --            --
     Other current liabilities                                   1,444         1,444             --            --
                                                             ---------     ---------      ---------     ---------
        Total current liabilities                               16,939        16,939             --            --
                                                             ---------     ---------      ---------     ---------

Notes payable                                                   55,000        55,000             --            --
Other noncurrent liabilities                                     1,449         1,449             --            --
Intercompany accounts payable                                    1,739         1,626             --         1,760
Intercompany notes payable                                      44,028        44,028             --        44,028

Minority interest                                                   --         1,361             --            --

Equity
     Partners' capital                                           1,986            --          1,344           590
     Common stock, $1.00 par value, 1,000 shares
        authorized, issued and outstanding                          --             1             --            --
     Additional paid-in capital                                     --        17,832             --            --
     Accumulated deficit                                            --       (17,223)            --            --
                                                             ---------     ---------      ---------     ---------
        Total equity                                             1,986           610          1,344           590
                                                             ---------     ---------      ---------     ---------
                                                             $ 121,141     $ 121,013      $   1,344     $  46,378
                                                             =========     =========      =========     =========
</TABLE>

  Natural gas and oil properties are accounted for using the full cost method.
          See accompanying notes to the condensed financial statements.


                                       8
<PAGE>   11


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                            CONDENSED BALANCE SHEETS
                             AS OF DECEMBER 31, 1998
                                 (in thousands)

<TABLE>
<CAPTION>
                                                              BRIGHAM                     BRIGHAM       BRIGHAM
                                                               OIL &        BRIGHAM,      HOLDINGS      HOLDINGS
                                                             GAS, L.P.        INC.         I, LLC        II, LLC
<S>                                                          <C>           <C>            <C>           <C>
                                                             ASSETS
Current assets:
     Cash and cash equivalents                               $   2,549     $   2,563      $       5     $       6
     Accounts receivable                                         7,938         7,938             --            --
     Prepaid expenses                                              290           290             --            --
                                                             ---------     ---------      ---------     ---------
        Total current assets                                    10,777        10,791              5             6
                                                             ---------     ---------      ---------     ---------

Natural gas and oil properties, at cost, net                   134,317       134,317             --            --
Other property and equipment, at cost, net                       2,014         2,014             --            --
Investment in subsidiaries
     and intercompany advances                                     115            16         11,714        46,913
Drilling advances paid                                             231           231             --            --
Deferred loan fees                                               1,397         1,397             --            --
Other noncurrent assets                                             12            12             --            --
                                                             ---------     ---------      ---------     ---------
                                                             $ 148,863     $ 148,778      $  11,719     $  46,919
                                                             =========     =========      =========     =========

                                                     LIABILITIES AND EQUITY
Current liabilities:
     Accounts payable                                        $  19,883     $  19,883      $      --     $      --
     Accrued drilling costs                                      1,219         1,219             --            --
     Participant advances received                                 764           764             --            --
     Other current liabilities                                   1,647         1,647             --            --
                                                             ---------     ---------      ---------     ---------
        Total current liabilities                               23,513        23,513             --            --
                                                             ---------     ---------      ---------     ---------

Notes payable                                                   59,000        59,000             --            --
Other noncurrent liabilities                                     7,536         7,536             --            --
Intercompany accounts payable                                    1,690         1,616             --         1,707
Intercompany notes payable                                      40,000        40,000             --        40,000

Minority interest                                                   --        11,730             --            --

Equity
     Partners' capital                                          17,124            --         11,719         5,212
     Common stock, $1.00 par value, 1,000 shares
        authorized, issued and outstanding                          --             1             --            --
     Additional paid-in capital                                     --        16,109             --            --
     Accumulated deficit                                            --       (10,727)            --            --
                                                             ---------     ---------      ---------     ---------
        Total equity                                            17,124         5,383         11,719         5,212
                                                             ---------     ---------      ---------     ---------
                                                             $ 148,863     $ 148,778      $  11,719     $  46,919
                                                             =========     =========      =========     =========
</TABLE>

  Natural gas and oil properties are accounted for using the full cost method.
          See accompanying notes to the condensed financial statements.


                                       9
<PAGE>   12


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                       CONDENSED STATEMENTS OF OPERATIONS
                  FOR THE THREE MONTHS ENDED SEPTEMBER 30, 1999
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                        BRIGHAM                   BRIGHAM      BRIGHAM
                                                         OIL &       BRIGHAM,     HOLDINGS     HOLDINGS
                                                       GAS, L.P.       INC.        I, LLC      II, LLC
<S>                                                    <C>           <C>          <C>          <C>
Revenues:
     Natural gas and oil sales                          $ 4,109      $ 4,109      $    --      $    --
     Workstation revenue                                     86           86           --           --
                                                        -------      -------      -------      -------
                                                          4,195        4,195           --           --
                                                        -------      -------      -------      -------
Costs and expenses:
     Lease operating                                        525          525           --           --
     Production taxes                                       300          300           --           --
     General and administrative                             901          901           --           --
     Depletion of natural gas and oil properties          2,839        2,839           --           --
     Depreciation and amortization                          132          132           --           --
     Amortization of stock compensation                    (123)        (123)          --           --
                                                        -------      -------      -------      -------
                                                          4,574        4,574           --           --
                                                        -------      -------      -------      -------
        Operating income (loss)                            (379)        (379)          --           --
                                                        -------      -------      -------      -------

Other income (expense):
     Interest income                                         40           40           --           --
     Interest expense                                    (1,586)      (1,586)          --           --
     Interest expense - intercompany                     (1,404)      (1,404)          --       (1,404)
     Loss on sale of natural gas and oil properties          --            0           --           --
                                                        -------      -------      -------      -------
                                                         (2,950)      (2,950)          --       (1,404)
                                                        -------      -------      -------      -------

Minority interest in net loss                                --       (2,280)          --           --

                                                        -------      -------      -------      -------
Net loss before income taxes                             (3,329)      (1,049)          --       (1,404)

Equity in net loss of investee                               --           --       (2,280)         389
                                                        -------      -------      -------      -------
     Net loss                                           $(3,329)     $(1,049)     $(2,280)     $(1,015)
                                                        =======      =======      =======      =======
</TABLE>



          See accompanying notes to the condensed financial statements.


                                       10
<PAGE>   13


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                       CONDENSED STATEMENTS OF OPERATIONS
                  FOR THE THREE MONTHS ENDED SEPTEMBER 30, 1998
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                     BRIGHAM                   BRIGHAM      BRIGHAM
                                                     OIL &        BRIGHAM,     HOLDINGS     HOLDINGS
                                                     GAS, L.P.      INC.       I, LLC       II, LLC
<S>                                                  <C>          <C>          <C>          <C>
Revenues:
     Natural gas and oil sales                       $ 4,162      $ 4,162      $    --      $    --
     Workstation revenue                                  75           75           --           --
                                                     -------      -------      -------      -------
                                                       4,237        4,237           --           --
                                                     -------      -------      -------      -------
Costs and expenses:
     Lease operating                                     564          564           --           --
     Production taxes                                    255          255           --           --
     General and administrative                        1,069        1,069           --           --
     Depletion of natural gas and oil properties       1,690        1,690           --           --
     Depreciation and amortization                       113          113           --           --
     Amortization of stock compensation                   65           65           --           --
                                                     -------      -------      -------      -------
                                                       3,756        3,756           --           --
                                                     -------      -------      -------      -------
        Operating income (loss)                          481          481           --           --
                                                     -------      -------      -------      -------

Other income (expense):
     Interest income                                      37           37           --           --
     Interest expense                                 (1,866)      (1,866)          --           --
                                                     -------      -------      -------      -------
                                                      (1,829)      (1,829)          --           --
                                                     -------      -------      -------      -------

Minority interest in net loss                             --         (923)          --           --
                                                     -------      -------      -------      -------
Net loss before income taxes                          (1,348)        (425)          --           --

Income tax benefit                                        --          145           --           --
Equity in net loss of investee                            --           --         (923)          96
                                                     -------      -------      -------      -------
     Net loss                                        $(1,348)     $  (280)     $  (923)     $    96
                                                     =======      =======      =======      =======
</TABLE>


                                       11
<PAGE>   14


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                       CONDENSED STATEMENTS OF OPERATIONS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1999
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                             BRIGHAM                     BRIGHAM       BRIGHAM
                                                             OIL &         BRIGHAM,      HOLDINGS      HOLDINGS
                                                             GAS, L.P.       INC.         I, LLC       II, LLC
<S>                                                          <C>           <C>           <C>           <C>
Revenues:
     Natural gas and oil sales                               $ 10,855      $ 10,855      $     --      $     --
     Workstation revenue                                          247           247            --            --
                                                             --------      --------      --------      --------
                                                               11,102        11,102            --            --
                                                             --------      --------      --------      --------
Costs and expenses:
     Lease operating                                            1,679         1,679            --            --
     Production taxes                                             685           685            --            --
     General and administrative                                 2,700         2,705             5             5
     Depletion of natural gas and oil properties                5,650         5,650            --            --
     Depreciation and amortization                                398           398            --            --
     Amortization of stock compensation                           (10)          (10)           --            --
                                                             --------      --------      --------      --------
                                                               11,102        11,107             5             5
                                                             --------      --------      --------      --------
        Operating income (loss)                                     0            (5)           (5)           (5)
                                                             --------      --------      --------      --------

Other income (expense):
     Interest income                                              134           134            --            --
     Interest expense                                          (4,464)       (4,464)           --            --
     Interest expense - intercompany                           (4,082)       (4,082)           --        (4,082)
     Loss on sale of natural gas and oil properties           (12,195)      (12,195)           --            --
                                                             --------      --------      --------      --------
                                                              (20,607)      (20,607)           --        (4,082)
                                                             --------      --------      --------      --------

Minority interest in net loss                                      --       (14,116)           --            --

                                                             --------      --------      --------      --------
Net loss before income taxes                                  (20,607)       (6,496)           (5)       (4,087)

Equity in net loss of investee                                     --            --       (14,116)       (2,203)
                                                             --------      --------      --------      --------
     Net loss                                                $(20,607)     $ (6,496)     $(14,121)     $ (6,290)
                                                             ========      ========      ========      ========
</TABLE>


          See accompanying notes to the condensed financial statements.


                                       12
<PAGE>   15


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                       CONDENSED STATEMENTS OF OPERATIONS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                     BRIGHAM                     BRIGHAM       BRIGHAM
                                                     OIL &         BRIGHAM,      HOLDINGS      HOLDINGS
                                                     GAS, L.P.       INC.         I, LLC       II, LLC
<S>                                                  <C>           <C>           <C>           <C>
Revenues:
     Natural gas and oil sales                       $ 11,292      $ 11,292      $     --      $     --
     Workstation revenue                                  322           322            --            --
                                                     --------      --------      --------      --------
                                                       11,614        11,614            --            --
                                                     --------      --------      --------      --------
Costs and expenses:
     Lease operating                                    1,542         1,542            --            --
     Production taxes                                     705           705            --            --
     General and administrative                         3,351         3,357             6             6
     Depletion of natural gas and oil properties        4,480         4,480            --            --
     Depreciation and amortization                        288           288            --            --
     Amortization of stock compensation                   298           298            --            --
                                                     --------      --------      --------      --------
                                                       10,664        10,670             6             6
                                                     --------      --------      --------      --------
       Operating income (loss)                            950           944            (6)           (6)
                                                     --------      --------      --------      --------

Other income (expense):
     Interest income                                      114           114            --            --
     Interest expense                                  (4,298)       (4,298)           --          (507)
                                                     --------      --------      --------      --------
                                                       (4,184)       (4,184)           --          (507)
                                                     --------      --------      --------      --------

Minority interest in net loss                              --        (2,215)           --            --
                                                     --------      --------      --------      --------
Net loss before income taxes                           (3,234)       (1,025)           (6)         (513)

Income tax benefit                                         --           337            --            --
Equity in net loss of investee                             --            --        (2,215)         (479)
                                                     --------      --------      --------      --------
     Net loss                                        $ (3,234)     $   (688)     $ (2,221)     $   (992)
                                                     ========      ========      ========      ========
</TABLE>



          See accompanying notes to the condensed financial statements.


                                       13
<PAGE>   16


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                       CONDENSED STATEMENTS OF CASH FLOWS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1999
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                                           BRIGHAM                       BRIGHAM       BRIGHAM
                                                                            OIL &         BRIGHAM,       HOLDINGS      HOLDINGS
                                                                           GAS, L.P.        INC.          I, LLC       II, LLC
<S>                                                                        <C>           <C>             <C>           <C>
Cash flows from operating activities:
     Net loss                                                              $(20,607)     $ (6,496)       $(14,121)     $ (6,290)
     Adjustments to reconcile net loss to cash
     provided by operating activities:
         Depletion of natural gas and oil properties                          5,650         5,650              --            --
         Depreciation and amortization                                          398           398              --            --
         Amortization of stock compensation                                     (10)          (10)             --            --
         Amortization of deferred loan fees and debt issuance costs             878           878              --            --
         Loss on sale of natural gas and oil properties                      12,195        12,195              --            --
         Minority interest in net loss                                           --       (14,116)             --            --
         Equity in net loss of investee                                          --            --          14,116         2,203
         Changes in working capital and other items:
            Decrease in accounts receivable                                   2,311         2,311              --            --
            Increase in prepaid expenses                                       (190)         (190)             --            --
            Decrease in accounts payable                                     (2,466)       (2,466)             --            --
            Increase in participant advances received                         1,040         1,040              --            --
            Decrease in other current liabilities                              (203)         (203)             --            --
            Increase in intercompany accounts payable                            49            11              --            53
            Other noncurrent assets                                             (76)          (76)             --            --
            Other noncurrent liabilities                                     (5,663)       (5,663)             --            --
                                                                           --------      --------        --------      --------
                                                                             (6,694)       (6,737)             (5)       (4,034)
                                                                           --------      --------        --------      --------
Cash flows from investing activities:
     Additions to natural gas and oil properties                            (18,310)      (18,310)             --            --
     Proceeds from sale of natural gas and oil properties                    27,122        27,122              --            --
     Additions to other property and equipment                                 (146)         (146)             --            --
     Change in investment in subsidiaries and intercompany advances            (191)           39               5             6
     Change in drilling advances paid                                          (302)         (302)             --            --
                                                                           --------      --------        --------      --------
                                                                              8,173         8,403               5             6
                                                                           --------      --------        --------      --------
Cash flows from financing activities:
     Increase in notes payable                                               12,750        12,750              --            --
     Repayment of notes payable                                             (16,750)      (16,750)             --            --
     Increase in intercompany notes payable                                   4,028         4,028              --         4,028
     Principal payments on capital lease obligations                           (193)         (193)             --            --
     Deferred loan fees paid                                                   (688)         (688)             --            --
                                                                           --------      --------        --------      --------
                                                                               (853)         (853)             --         4,028
                                                                           --------      --------        --------      --------

Net increase in cash and cash equivalents                                       626           813              --            --

Cash and cash equivalents, beginning of period                                2,549         2,563               5             6
                                                                           --------      --------        --------      --------
Cash and cash equivalents, end of period                                   $  3,175      $  3,376        $      5      $      6
                                                                           ========      ========        ========      ========

Supplemental disclosure of cash flow information:
     Cash paid during the period for interest                              $  3,739      $  3,739        $     --      $     --

Supplemental disclosure of noncash investing and financing activities:
     Capital lease asset additions                                         $     51      $     51        $     --      $     --
     Increase in accounts payable for deferred loan fees to be
         paid in future periods                                            $    150      $    150        $     --      $     --
     Capital contribution received in exchange for accounts
         payable and other noncurrent liabilities                          $  5,469      $     --        $     --      $     --
     Intercompany capital contributions                                    $     --      $  1,723        $  3,746      $  1,668

</TABLE>


          See accompanying notes to the condensed financial statements.


                                       14
<PAGE>   17


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                       CONDENSED STATEMENTS OF CASH FLOWS
                  FOR THE NINE MONTHS ENDED SEPTEMBER 30, 1998
                                 (in thousands)
                                   (unaudited)

<TABLE>
<CAPTION>
                                                                           BRIGHAM                      BRIGHAM       BRIGHAM
                                                                            OIL &        BRIGHAM,       HOLDINGS      HOLDINGS
                                                                           GAS, L.P.       INC.        I, LLC         II, LLC
<S>                                                                        <C>           <C>            <C>           <C>
Cash flows from operating activities:
     Net loss                                                              $ (3,234)     $   (688)      $ (2,221)     $   (992)
     Adjustments to reconcile net loss to cash
     used by operating activities:
         Depletion of natural gas and oil properties                          4,480         4,480             --            --
         Depreciation and amortization                                          288           288             --            --
         Amortization of stock compensation                                     298           298             --            --
         Amortization of deferred loan fees and debt issuance costs             425           425             --            --
         Minority interest in net loss                                           --        (2,215)            --            --
         Equity in net loss of investee                                          --            --          2,215           479
         Changes in working capital and other items:
            Increase in accounts receivable                                  (3,198)       (3,198)            --            --
            Increase in prepaid expenses                                        (74)          (74)            --            --
            Increase in accounts payable                                      1,759         1,759             --            --
            Increase in participant advances received                           437           437             --            --
            Increase in other current liabilities                             1,612         1,612             --            --
            Decrease in deferred income tax liability                            --          (336)            --            --
            Other noncurrent assets                                               6             6             --            --
            Other noncurrent liabilities                                        (94)          (94)            --            --
                                                                           --------      --------       --------      --------
                                                                              2,705         2,700             (6)         (513)
                                                                           --------      --------       --------      --------
Cash flows from investing activities:
     Additions to natural gas and oil properties                            (52,782)      (52,782)            --            --
     Additions to other property and equipment                                 (511)         (511)            --            --
     Change in investment in subsidiaries and intercompany advances            (408)          (13)        (5,223)      (41,812)
     Change in drilling advances paid                                          (326)         (326)            --            --
                                                                           --------      --------       --------      --------
                                                                            (54,027)      (53,632)        (5,223)      (41,812)
                                                                           --------      --------       --------      --------
Cash flows from financing activities:
     Capital contributions received                                           7,642         7,642          5,235        42,331
     Increase in notes payable                                               83,800        83,800             --            --
     Repayment of notes payable                                             (78,800)      (78,800)            --            --
     Increase in intercompany notes payable                                  40,000        40,000             --            --
     Principal payments on capital lease obligations                           (176)         (176)            --            --
     Deferred loan fees paid                                                 (1,990)       (1,990)            --            --
                                                                           --------      --------       --------      --------
                                                                             50,476        50,476          5,235        42,331
                                                                           --------      --------       --------      --------

Net decrease in cash and cash equivalents                                      (846)         (456)             6             6

Cash and cash equivalents, beginning of period                                1,701         1,701             --            --
                                                                           --------      --------       --------      --------
Cash and cash equivalents, end of period                                   $    855      $  1,245       $      6      $      6
                                                                           ========      ========       ========      ========

Supplemental disclosure of cash flow information:
     Cash paid during the period for interest                              $  3,182      $  3,182       $     --      $     --

Supplemental disclosure of noncash investing and financing activities:
     Capital lease asset additions                                         $    320      $    320       $     --      $     --
     Intercompany capital contributions                                    $     --      $     --       $ 29,911      $ 13,318

</TABLE>



          See accompanying notes to the condensed financial statements.


                                       15
<PAGE>   18


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                    CONDENSED STATEMENTS OF CHANGES IN EQUITY
                          (in thousands, except shares)
                                   (unaudited)


<TABLE>
<CAPTION>
                                                                                       Retained
                                             Common Stock              Additional     Earnings/
                                        --------------------------       Paid-in     Accumulated     Partners'
                                          Shares        Amounts          Capital       Deficit        Capital       Total
                                        ----------     -----------     -----------     --------      --------      --------
<S>                                     <C>            <C>             <C>             <C>            <C>          <C>
Brigham Oil & Gas, L.P.
     Balance,
       December 31, 1998                        --     $        --     $        --     $     --      $ 17,124      $ 17,124
     Capital contribution                       --              --              --           --         5,469         5,469
     Net loss                                   --              --              --           --       (20,607)      (20,607)
                                        ----------     -----------     -----------     --------      --------      --------
     Balance,
       September 30, 1999                       --     $        --     $        --     $     --      $  1,986      $  1,986
                                        ==========     ===========     ===========     ========      ========      ========

Brigham Inc.
     Balance,
       December 31, 1998                     1,000     $         1     $    16,109     $(10,727)     $     --      $  5,383
     Capital contribution                       --              --           1,723           --            --         1,723
     Net loss                                   --              --              --       (6,496)           --        (6,496)
                                        ----------     -----------     -----------     --------      --------      --------
     Balance,
       September 30, 1999                    1,000     $         1     $    17,832     $(17,223)     $     --      $    610
                                        ==========     ===========     ===========     ========      ========      ========

Brigham Holding I, LLC
     Balance,
       December 31, 1998                        --     $        --     $        --     $     --      $ 11,719      $ 11,719
     Capital contribution                       --              --              --           --         3,746         3,746
     Net loss                                   --              --              --           --       (14,121)      (14,121)
                                        ----------     -----------     -----------     --------      --------      --------
     Balance,
       September 30, 1999                       --     $        --     $        --     $     --      $  1,344      $  1,344
                                        ==========     ===========     ===========     ========      ========      ========

Brigham Holdings II, LLC
     Balance,
       December 31, 1998                        --     $        --     $        --     $     --      $  5,212      $  5,212
     Capital contribution                       --              --              --           --         1,668         1,668
     Net loss                                   --              --              --           --        (6,290)       (6,290)
                                        ----------     -----------     -----------     --------      --------      --------
     Balance,
       September 30, 1999                       --     $        --     $        --     $     --      $    590      $    590
                                        ==========     ===========     ===========     ========      ========      ========
</TABLE>


          See accompanying notes to the condensed financial statements.


                                       16
<PAGE>   19


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                   NOTES TO THE CONDENSED FINANCIAL STATEMENTS
                                   (unaudited)



1.     ORGANIZATION AND BACKGROUND

       In August 1998, upon the filing of a registration statement with the SEC,
       Brigham Exploration Company, a Delaware corporation, (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"). The Notes are fully and unconditionally guaranteed, on a joint
       and several basis, by each of the Company's directly or indirectly
       wholly-owned subsidiaries which are Brigham Oil & Gas, L.P. (the
       "Partnership"), Brigham Inc., Brigham Holdings I LLC ("Holdings I"), and
       Brigham Holdings II LLC ("Holdings II"). Furthermore, these subsidiaries
       have pledged their respective stock and partnership interests as
       collateral for the Notes. These financial statements include the
       financial statements for the wholly owned subsidiaries whose securities
       and partnership interests comprise substantially all of the collateral
       pledged for the Notes.

       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.
       Brigham, Inc. is a Nevada corporation whose only asset prior to the
       Exchange was its less than 1% ownership interest in the Partnership.
       Brigham, Inc. is the managing general partner of the Partnership.

       On February 25, 1997, the Company was formed for the purpose of
       exchanging its common stock for the common stock of Brigham, Inc. and the
       partnership interests of the Partnership. Subsequent to the Exchange and
       the Offering, the Company owned a 68.5% interest in the Partnership and
       Brigham, Inc. owned a 31.50% interest in the Partnership. Effective
       January 1, 1998, Brigham, Inc. contributed 30.5% of its 31.5% interest in
       the Partnership to Holdings II, a newly formed Nevada LLC and wholly
       owned subsidiary of Brigham, Inc., whose only asset is its investment in
       the Partnership. Also effective January 1, 1998 the Company contributed
       its 68.5% interest in the Partnership to Brigham Holdings I, a newly
       formed Nevada LLC and wholly owned subsidiary of the Company whose only
       asset is its investment in the Partnership

2.     BASIS OF PRESENTATION

       The accompanying financial condensed financial statements are unaudited,
       and in the opinion of management, reflect all adjustments that are
       necessary for a fair presentation of the financial position and results
       of operations for the periods presented. All such adjustments are of a
       normal and recurring nature. The results of operations for the periods
       presented are not necessarily indicative of the results to be expected
       for the entire year. The unaudited condensed financial statements should
       be read in conjunction with the Company's 1998 Annual Report on Form 10-K
       pursuant to Section 13 or 15(d) of the Securities and Exchange Act of
       1934.

3.     SALE OF NATURAL GAS AND OIL PROPERTIES

       In February 1999, the Partnership 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 Partnership 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 Partnership 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 Partnership pays 100% of the drilling and
       completion costs for all wells drilled by the Duke LLC


                                       17
<PAGE>   20
                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                   NOTES TO THE CONDENSED FINANCIAL STATEMENTS
                                   (unaudited)


       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 Partnership has certain rights to back-in for up to a 94%
       effective working interest in the Duke LLC properties.

       In June 1999, the Company sold all of its interests in certain producing
       and non-producing natural gas and oil properties for a total sales price
       of $17.1 million. Due to the magnitude of the reserve volumes that were
       attributable to these properties relative to the Company's remaining net
       reserve volumes, the Company recognized as a loss the difference between
       the sales price received, after adjustment for transaction costs, and the
       $28.9 million basis allocated to the divested properties in accordance
       with the full-cost method of accounting for oil and gas properties.

4.     ISSUANCE OF COMMON STOCK

       In March 1999, the Partnership entered into an agreement with Veritas DGC
       Land, Inc. ("Veritas") to exchange 1,002,865 shares of newly issued
       Brigham Exploration Company common stock valued at $3.50 per share for
       approximately $3.5 million of payment obligations due from the
       Partnership to Veritas in 1999 for certain seismic acquisition and
       processing services previously performed. In addition, this agreement
       provides for the payment by the Partnership of up to $1 million in
       future seismic processing services to be performed by Veritas through
       December 31, 1999, in newly issued shares of the Company's common stock
       valued at $3.50 per share, in the event that the Partnership does not
       elect to pay for such services in cash. The settlement of these seismic
       processing services has been determined on a quarterly basis. Subsequent
       to March 30, 1999, the Company issued an additional 208,715 shares of
       common stock valued at $3.50 per share to Veritas pursuant to the
       Partnership's election to settle certain seismic processing service
       obligations incurred during the second and third quarters of 1999 in the
       Company's common stock instead of cash.

5.     AMENDMENT TO REVOLVING CREDIT FACILITY

       In July 1999, the Partnership and its senior lenders entered into an
       amendment to the Partnership's revolving credit facility  (the "Credit
       Facility"). This amendment provides the Partnership with borrowing
       availability of $56 million principally to fund its planned drilling
       activities and anticipated working capital requirements through the end
       of 1999. The Partnership's senior lenders have indicated that the
       borrowing availability provided under the amended Credit Facility exceeds
       that which would otherwise be made available under a more traditional
       conforming borrowing base calculation based on the estimated value of the
       Partnership's current net proved reserves and its cash flow. As
       consideration for this amendment to the Credit Facility, in July 1999
       Brigham Exploration Company issued to the Partnership's senior lenders
       one million warrants to purchase the Company's common stock at an
       exercise price of $2.25 per share. The warrants have a seven-year term
       from the date of issuance and are exercisable at the holders' option at
       any time. An estimated value of $1.2 million was attributed to these
       warrants by the Partnership and was recognized as additional deferred
       loan fees which will be amortized over the remaining period to maturity
       of the Credit Facility borrowings at January 26, 2001.

6.     HEDGING ACTIVITIES

       In September 1999, the Partnership entered into five call options with a
       counterparty for certain future oil and natural gas production. Under the
       terms of the contracts, for any month where the average index price (WTI
       or ANR Pipeline Company - Oklahoma) is greater than the strike price per
       the contract, the Partnership is required to pay to the counterparty the
       absolute value of that difference times the production volumes covered
       under the contract. If the average index price is less than the strike
       price for a given month, no settlement is required. These contracts are


                                       18
<PAGE>   21

       summarized as follows:

<TABLE>
<CAPTION>
                  Daily                           Total Volumes Hedged       Average
  Call           Volumes                       -------------------------      Fixed
Options           Hedged      Monthly Term      2000     2001      2000   Contract Price
- -------         --------     -------------     ------  -------   -------  --------------
<S>             <C>         <C>                <C>     <C>       <C>      <C>
Contract #1       600        October 1999 -    55,200   54,000      -         $24.00
                  Bbls        March 2000        Bbls     Bbls                per Bbl

Contract #2       600         April 2000 -     54,600     -         -         $22.00
                  Bbls         June 2000        Bbls                         per Bbl

Contract #3      10,000        May 2001 -        -     1,840,000    -         $2.665
                 MMBtu       October 2001                MMBtu               per MMBtu

Contract #4      10,000      November 2000 -     -      610,000  1,200,000    $2.670
                 MMBtu         April 2002                MMBtu    MMBtu      per MMBtu

Contract #5      10,000        May 2002 -        -        -       610,000     $2.670
                 MMBtu        June 2002                            MMBtu     per MMBtu
</TABLE>

7.     ACCOUNTING FOR DERIVATIVE INSTRUMENTS AND HEDGING ACTIVITIES

       In June 1998, the Financial Accounting Standards Board (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 Partnership
       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
       Partnership 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 Partnership
       must adopt SFAS No. 133, as amended by SFAS No. 137, effective January 1,
       2001. The Partnership is in the process of analyzing the potential impact
       of this standard on its financial statement presentations.


                                       19
<PAGE>   22



Item 2.  Management's Discussion and Analysis of Results of Operations and
         Financial Condition

RESULTS OF OPERATIONS

Comparison of three month periods ended September 30, 1998 and September 30,
1999

      Natural gas and oil sales. Natural gas and oil sales decreased 1% from
$4.2 million in the third quarter of 1998 to $4.1 million in the third quarter
of 1999. Of this net decrease, $483,000 was attributable to a decrease in
production volumes, offset in part by $430,000 attributable to an increase in
the average sales price for natural gas and oil. Production volumes for natural
gas decreased 5% from 1,198 MMcf in the third quarter of 1998 to 1,142 MMcf in
the third quarter of 1999. Net natural gas volumes for the third quarter of 1998
included approximately 205 MMcf attributable to properties sold by Brigham in
June 1999. Therefore, after adjusting for the effects of the property
divestitures, net natural gas volumes increased 15% in the third quarter of
1999, compared to the same period in 1998, as a result of the completion of
wells drilled early in 1999 and recompletion and workover projects performed by
the Company on certain producing wells. The average price received for natural
gas decreased 13% from $2.32 per Mcf in the third quarter of 1998 to $2.01 per
Mcf in the third quarter of 1999. As a result of natural gas hedging activities,
losses of $610,000, or $0.53 per Mcf, were realized in the third quarter of
1999, compared to gains of $236,000, or $0.20 per Mcf, in the third quarter of
1998. Production volumes for oil decreased 24% from 114 MBbls in the third
quarter of 1998 to 87 MBbls in the third quarter of 1999. This decrease in net
oil production volumes was primarily due to the natural decline of existing
producing oil wells coupled with the Company's strategic decision to reduce its
drilling for oil prospects during the previous 12 months in favor of natural gas
projects. Additionally, Brigham's June 1999 property divestitures resulted in a
9 MBbl reduction of net oil production volumes in the third quarter of 1999
compared to the third quarter of 1998. The average price received for oil
increased 71% from $12.14 per Bbl in the third quarter of 1998 to $20.76 per Bbl
in the third quarter of 1999.

      Workstation revenue. Workstation revenue increased 15% from $75,000 in the
third quarter of 1998 to $86,000 in the third quarter of 1999. Brigham
recognizes workstation revenue as industry participants in the Company's seismic
programs are charged an hourly rate for the work performed by Brigham on its 3-D
seismic interpretation workstations.

      Lease operating expenses. Lease operating expenses decreased 7% from
$564,000 for the third quarter of 1998 to $525,000 for the third quarter of 1999
and, on a per unit of production basis, lease operating expenses for the same
periods increased 7% from $0.30 per Mcfe to $0.32 per Mcfe. The decrease in
lease operating expenses was primarily due to a decrease in the number of
producing wells in the third quarter of 1999, as compared with the same period
in 1998, as a result of Brigham's June 1999 property divestitures.

      Production taxes. Production taxes increased 18% from $255,000 ($0.14 per
Mcfe) for the third quarter of 1998 to $300,000 ($0.18 per Mcfe) for the third
quarter of 1999, primarily as a result of a 36% increase in the average price
received for natural gas and oil sales before the effects of hedging gains and
losses, partially offset by the 12% decrease in equivalent natural gas and oil
production volumes during the third quarter of 1999.

      General and administrative expenses. General and administrative expenses
decreased 16% from $1.1 million for the third quarter of 1998 to $901,000 for
the third quarter of 1999 primarily due to the reduction of various
administrative costs, including the elimination of accrued employee bonuses for
1999, a 10% payroll reduction effective mid-May 1999, and a $66,000 increase in
overhead fees billed to working interest participants on Company-operated wells.
On a per unit of production basis, general and administrative


                                       20

<PAGE>   23


expenses decreased from $0.57 per Mcfe for the third quarter of 1998 to $0.54
per Mcfe for the third quarter of 1999.

      Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased from $1.7 million ($0.90 per Mcfe) in the third quarter
of 1998 to $2.8 million ($1.71 per Mcfe) in the third quarter of 1999. Of this
net increase, $1.4 million was due to an increase in the depletion rate per unit
of production, partially offset by $196,000 due to a 12% decrease in production
volumes. The increased depletion rate reflected the effect of revising the 1999
year to date depletion rate to recognize lower reserve volume estimates
resulting from Brigham's reduced level of drilling activity during 1999 and the
Company's June 1999 property divestitures.

      Interest expense. Net interest expense increased 65% from $1.9 million in
the third quarter of 1998 to $3.2 million in the third quarter of 1999. This
increase was due to a higher average debt balance with a higher average interest
rate in the third quarter of 1999 compared with the third quarter of 1998. The
weighted average outstanding debt balance increased from $71.6 million in the
third quarter of 1998 to $94.7 million in the third quarter of 1999. The average
effective annual interest rate on borrowings outstanding during the third
quarter of 1998 was 10.8% compared to 13.4% for the third quarter of 1999.
Interest expense in the third quarter of 1999 included $2.1 million of non-cash
charges, including (i) $1.4 million of interest expense related to the
Subordinated Notes that was paid through the issuance of additional Subordinated
Notes (or "paid-in-kind"), (ii) $533,000 for amortization of deferred financing
fees, and (iii) $166,000 for amortization of debt discounts related to the
issuance of the Subordinated Notes. In connection with issuance of the
Subordinated Notes in August 1998, the Company recorded the Subordinated Notes
at a discount of $4.5 million to reflect the estimated value of the warrants to
purchase common stock that were issued in connection with the issuance of the
Subordinated Notes. This discount was increased by $479,000 in March 1999 to
adjust the estimated value of the warrants based on the amendment of certain
terms of the warrants, including a decrease in the exercise price per share and
an increase in the term of the warrants. The Company amortizes this debt
discount over the five-year term of the Subordinated Notes based on the interest
method of amortization and includes such amortization in interest expense. In
connection with the amendment to the Credit Facility executed in July 1999, the
Company issued to its senior lenders one million warrants to purchase the
Company's common stock at an exercise price of $2.25 per share. An estimated
value of $1.2 million was attributed to these warrants by the Company and was
recognized as additional deferred loan fees which will be amortized and included
in interest expense over the remaining period to maturity of the Credit Facility
borrowings at January 26, 2001.


Comparison of nine month periods ended September 30, 1998 and September 30, 1999

      Natural gas and oil sales. Natural gas and oil sales decreased 4% from
$11.3 million in the first nine months of 1998 to $10.9 million in the first
nine months of 1999. Of this net decrease, $938,000 was attributable to a
decrease in production volumes, offset in part by $501,000 attributable to an
increase in the average sales price for natural gas and oil. Production volumes
for natural gas increased 2% from 3,145 MMcf in the first nine months of 1998 to
3,194 MMcf in the first nine months of 1999. Net natural gas volumes decreased
in the first nine months of 1999 compared to the first nine months of 1998 by
219 MMcf attributable to the properties sold by Brigham in June 1999. Therefore,
after adjusting for the effects of the property divestitures, net natural gas
volumes for the period increased by 11% as a result of the completion of wells
drilled early in 1999, and recompletion and workover projects performed by the
Company on certain producing wells. The average price received for natural gas
decreased 6% from $2.18 per Mcf in the first nine months of 1998 to $2.06 per
Mcf in the first nine months of 1999. As a result of natural gas hedging
activities, losses


                                       21

<PAGE>   24



of $42,000, or $0.01 per Mcf, were realized in the first nine months of 1999,
compared to gains of $275,000, or $0.09 per Mcf in the first nine months of
1998. Production volumes for oil decreased 23% from 346 MBbls in the first nine
months of 1998 to 266 MBbls in the first nine months of 1999. This decrease in
net oil production volumes was primarily due to the natural decline of existing
producing oil wells coupled with the Company's strategic decision to reduce its
drilling for oil prospects during 1998 and 1999 and the curtailment of certain
producing oil wells in early 1999, both in response to low oil prices.
Additionally, Brigham's June 1999 property divestitures resulted in a 9 MBbl
reduction of net oil production volumes for the first nine months of 1999
compared to the first nine months of 1998. The average price received for oil
increased 26% from $12.82 per Bbl in the first nine months of 1998 to $16.12 per
Bbl in the first nine months of 1999.

      Workstation revenue. Workstation revenue decreased 23% from $322,000 in
the first nine months of 1998 to $247,000 in the first nine months of 1999.
Brigham recognizes workstation revenue as industry participants in the Company's
seismic programs are charged an hourly rate for the work performed by Brigham on
its 3-D seismic interpretation workstations. This decrease is primarily
attributable to the Company's increased working interests in its most recently
acquired 3-D seismic data, which reduces the amount of workstation
interpretation costs that Brigham can bill to its project 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 9% from $1.5
million for the first nine months of 1998 to $1.7 million for the first nine
months of 1999, and, on a per unit of production basis, lease operating expenses
for the same periods increased 17% from $0.30 per Mcfe to $0.35 per Mcfe. The
increase in lease operating expenses was primarily attributable to higher costs
incurred related to recompletion and workover projects performed during 1999 on
certain producing wells. This increase was partially offset by a 5% decrease in
lease operating expenses resulting from Brigham's June 1999 property
divestitures.

      Production taxes. Production taxes decreased 3% from $705,000 ($0.14 per
Mcfe) for the first nine months of 1998 to $685,000 ($0.14 per Mcfe) for the
first nine months of 1999, primarily as a result of the 8% decrease in
equivalent natural gas and oil production volumes, partially offset by the 5%
increase in the average price received for equivalent natural gas and oil sales
during the first nine months of 1999.

      General and administrative expenses. General and administrative expenses
decreased 19% from $3.4 million for the first nine months of 1998 to $2.7
million for the first nine months of 1999 primarily due to the reduction of
various administrative costs, including the elimination of accrued employee
bonuses for 1999, a 10% payroll reduction effective mid-May 1999, and a $331,000
increase in overhead fees billed to working interest participants on
Company-operated wells. On a per unit of production basis, general and
administrative expenses decreased 12% from $0.64 per Mcfe for the first nine
months of 1998 to $0.57 per Mcfe for the first nine months of 1999.

      Depletion of natural gas and oil properties. Depletion of natural gas and
oil properties increased from $4.5 million ($0.86 per Mcfe) in the first nine
months of 1998 to $5.7 million ($1.18 per Mcfe) in the first nine months of
1999. Of this net increase, $1.5 million was due to a 37% increase in the
depletion rate per unit of production, which was partially offset by $372,000
due to the decrease in production volumes. The increased depletion rate
reflected the recognition of lower reserve volume estimates as a result of
Brigham's reduced level of drilling activity during 1999 and the Company's June
1999 property divestitures.

      Interest expense. Net interest expense increased 115% from $4.3 million in
the first nine months of 1998 to $9.1 million in the first nine months of 1999.
This increase was due to a higher average debt balance with


                                       22

<PAGE>   25



a higher average interest rate in the first nine months of 1999 compared with
the first nine months of 1998. The weighted average outstanding debt balance
increased from $58.1 million in the first nine months of 1998 to $99.5 million
in the first nine months of 1999. The average effective annual interest rate on
borrowings outstanding during the first nine months of 1999 was 12.2% compared
to 10% for the first nine months of 1998. Interest expense in the first nine
months of 1999 included $5.6 million of non-cash charges, including (i) $4.1
million of interest expense related to the Subordinated Notes that was paid
through the issuance of additional Subordinated Notes (or "paid-in-kind"), (ii)
$1.2 million for amortization of deferred financing fees, and (iii) $393,000 for
amortization of debt discounts related to the issuance of the Subordinated
Notes. In connection with issuance of the Subordinated Notes in August 1998, the
Company recorded the Subordinated Notes at a discount of $4.5 million to reflect
the estimated value of the warrants to purchase common stock that were issued in
connection with the issuance of the Subordinated Notes. This discount was
increased by $479,000 in March 1999 to adjust the estimated value of the
warrants based on the amendment of certain terms of the warrants, including a
decrease in the exercise price per share and an increase in the term of the
warrants. The Company amortizes this debt discount over the five-year term of
the Subordinated Notes based on the interest method of amortization and includes
such amortization in interest expense. In connection with the amendment to the
Credit Facility executed in July 1999, the Company issued to its senior lenders
one million warrants to purchase the Company's common stock at an exercise price
of $2.25 per share. An estimated value of $1.2 million was attributed to these
warrants by the Company and was recognized as additional deferred loan fees
which will be amortized and included in interest expense over the remaining
period to maturity of the Credit Facility borrowings at January 26, 2001.

      Loss on sale of natural gas and oil properties. In June 1999, the Company
sold all of its interests in certain producing and non-producing natural gas and
oil properties for a total sales price of $17.1 million. Due to the magnitude of
the reserve volumes that were attributable to these properties relative to the
Company's remaining net reserve volumes, the Company recognized as a loss the
difference between the sales price received, after adjustment for transaction
costs, and the $28.9 million basis allocated to the divested properties in
accordance with the full-cost method of accounting for oil and natural gas
properties. No property divestitures occurred during the first nine months of
1998 for which recognition of gain or loss was appropriate.


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 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 during the
second half of 1998 and the early part of 1999, 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 during the second
half of 1998, resulting in lower levels of project cost recoupment than
budgeted, (iv) high levels of expenditures in 1997 and 1998 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 on a number of high equity interest exploratory and development
wells.

      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


                                       23

<PAGE>   26



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 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) elimination of substantially all
planned seismic and land expenditures for new projects until its capital
resources can support such additional activity, (iii) divestitures of certain
producing natural gas and oil properties 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)
implementation of an overhead reduction plan to reduce general and
administrative expenses, and (vi) evaluating opportunities to raise additional
capital either through the sales of project equity interests, further
restructuring of its senior debt or the issuance of equity or equity-linked
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 1999, and has
effected certain of them to date, the successful completion of any or all of
these efforts to improve the Company's liquidity and 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 through December 31, 1999, 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
seismic processing services has been determined on a quarterly basis. Subsequent
to March 30, 1999, Brigham issued an additional 208,715 shares of common stock
valued at $3.50 per share to Veritas pursuant to its election to settle certain
seismic processing service obligations incurred during the second and third
quarters of 1999 in common stock instead of cash. Brigham considers this
arrangement to have been beneficial as it has enabled 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 its revolving credit
facility and other debt borrowings, public and private equity financings, the
sale of interests in projects and properties, 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. In January 1998, the Company entered into a new revolving credit
facility that provided for an initial borrowing availability of $75 million that
was used to repay its then outstanding borrowings under its previous credit
facility and to fund capital expenditures. This Credit Facility has been
subsequently amended, most recently in July 1999, to provide for a borrowing
availability of $56 million. In August 1998, the Company issued $50 million of
debt and equity securities, including $40 million of Subordinated Notes, that
generated proceeds of approximately $47.5


                                       24

<PAGE>   27



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. In late June 1999, the Company received $17.1 million ($16.8
million after the adjustment for transaction costs and post-closing adjustments)
from the sale of its interests in producing and non-producing natural gas and
oil properties within two non-operated fields in its Anadarko Basin province.

Cash Flow Analysis

      In the first nine months of 1999, cash flow used by operating activities
was $2.7 million primarily as a result of a $5.7 million decrease in other
noncurrent liabilities partially offset by a net $458,000 increase in non-cash
working capital and a net $2.5 million from total revenues, less lease operating
expenses, production taxes, general and administrative expenses and cash
interest expenses. Cash flow provided by investing activities was $8.4 million
in the first nine months of 1999 primarily as a net result of $18.3 million of
capital expenditures related to exploration activities and $27.1 million of
proceeds received from the sale of interests in certain seismic projects and
natural gas and oil properties. Cash flow used in financing activities was $4.9
million in the first nine months of 1999 resulting from a $4.0 million net
reduction in notes payable attributable to the repayment of outstanding
borrowings under the Credit Facility and the payment of deferred loan fees and
principal payments made on capital lease obligations.

Revolving Credit Facility

      In January 1998, the Company entered into a new revolving credit agreement
(the "Credit Facility"), which provided for an initial borrowing availability of
$75 million. The Credit Facility was amended in March 1999 to reduce the
borrowing availability, extend the date of borrowing base redetermination,
modify certain financial covenants, include certain additional covenants that
place significant restrictions on the Company's ability to incur certain capital
expenditures, and to increase the interest rate on outstanding borrowings.

      As a result of the completion of the majority of the Company's strategic
initiatives to improve its capital resources, including the late June 1999
property divestitures and the application of the net sales proceeds to reduce
borrowings outstanding under the Credit Facility, the Company and its senior
lenders entered into an amendment to the Credit Facility in July 1999. This
amendment provides the Company with borrowing availability of $56 million
principally to fund its planned drilling activities and anticipated working
capital requirements through the end of 1999. The Company's lenders have
indicated that the borrowing availability provided under the amended Credit
Facility exceeds that which would otherwise be made available under a more
traditional conforming borrowing base calculation based on the estimated value
of the Company's current net proved reserves and its cash flow. As consideration
for this amendment to the Credit Facility, in July 1999 the Company issued to
its senior lenders one million warrants to purchase the Company's common stock
at an exercise price of $2.25 per share. The warrants have a seven-year term
from the date of issuance and are exercisable at the holders' option at any
time. An estimated value of $1.2 million was attributed to these warrants by the
Company and was recognized as additional deferred loan fees which will be
amortized over the remaining period to maturity of the Credit Facility
borrowings at January 26, 2001.

      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 is either the lender's base rate or LIBOR plus 3.00%,
at the Company's option. 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. The borrowing availability will be redetermined
by the senior lenders at January 31, 2000, based on the Company's then estimated
net proved reserve value and cash flow.


                                       25

<PAGE>   28


      At November 10, 1999, the Company had $55 million in borrowings
outstanding under the Credit Facility, which bear interest at an average annual
rate of 8.54%.

      The Credit Facility has certain financial covenants including current and
interest coverage ratios, as defined. The Company and its lenders effected the
March 1999 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 its
amendments are indicative of its senior lenders' cooperation in the current oil
and natural gas industry environment. If oil and natural prices deteriorate
beyond the date of redetermination of borrowing availability or the Company does
not generate its expected growth in proved reserves through its drilling
activities planned for the remainder of 1999, the Company believes its senior
lenders may require the Company to reduce its level of borrowing under the
Credit Facility accordingly. Should the Company be unable to comply with certain
of the financial covenants, its senior 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. 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 the Company may pay interest in kind
for a cumulative total of six quarterly interest payments 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.


                                       26

<PAGE>   29



      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 and extended the term of the Warrants from seven to ten years.

      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.

      At September 30, 1999 and November 10, 1999, the Company has $44 million
principal amount of Subordinated Notes outstanding.

Capital Expenditures

      As a result of the Company's limited available capital resources, Brigham
has significantly reduced its capital expenditure budget for 1999 from the
Company's previously anticipated levels in an effort to match its current and
expected future capital resources. The Company's current 1999 capital budget is
estimated to be $25 million, or approximately 30% of 1998 expenditures. The
Company's budgeted 1999 capital expenditures consist of approximately $15.5
million to drill an estimated 25 to 30 gross wells, $6 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 to prospects identified among
its 3-D projects primarily in its Anadarko Basin and Gulf Coast provinces, and
such expenditures will be devoted to the drilling of the highest grade prospects
in the Company's inventory of 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 and equity interests (including the Anadarko Basin property
divestitures completed in late June 1999, the sale of interests in certain 3-D
seismic projects for $11.5 million completed in January 1999 and the potential
sales of additional interests in certain 3-D seismic projects during the second
half of 1999). The Company's capital availability during 1999 will depend to a
large extent on its success raising additional financing through its planned and
potential strategic initiatives discussed above, and therefore 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.


                                       27

<PAGE>   30

OTHER 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 developed a plan to address this issue and has reviewed 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 internal identification and remediation
phases of its plan by identifying all computerized systems and completing an
inventory of its equipment and component parts. The Company reviewed the
manufacturer's information and/or performance testing with respect to its
inventory. Where material problems were identified, the Company has undertaken
remediation, replacement or alternative procedures for non-compliant equipment
or facilities on a business priority basis. In addition, in the ordinary course
of replacing computer equipment and software, the Company attempts to obtain
replacements that are Year 2000 compliant

      As of September 30, 1999, 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 currently
estimates that its total out-of-pocket costs to become Year 2000 compliant will
be insignificant. The Company currently expects that such costs will not have a
material adverse effect on the Company's financial condition, operations or
liquidity.

      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 participants, financial institutions,
customers and governments do not become Year 2000 compliant on a timely basis.
The Company has identified third parties whose business significantly impacts
the Company and has attempted to contact those significant third parties to
determine the extent to which interfaces with such entities are vulnerable to
Year 2000 issues. All significant third party responses received to date have
indicated that such entities are either Year 2000 compliance or expect to be
Year 2000 compliant prior to January 1, 2000. The Company is in the process of
performing follow-up inquiries with respect to those significant third parties
that have not responded to the Company's previous Year 2000 compliance
information requests. The Company expects to have completed the remaining follow
up inquiries by November 30, 1999, and will endeavor to undertake any
appropriate remediation efforts that may be required as a result of those third
party investigations.

      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. In the event third
parties are unable to timely resolve their Year 2000 problems, such failure
could partially affect the Company's ability to conduct its operations, sell its
oil and natural gas and receive related payments. Year 2000 failures could also
cause a shutdown of the pipeline systems into which the Company markets its
natural gas and oil production. In addition, there could be disruptions in
getting certain vendors to provide supplies and /or services in support of the
Company's operation. While this is the most likely worst case scenario, based
upon the responses received from industry partners and an analysis of the
services and products that are provided by those from whom the Company has not
yet received a response, the Company is not


                                       28

<PAGE>   31


currently aware of a likely business disruption. Since the elements of such a
scenario are outside of the Company's control and an effective contingency plan
would not be economically feasible, the Company has not developed a contingency
plan for dealing with a worst case scenario. 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 Information." 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.

Forward Looking Information

      The Company may make forward looking statements, oral or written,
including statements in this report, press releases and other filings with the
SEC, relating to the Company's drilling plans, its potential drilling locations,
capital expenditures, use of offering proceeds, the ability of expected sources
of liquidity to support working capital and capital expenditure requirements and
the Company's financial position, business strategy and other plans and
objectives for future operations. Such statements involve risks and
uncertainties, including those relating to the Company's dependence on
exploratory drilling activities, the volatility of natural gas and oil prices,
the risks associated with growth (including the risk of reduced availability of
seismic gathering and drilling services in the face of growing demand), the
substantial capital requirements of the Company's exploration and development
projects, operating hazards and uninsured risks and other factors detailed in
the Company's registration statement and other filings with the SEC. All
subsequent oral and written forward looking statements attributable to the
Company are expressly qualified in their entirety by these factors. The Company
assumes no obligation to update these statements.


                                       29

<PAGE>   32


PART II.  OTHER INFORMATION:

Item 2.   Changes in Securities

          In July 1999, the Company issued to Bank of Montreal and Societe
          General, Southwest Agency (the "Lenders"), warrants to purchase a
          total of one million shares of Brigham Exploration Company common
          stock at an exercise price of $2.25 per share. The warrants have a
          seven year term from the date of issuance and are exercisable at the
          holders' option at any time. The warrants were issued as consideration
          for an amendment executed in July 1999 to the revolving credit
          agreement between the Company and the Lenders. These shares were
          issued pursuant to the exemption provided by Section 4(2) of the
          Securities Act of 1933, as amended.

          Pursuant to the Company's agreement dated March 30, 1999 with Veritas
          DGC Land, Inc. ("Veritas"), in August 1999 the Company exchanged
          89,165 shares of newly issued Brigham Exploration Company common stock
          valued at $3.50 per share for approximately $312,000 of payment
          obligations due to Veritas in 1999 for certain seismic acquisition and
          processing services. These shares were issued pursuant to the
          exemption provided by Section 4(2) of the Securities Act of 1933, as
          amended. Veritas represented its intention to acquire the shares for
          investment purposes only and not for the purpose of resale or
          distribution, and appropriate legends were affixed to the certificate
          issued in such transaction. Veritas was given access to information
          about the Company.

Item 6.   Exhibits and Reports on Form 8-K

          (a)     Exhibits

                  10.1     Agreement dated as of August 16, 1999 between Brigham
                           Exploration Company and Jon L. Glass for the
                           amendment of an Employee Stock Ownership Agreement
                           and Option Agreements.

                  10.2     Agreement dated as of August 16, 1999 between Brigham
                           Exploration Company and Craig M. Fleming for the
                           amendment of an Employee Stock Ownership Agreement
                           and Option Agreement.

                  10.3     Form Change of Control Agreement dated as of
                           September 20, 1999 between Brigham Exploration
                           Company and certain Officers.

                  10.4     Warrant Agreement for the Purchase of Common Stock
                           dated as of July 19, 1999 by and between Brigham
                           Exploration Company and Bank of Montreal.

                  10.5     Warrant Agreement for the Purchase of Common Stock
                           dated as of July 19, 1999 by and between Brigham
                           Exploration Company and Societe Generale, Southwest
                           Agency.

                  27       Financial Data Schedule


                                       30

<PAGE>   33


                                   SIGNATURES

     Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto, duly authorized, in the City of Austin, State of Texas,
on the 12th day of November, 1999.

                                       BRIGHAM EXPLORATION COMPANY


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



                                   By:    /s/ CURTIS F. HARRELL
                                       ---------------------------------------
                                       Curtis F. Harrell
                                       Chief Financial Officer


                                       31

<PAGE>   34


                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>
    EXHIBIT
      NO.                                 DESCRIPTION
    -------                               -----------
<S>                 <C>
     10.1           Agreement dated as of August 16, 1999 between Brigham
                    Exploration Company and Jon L. Glass for the amendment of an
                    Employee Stock Ownership Agreement and Option Agreements.

     10.2           Agreement dated as of August 16, 1999 between Brigham
                    Exploration Company and Craig M. Fleming for the amendment
                    of an Employee Stock Ownership Agreement and Option
                    Agreements.

     10.3           Change of Control Agreement dated as of September 20, 1999
                    between Brigham Exploration Company and certain Officers.

     10.4           Warrant Agreement for the Purchase of Common Stock dated as
                    of July 19, 1999 by and between Brigham Exploration Company
                    and Bank of Montreal.

     10.5           Warrant Agreement for the Purchase of Common Stock dated as
                    of July 19, 1999 by and between Brigham Exploration Company
                    and Societe Generale, Southwest Agency.

      27            Financial Data Schedule
</TABLE>


<PAGE>   1
                                                                    EXHIBIT 10.1

                                    AGREEMENT


         This AGREEMENT (this "Amendment") is executed as of the 16th day of
August, 1999, between Brigham Exploration Company (the "Company"), a Delaware
corporation, and Jon L. Glass ("Employee").

                                   WITNESSETH:

         WHEREAS, the Company and Employee entered into that certain Employee
Stock Ownership Agreement dated as of February 27, 1997 (the "Stock Agreement");

         WHEREAS, the Company and Employee entered into those two certain Option
Agreements, each dated as of March 4, 1999, as amended (collectively, the
"Option Agreements"); and

         WHEREAS, the parties hereto desire to enter into this Amendment in
order to amend the Stock Agreement, to amend each Option Agreement and to enter
into certain other agreements;

         WHEREAS, the amendment to each Option Agreement effected hereby extends
the period during which Employee may exercise certain stock options after
certain terminations of Employee's employment with the Company, and Employee is
therefore willing to extend the term of the noncompetition provisions provided
in the Stock Agreement for the benefit of the Company, its successors and
assigns and to agree to the other provisions in this Amendment;

         WHEREAS, the protections afforded by the Stock Agreement, as amended by
this Amendment, are necessary in order for the Company to protect the goodwill
and other business interests of the Company; and

         WHEREAS, Employee acknowledges and agrees that the Stock Agreement, as
amended hereby, places on him limitations as to the business or investment
activities he may pursue as well as the time during which and the geographic
area over which such limitations will remain in effect, which limitations are
deemed by him to be reasonable, ancillary to an otherwise enforceable agreement
and no greater than are necessary under the circumstances to protect the
goodwill and other business interests of the Company;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements contained herein and in each Option Agreement and the
Stock Agreement and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Company and Employee hereby
agree as follows:

         1. Amendment to each Option Agreement. Subject to Section 3 of this
Amendment, Section 4(d) of each Option Agreement is amended in its entirety to
read as follows:

                  (d) If Optionee's employment by the Companies terminates
         voluntarily by Optionee or by action of the Companies for reasons other
         than as specified in subsection (c), this Option may be exercised, but
         only (i) within 360 days after such termination (if otherwise prior to
         the date of expiration of this Option), and


<PAGE>   2


         not thereafter, and (ii) to purchase the number of Shares, if any, that
         could be purchased upon exercise of this Option at the date of
         termination of Optionee's employment.

         2. Amendment to the Stock Agreement. The first sentence of Section 3 of
the Stock Agreement is amended by replacing the phrase "for a period of one year
thereafter" with "for a period of three years thereafter". In addition, and
without limiting the foregoing, Employee hereby agrees that the Company's
Angelton Project (as described on Exhibit A hereto) shall constitute a protected
Company "area of mutual interest" for purposes of Section 3 of the Stock
Agreement. However, in the event that the Company is acquired by or merges with
another company (the "Acquiring Company") and as a result of such merger or
acquisition (i) the Acquiring Company acquires more than 50% of the outstanding
common stock of the Company and (ii) Ben M. Brigham does not hold the position
of either President, CEO or Vice President in the surviving company, then in
such event the amendment provided for in this Section 2 shall be of no further
force and effect.

         3. Contingency of Amendment to each Option Agreement. In the event that
either (a) Employee voluntarily terminate his employment with the Company
effective prior to September 30, 1999 or (b) prior to the expiration of the
period provided in Section 4(d) of each Option Agreement (as amended hereby),
Employee breaches the provisions of Section 3 of the Stock Agreement, then at
the discretion of the Company the provisions of Section 1 of this Amendment
shall immediately be of no further force and effect.

         4. Forfeiture of Certain Options . Employee hereby forfeits all options
to purchase shares of common stock of the Company which have previously been
granted to Employee, to the extent that the rights to exercise such options have
not vested as of the date hereof.

         5. Ratification of Agreement. The Stock Agreement and each Option
Agreement, each as amended by this Amendment, are hereby ratified and confirmed
in all respects. Except as expressly set forth herein, the terms, provisions and
conditions of the Stock Agreement and each Option Agreement shall remain in full
force and effect.

         6. Counterparts. This Amendment may be signed in counterparts, each of
which shall be deemed an original and all of which shall constitute one and the
same agreement.

         7. Effect of Agreement. This Amendment shall not enlarge or otherwise
affect the terms of Employee's employment with the Company, if any, and the
Company or an affiliate employing Employee may terminate his employment as
freely and with the same effect as if this Amendment had not been established.

         IN WITNESS WHEREOF, the parties hereto have executed this Amendment as
of the date first set forth above, to be effective as of August 16, 1999.

                                    BRIGHAM EXPLORATION COMPANY


   /s/ Jon L. Glass                 By: /s/ Ben M. Brigham
- -------------------------------        ------------------------------
Jon L. Glass                        Name:   Ben M. Brigham
                                    Title:  President and Chief
                                            Executive Officer



<PAGE>   1


                                                                    EXHIBIT 10.2

                                    AGREEMENT


         This AGREEMENT (this "Amendment") is executed as of the 16th day of
August, 1999, between Brigham Exploration Company (the "Company"), a Delaware
corporation, and Craig M. Fleming ("Employee").

                                   WITNESSETH:

         WHEREAS, the Company and Employee entered into that certain Employee
Stock Ownership Agreement dated as of February 27, 1997 (the "Stock Agreement");

         WHEREAS, the Company and Employee entered into that certain Option
Agreement dated as of March 4, 1999 (the "Option Agreement"); and

         WHEREAS, the parties hereto desire to enter into this Amendment in
order to amend the Stock Agreement, to amend the Option Agreement and to enter
into certain other agreements;

         WHEREAS, the amendment to the Option Agreement effected hereby extends
the period during which Employee may exercise certain stock options after
certain terminations of Employee's employment with the Company, and Employee is
therefore willing to extend the term of the noncompetition provisions provided
in the Stock Agreement for the benefit of the Company, its successors and
assigns and to agree to the other provisions in this Amendment;

         WHEREAS, the protections afforded by the Stock Agreement, as amended by
this Amendment, are necessary in order for the Company to protect the goodwill
and other business interests of the Company; and

         WHEREAS, Employee acknowledges and agrees that the Stock Agreement, as
amended hereby, places on him limitations as to the business or investment
activities he may pursue as well as the time during which and the geographic
area over which such limitations will remain in effect, which limitations are
deemed by him to be reasonable, ancillary to an otherwise enforceable agreement
and no greater than are necessary under the circumstances to protect the
goodwill and other business interests of the Company;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements contained herein and in the Option Agreement and the
Stock Agreement and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Company and Employee hereby
agree as follows:

         1. Amendment to the Option Agreement. Subject to Section 3 of this
Amendment, Section 4(d) of the Option Agreement is amended in its entirety to
read as follows:

                  (d) If Optionee's employment by the Companies terminates
         voluntarily by Optionee or by action of the Companies for reasons other
         than as specified in subsection (c), this Option may be exercised, but
         only (i) within 360 days after such termination (if otherwise prior to
         the date of expiration of this Option), and not thereafter, and (ii) to
         purchase the number of Shares, if any, that could be purchased upon
         exercise of this Option at the date of termination of Optionee's
         employment.


<PAGE>   2


         2. Amendment to the Stock Agreement. The first sentence of Section 3 of
the Stock Agreement is amended by replacing the phrase "for a period of one year
thereafter" with "for a period of three years thereafter". In addition, and
without limiting the foregoing, Employee hereby agrees that the Company's
Angleton Project (as described on Exhibit A hereto) shall constitute a protected
Company "area of mutual interest" for purposes of Section 3 of the Stock
Agreement. However, in the event that the Company is acquired by or merges with
another company (the "Acquiring Company") and as a result of such merger or
acquisition (i) the Acquiring Company acquires more than 50% of the outstanding
common stock of the Company and (ii) Ben M. Brigham does not hold the position
of either President, CEO or Vice President in the surviving company, then in
such event the amendment provided for in this Section 2 shall be of no further
force and effect.

         3. Contingency of Amendment to the Option Agreement. In the event that
either (a) Employee voluntarily terminate his employment with the Company
effective prior to September 30, 1999 or (b) prior to the expiration of the
period provided in Section 4(d) of the Option Agreement (as amended hereby),
Employee breaches the provisions of Section 3 of the Stock Agreement, then at
the discretion of the Company the provisions of Section 1 of this Amendment
shall immediately be of no further force and effect.

         4. Forfeiture of Certain Options. Employee hereby forfeits all options
to purchase shares of common stock of the Company which have previously been
granted to Employee, to the extent that the rights to exercise such options have
not vested as of the date hereof.

         5. Ratification of Agreement. The Stock Agreement and the Option
Agreement, each as amended by this Amendment, are hereby ratified and confirmed
in all respects. Except as expressly set forth herein, the terms, provisions and
conditions of the Stock Agreement and the Option Agreement] shall remain in full
force and effect.

         6. Counterparts. This Amendment may be signed in counterparts, each of
which shall be deemed an original and all of which shall constitute one and the
same agreement.

         7. Effect of Agreement. This Amendment shall not enlarge or otherwise
affect the terms of Employee's employment with the Company, if any, and the
Company or an affiliate employing Employee may terminate his employment as
freely and with the same effect as if this Amendment had not been established.

         IN WITNESS WHEREOF, the parties hereto have executed this Amendment as
of the date first set forth above, to be effective as of August 16, 1999.

                                        BRIGHAM EXPLORATION COMPANY


 /s/ Craig M. Fleming                   By: /s/ David T. Brigham
- -----------------------------              ----------------------------------
Craig M. Fleming                        Name:  David T. Brigham
                                        Title: Vice President



<PAGE>   1

                                                                    Exhibit 10.3

                           CHANGE OF CONTROL AGREEMENT


     This Change of Control ("Agreement") is made and entered into as of this
20th day of September, 1999, by and between Brigham Exploration Company, a
Delaware corporation (the "Company"), and [See Schedule I], an individual
currently residing in Austin, Texas ("Officer").

                                    RECITALS

         The Board of Directors of the Company (the "Board") has determined that
it is in the best interest of the Company to assure that the Company will have
the continued dedication of Officer, notwithstanding the possibility, threat or
occurrence of a Change of Control (as defined below). The Board believes it is
imperative to diminish the inevitable distraction of Officer by virtue of the
personal uncertainties and risks created by a pending or threatened Change of
Control, to encourage Officer's full attention and dedication to the Company
currently and in the event of any threatened or pending Change of Control, and
to provide Officer with compensation and benefit arrangements upon a Change of
Control which ensures that such compensation and benefits are competitive with
other corporations.

                                    AGREEMENT

         Now, therefore, in consideration of Officer's continued employment by
the Company and execution of a General Release materially in the form attached
hereto as Exhibit A (the "General Release"), as well as the promises, covenants
and obligations contained herein, the Company and Officer agree as follows:

         1.       Severance and Other Benefits.

                  (a) Severance Payment. Prior to the end of the Retention
         Period, upon the occurrence of a Termination Event (as defined in
         Paragraph 2) and Officer's execution of the General Release--

                           (i) the Company or its successor shall pay Officer an
                  amount equal to Officer's Annual Base Salary (as defined in
                  Paragraph 2) multiplied by 2.0, payable as a lump sum cash
                  payment within 30 business days after the date of execution of
                  the General Release;

                           (ii) if Officer was participating in a life insurance
                  and/or disability benefit plan maintained by an Employer as of
                  [his/her] Termination Date, such coverage will be continued at
                  the same cost, if any, charged to similarly situated active
                  employees under such plans for a period of eighteen months
                  following the Termination Date or, if earlier, the date as of
                  which Officer obtains other employment. Officer shall
                  immediately notify the Company upon obtaining other
                  employment;

                           (iii) if Officer was participating in a hospital,
                  surgical, medical or dental benefit plan maintained by an
                  Employer as of [his/her] Termination Date and if Officer
                  elects to continue such coverage under the Consolidated
                  Omnibus Budget Reconciliation Act of 1985 ("COBRA"), Officer
                  will be reimbursed the premiums paid to continue such coverage
                  under COBRA until the date as of which Officer obtains other
                  employment. Officer shall immediately notify the Company upon
                  obtaining other employment; and

                           (iv) the Company shall pay all reasonable legal fees
                  and expenses promptly as they are incurred by Officer in
                  seeking to obtain or enforce any right or benefit provided by


<PAGE>   2


                  this Agreement other than fees or expenses incurred in
                  connection with any challenge by Officer to the enforceability
                  of the General Release.

                  (b) Option Vesting. In the event of a Change of Control, the
         Company or any successor thereto (or an affiliate of the Company or any
         successor thereto) shall take all such action as may be necessary or
         appropriate to amend any option to purchase Brigham common stock held
         by Officer to provide that, with respect to any portion of such option
         which has not then vested but is scheduled to vest within five years of
         the date of the Change of Control, such portion of the option shall
         immediately vest.

         2.       Definitions.

                  (a) "Annual Base Salary," as determined on the Termination
         Date or Retention Date, as the case may be, shall be equal to the
         greater of (i) the annual base salary payable to Officer by the Company
         or any successor thereto (or any affiliate of the Company or a
         successor thereto) as of the date of the earliest Change of Control to
         occur during the eighteen-month period prior to the Termination Date or
         Retention Date plus any bonuses or special incentive payments received
         by Officer from the Company or any successor thereto (or any affiliate
         of the Company or a successor thereto) during the twelve-month period
         prior to such Change of Control, determined prior to reduction for any
         employee-elected salary reduction contributions made to an
         employer-sponsored plan pursuant to Section 401(k) or 125 of the
         Internal Revenue Code of 1986, as amended (the "Code"), or (ii) the
         annual base salary payable to Officer by the Company or any successor
         thereto (or any affiliate of the Company or a successor thereto) as of
         the Termination Date or Retention Date plus any bonuses or special
         incentive payments received by Officer from the Company or any
         successor thereto (or an affiliate of the Company or a successor
         thereto) during the twelve-month period prior to the Termination Date
         or Retention Date, determined prior to reduction for any
         employee-elected salary reduction contributions made to an
         employer-sponsored plan pursuant to Section 401(k) or 125 of the Code.
         In the event Officer has not been employed by the Company for one year,
         such bonus shall be assumed to equal 50% of the Officer's annual base
         salary for purposes of determining "Annual Base Salary."

                  (b) "Brigham" means Brigham Exploration Company, a Delaware
         corporation, or any successor thereto.

                  (c) "Cause" as used herein with respect to Officer's
         termination of employment shall include any of the following: (A)
         Officer's conviction of, or plea of nolo contendere to, any felony of
         theft, fraud, embezzlement or violent crime causing substantial harm to
         the Company or its affiliates; (B) the willful and continued failure by
         Officer to substantially perform Officer's duties with the Company
         (other than such failure resulting from Officer's incapacity due to
         physical or mental illness), after a written demand for substantial
         performance is delivered to Officer by the Chief Executive Officer of
         the Company and the Board, which specifically identifies the manner in
         which the Chief Executive Officer and the Board believes that Officer
         has not substantially performed Officer's duties or (C) the willful
         engaging by Officer in misconduct which is materially injurious to the
         interests of the Company or any successor thereto (or any affiliate of
         the Company or a successor thereto). For purposes of this Paragraph, no
         act, or failure to act, on Officer's part shall be considered "willful"
         unless done, or omitted to be done, by Officer not in good faith and
         without reasonable belief that Officer's action or omission was in the
         best interest of the Company. Notwithstanding the foregoing, Officer
         shall not be deemed to have been terminated for cause unless and until
         there shall have been delivered to Officer a copy of a notice of
         termination from the Chief Executive Officer of the Company and the
         Board, after (x) reasonable notice to Officer, (y) an opportunity for
         Officer, together with Officer's counsel (the reasonable fees of which
         the Company shall pay promptly as incurred), to be heard before the
         Board, finding that, in the good faith opinion of the Board, Officer
         was guilty of conduct set forth above in clauses (A), (B) or (C)


<PAGE>   3


         of the first sentence of this Subparagraph and specifying the
         particulars thereof in detail.

                  (d) A "Change of Control" shall be deemed to have occurred for
         purposes of this Agreement if:

                           (i) any "affiliates" and "associates" (as such terms
         are defined in Rule 12b-2 under the Securities Exchange Act of 1934, as
         amended (the "Exchange Act")) of any "person," as that term is defined
         in Section 3(a)(9) of the Exchange Act (other than Ben Brigham or Anne
         Brigham or Brigham, any of its subsidiaries, any employee benefit plan
         of Brigham or any of its subsidiaries, or any entity organized,
         appointed or established by Brigham for or pursuant to the terms of
         such a plan), together with any nominees or appointees of such person
         (excluding in any event Ben Brigham and Anne Brigham), constitute at
         least 51% of members of the Board of Directors of Brigham;

                           (ii) the stockholders of Brigham approve a
         reorganization, merger or consolidation, in each case, with respect to
         which persons who were the stockholders of the Company immediately
         prior to such reorganization, merger or consolidation do not,
         immediately thereafter, own more than 50% of the combined voting power
         entitled to vote generally in the election of directors ("Voting
         Securities") of the reorganized, merged or consolidated company's then
         outstanding voting securities;

                           (iii) Brigham sells, leases or exchanges or agrees to
         sell, lease or exchange all or substantially all of its assets to any
         other person or entity and following such transaction does not continue
         its business following substantially the same business plan that is in
         existence as of the date of this Agreement; or Brigham is to be
         dissolved and liquidated; or

                           (iv) any "person," as that term is defined in Section
         3(a)(9) of the Exchange Act (other than Brigham, any of its
         subsidiaries, any employee benefit plan of Brigham or any of its
         subsidiaries, or any entity organized, appointed or established by
         Brigham for or pursuant to the terms of such a plan), together with all
         "affiliates" and "associates" (as such terms are defined in Rule 12b-2
         under the Exchange Act) of such person (as well as any "Person" or
         "group" as those terms are used in Sections 13(d) and 14(d) of the
         Exchange Act), shall become the "beneficial owner" or "beneficial
         owners" (as defined in Rules 13d-3 and 13d-5 under the Exchange Act),
         directly or indirectly, of securities of Brigham representing in the
         aggregate 50% or more of either (A) the then outstanding shares of
         common stock, par value $.01 per share, of Brigham ("Common Stock") or
         (B) the Voting Securities of Brigham, in either such case other than
         solely as a result of acquisitions of such securities directly from
         Brigham.

                           Notwithstanding the foregoing, a "Change in Control"
         of Brigham shall not be deemed to have occurred for purposes of
         subparagraph (iv) of this paragraph 2(d) solely as the result of an
         acquisition of securities by Brigham which, by reducing the number of
         shares of Common Stock or other Voting Securities of Brigham
         outstanding, increases (i) the proportionate number of shares of Common
         Stock beneficially owned by any person to 50% or more of the shares of
         Common Stock then outstanding or (ii) the proportionate voting power
         represented by the Voting Securities of Brigham beneficially owned by
         any person to 50% or more of the combined voting power of all then
         outstanding Voting Securities; provided, however, that if any person
         referred to in clause (i) or (ii) of this sentence shall thereafter
         become the beneficial owner of any additional shares of Common Stock or
         other Voting Securities of Brigham (other than a result of a stock
         split, stock dividend or similar transaction), then a Change in Control
         of Brigham shall be deemed to have occurred for purposes of
         subparagraph (iv) of this paragraph 2(d).


<PAGE>   4


                  (e) The "Retention Date" shall mean the last day of the
         Retention Period.

                  (f) The "Retention Period" shall be the period commencing on
         the date of the first Change of Control to occur after the execution of
         this Agreement and ending on the second anniversary of such Change of
         Control date.

                  (f) The "Termination Date" shall mean the date of the
         termination of Officer's employment in connection with a Termination
         Event.

                  (g) A "Termination Event" shall be deemed to have occurred if
         at any time within the Retention Period:

                           (i) the Company or any successor thereto (or an
                  affiliate of the Company or any successor thereto) shall
                  terminate Officer's employment for any reason other than for
                  Cause; or

                           (ii) Officer shall voluntarily terminate [his/her]
                  employment with the Company or any successor thereto (or an
                  affiliate of the Company or any successor thereto) for "Good
                  Reason." For purposes of this Agreement, "Good Reason" shall
                  mean any of the following (without Officer's express written
                  consent):

                                    (A) A material change in the nature or scope
                           of Officer's duties from those engaged in by Officer
                           immediately prior to the date on which a Change of
                           Control occurs;

                                    (B) A reduction in Officer's annual base
                           salary from that provided to [him/her] immediately
                           prior to the date on which the Change of Control
                           occurs;

                                    (C) A material diminution in Officer's
                           eligibility to participate in, or in the benefits
                           provided to Officer, under any bonus, stock option or
                           other incentive compensation plans or employee
                           welfare and pension benefit plans (including medical,
                           dental, life insurance, retirement and long-term
                           disability plans) from that provided to [him/her]
                           immediately prior to the date on which the Change of
                           Control occurs; or

                                    (D) Any required relocation of Officer of
                           more than thirty miles from the location where
                           Officer was based and performed services on the date
                           of this Agreement (including any required business
                           travel in excess of the greater of 90 days per year
                           or the level of business travel of Officer for the
                           year prior to the most recent Change of Control).

                  3. Adjustments. Any provision of this Agreement to the
contrary notwithstanding, if, in the Company's determination, the total sum of
(i) the payments and benefits to be paid or provided to (or with respect to)
Employee under this Agreement which are considered to be "parachute payments"
within the meaning of Section 280G of the Internal Revenue Code of 1986, as
amended (the "Code") and (ii) any other payments and benefits which are
considered to be "parachute payments," as so defined, to be paid or provided to
(or with respect to) Employee by the Company or a member of the Company's
affiliated group (within the meaning of Section 280G(d)(5) of the Code) (the
"Total Amount") exceeds the amount


<PAGE>   5


Employee can receive without having to pay excise tax with respect to all or any
portion of such payments or benefits under Section 4999 of the Code (the
"Reduced Amount"), then the amount payable to Employee pursuant to paragraphs
1(a) and 1(b) of this Agreement shall be reduced to the greater of zero or the
highest amount which will not result in Employee having to pay excise tax with
respect to any payments and benefits under Section 4999 of the Code; provided,
however, that in the event that the Reduced Amount minus any and all applicable
federal, state and local taxes (including but not limited to income and
employment taxes imposed by the Code) is less than the Total Amount minus any
and all applicable federal, state and local taxes (including but not limited to
income and employment taxes imposed by the Code and excise taxes applicable to
such payments under Section 4999 of the Code), then the reduction of the amount
payable to Employee under paragraphs 1(a) and 1(b) of this Agreement provided
for in the preceding provisions of this paragraph 3 shall not be made.

         4. Notices. For purposes of this Agreement, notices and all other
communications provided for herein shall be in writing and shall be deemed to
have been duly given when personally delivered or when mailed by United States
registered or certified mail, return receipt requested, postage prepaid,
addressed as follows:

         If to the Company to:       Brigham Exploration Company
                                     6300 Bridge Point Parkway
                                     Building 2, Suite 500
                                     Austin, Texas 78730

         If to Officer to:
                                     ---------------------------------

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

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

or to such other address as either party may furnish to the other in writing in
accordance herewith, except that notices of changes of address shall be
effective only upon receipt.

                  5. Applicable Law. This contract is entered into under, and
shall be governed for all purposes by, the laws of the State of Texas.

                  6. Severability. If a court of competent jurisdiction
determines that any provision of this Agreement is invalid or unenforceable,
then the invalidity or unenforceability of that provision shall not affect the
validity or enforceability of any other provision of this Agreement, and all
other provisions shall remain in full force and effect.

                  7. Counterparts. This Agreement may be executed in one or more
counterparts, each of which shall be deemed to be an original, but all of which
together will constitute one and the same Agreement.

                  8. Withholding. The Company or any affiliate of the Company
employing Officer shall withhold from any amount payable to Officer pursuant to
this Agreement or from other remuneration payable to Officer, and shall remit to
the appropriate governmental authority if required by applicable law, any
income, employment or other tax such entity is required by applicable law to so
withhold from and remit on behalf of Officer and any other amounts authorized in
writing by Officer.


<PAGE>   6


                  9. No Continued Employment and Effect of Agreement. This
Agreement shall not enlarge or otherwise affect the terms of Officer's
employment with the Company, if any, and the Company or an affiliate employing
Officer may terminate [his/her] employment as freely and with the same effect as
if this Agreement had not been established. This Agreement is the sole and
exclusive program of severance benefits provided to Officer. It is intended that
any and all other representations, agreements or descriptions of similar
benefits be superseded hereby with respect to Officer; provided, however, that
nothing herein is intended to modify or affect in any way the terms of any
written employment agreement signed between the Company and Officer. No oral or
written representation or promise concerning severance which is inconsistent
with the provisions of this Agreement shall have any force or effect.

         10. Assignment.

                  (a) This Agreement is personal in nature and neither of the
         parties hereto shall, without the consent of the other, assign or
         transfer this Agreement or any rights or obligations hereunder, except
         as provided in the remainder of this Paragraph 10. Without limiting the
         foregoing, Officer's right to receive payments hereunder shall not be
         assignable or transferable, whether by pledge, creation of a security
         interest or otherwise, other than a transfer by [his/her] will or by
         the laws of descent or distribution, and in the event of any attempted
         assignment or transfer contrary to this Paragraph 10 the Company shall
         have no liability to pay any amount so attempted to be assigned or
         transferred. This Agreement shall inure to the benefit of and be
         enforceable by Officer's personal or legal representatives, executors,
         administrators, successors, heirs, distributees, devisees and legatees.

                  (b) The Company may: (x) as long as it remains obligated with
         respect to this Agreement, cause its obligations hereunder to be
         performed by a subsidiary or subsidiaries for which Officer performs
         services, in whole or in part; (y) assign this Agreement and its rights
         hereunder in whole, but not in part, to any corporation with or into
         which it may hereafter merge or consolidate or to which it may transfer
         all or substantially all of its assets, if said corporation shall by
         operation of law or expressly in writing assume all liabilities of the
         Company hereunder as fully as if it has been originally named the
         Company herein; but may not otherwise assign this Agreement or its
         rights hereunder. Subject to the foregoing, this Agreement shall inure
         to the benefit of and be enforceable by the Company's successors and
         assigns.

         11. Modifications. This Agreement shall not be varied, altered,
modified, canceled, changed or in any way amended except by mutual agreement of
the parties in a written instrument executed by the parties hereto or their
legal representatives.

         12. No Violations. To the extent any provision of this Agreement would
trigger a breach of any material agreement to which the Company or any of its
subsidiaries is a party or would cause a violation of applicable law, it shall
be invalid and of no force and effect.

         IN WITNESS WHEREOF, the parties have caused this Agreement to be
executed and delivered as of the day and year first above written.

                                        BRIGHAM EXPLORATION COMPANY



                                        By:
                                           --------------------------------
                                        Name:
                                             ------------------------------
                                        Title:
                                              -----------------------------



                                        OFFICER



                                        -----------------------------------
                                        [See Schedule I]
<PAGE>   7
                                                                       EXHIBIT A

                            GENERAL RELEASE AGREEMENT

NOTICE: If you wish to accept the Severance Payment, you must return an executed
copy of this form to the Company by the close of business on the forty-fifth day
after the Termination Event or the expiration of the Retention Period, whichever
is applicable, as defined in the Change of Control Agreement between you and
Brigham Exploration Company.

GENERAL RELEASE: IN CONSIDERATION OF THE SEVERANCE PAYMENT (PAYMENT) TO BE MADE
TO ME UNDER THE BRIGHAM EXPLORATION COMPANY CHANGE OF CONTROL AGREEMENT (THE
AGREEMENT), I HEREBY RELEASE, ACQUIT, AND FOREVER DISCHARGE (i) BRIGHAM
EXPLORATION COMPANY INC. AND ANY PARENT, SUBSIDIARY, AFFILIATED ENTITY,
SUCCESSORS OR ASSIGNS (THE COMPANY), AND (ii) THE STOCKHOLDERS, OFFICERS,
DIRECTORS, EMPLOYEES, AGENTS, REPRESENTATIVES, AND FIDUCIARIES OF THE COMPANY
(COLLECTIVELY THE RELEASED PARTIES), FROM ANY AND ALL CLAIMS, LIABILITIES,
DEMANDS, AND CAUSES OF ACTION OF WHATEVER KIND OR CHARACTER, WHETHER VICARIOUS,
DERIVATIVE, OR DIRECT, THAT I NOW HAVE OR CLAIM AGAINST THEM CONNECTED IN ANY
WAY TO THE AGREEMENT OR ANY CLAIM FOR BENEFITS UNDER THE AGREEMENT, OR MY
EMPLOYMENT, CONTINUATION OF EMPLOYMENT, OR, IF APPLICABLE, TERMINATION OF
EMPLOYMENT WITH ANY OF THE RELEASED PARTIES, OR WITH ANY OTHER ACT, CONDUCT, OR
OMISSION OF ANY OF THE RELEASED PARTIES, INCLUDING BUT NOT LIMITED TO CLAIMS
ARISING UNDER ANY FEDERAL, STATE, OR LOCAL LAWS RELATING TO THE EMPLOYMENT
RELATIONSHIP, INCLUDING THE AGE DISCRIMINATION IN EMPLOYMENT ACT. THIS GENERAL
RELEASE DOES NOT WAIVE RIGHTS OR CLAIMS THAT MAY ARISE AFTER THE DATE THIS
GENERAL RELEASE IS EXECUTED. FURTHER IN CONSIDERATION OF THE PAYMENT TO BE MADE
TO ME UNDER THE AGREEMENT, I ACKNOWLEDGE AND AGREE THAT THE RELEASED PARTIES MAY
RECOVER FROM ME ANY LOSS, INCLUDING ATTORNEY'S FEES AND COSTS OF DEFENDING
AGAINST ANY CLAIM BROUGHT BY ME, THEY MAY INCUR ARISING OUT OF MY BREACH OF THIS
GENERAL RELEASE.

I understand that I may revoke my acceptance of this General Release by so
notifying the Company within seven days of the date I execute this General
Release. I further understand that if I do not timely revoke my acceptance, this
General Release is final and binding, and I agree not to challenge its
enforceability. If I do challenge the enforceability of this General Release, I
agree initially to tender to the Company the Payment made under the Agreement,
and invite the Company to retain such money and agree with me to cancel this
General Release. In the event the Company accepts my offer, the Company shall
retain such money and this General Release will be void. In the event the
Company does not accept my offer, the Company shall place such money in an
escrow account pending the resolution of any dispute as to whether this General
Release shall be set aside and/or otherwise rendered unenforceable.

I have read and fully understand all of the provisions of this General Release.
I acknowledge that none of the Released Parties have made any promise or
representation to me that is not set out in this General Release, and that in
executing this General Release I am not relying on any such promise or
representation but instead am relying solely on my own judgment. I further
acknowledge that my execution of this General Release is knowing and voluntary,
that I have had a reasonable time to consider its terms, and that I have been
advised to consult with an attorney about this General Release.


Date signed:
             -----------------------------        -----------------------------
                                                      Signature of Employee

Date signed:
             -----------------------------        -----------------------------
                                                            Witness
<PAGE>   8


                                   Schedule I


David T. Brigham
A. Lance Langford
Curtis F. Harrell
Karen E. Lynch
Christopher A. Phelps
Jeffrey E. Larson

<PAGE>   1
                                                                    EXHIBIT 10.4


                                                                  Execution Copy

THIS WARRANT AGREEMENT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THE WARRANTS
HEREIN HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH
ACT, THE RULES AND REGULATIONS PROMULGATED THEREUNDER, ANY SUCH STATE SECURITIES
LAWS OR THE PROVISIONS OF THIS WARRANT AGREEMENT.



                                WARRANT AGREEMENT


                                     for the


                            Purchase of Common Stock

                                 By and Between



                           BRIGHAM EXPLORATION COMPANY

                                       and

                                BANK OF MONTREAL



                                   Dated as of

                                  July 19, 1999

<PAGE>   2
                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                               Page

<S>                                                                                                            <C>
1.       DEFINITIONS.............................................................................................2

2.       ISSUANCE AND EXERCISE OF WARRANTS.......................................................................6

         2.1      Issuance of Warrants...........................................................................6

         2.2      Manner of Exercise.............................................................................6

         2.3      Payment of Taxes...............................................................................8

         2.4      Fractional Shares..............................................................................8

         2.5      Continued Validity.............................................................................9

3.       TRANSFERS, DIVISION AND COMBINATION.....................................................................9

         3.1      Transfer.......................................................................................9

         3.2      Division and Combination.......................................................................9

         3.3      Expenses.......................................................................................9

         3.4      Maintenance of Books...........................................................................9

4.       ADJUSTMENTS.............................................................................................9

         4.1      Stock Dividends, Subdivisions and Combinations.................................................9

         4.2      Certain Other Distributions...................................................................10

         4.3      Issuance of Additional Shares of Stock........................................................11

         4.4      Issuance of Warrants or Other Rights..........................................................11

         4.5      Issuance of Convertible Securities............................................................12

         4.6      Superseding Adjustment........................................................................13

         4.7      Other Provisions Applicable to Adjustments Under This Section.................................13

         4.8      Reorganization, Reclassification, Merger, Consolidation or Disposition of Assets..............14

5.       NOTICES TO WARRANT HOLDERS.............................................................................15

         5.1      Notice of Adjustments.........................................................................15

         5.2      Notice of Certain Corporate Action............................................................15

6.       REPRESENTATIONS AND WARRANTIES.........................................................................16

7.       CERTAIN COVENANTS......................................................................................17

         7.1      No Impairment.................................................................................17

         7.2      Reservation and Authorization of Common Stock; Registration with, or Approval of, any
                  Governmental Authority........................................................................18

8.       TAKING OF RECORD; STOCK AND WARRANT TRANSFER BOOKS.....................................................18
</TABLE>


                                       i
<PAGE>   3
<TABLE>
<S>                                                                                                             <C>
9.       RESTRICTIONS ON TRANSFERABILITY........................................................................18

         9.1      Restrictive Legend............................................................................18

         9.2      Notice of Proposed Transfers; Requests for Registration.......................................19

         9.3      Incidental Registration.......................................................................19

         9.4      Registration Procedures.......................................................................20

         9.5      Expenses......................................................................................21

         9.6      Indemnification and Contribution..............................................................21

         9.7      Termination of Restrictions...................................................................24

         9.8      Listing on Securities Exchange................................................................25

10.      SUPPLYING INFORMATION..................................................................................25

11.      LOSS OR MUTILATION.....................................................................................25

12.      OFFICE OF THE ISSUER...................................................................................25

13.      APPRAISAL..............................................................................................25

14.      LIMITATION OF LIABILITY; NO RIGHTS AS STOCKHOLDER......................................................26

15.      MISCELLANEOUS..........................................................................................26

         15.1     Non-waiver and Expenses.......................................................................26

         15.2     Notice Generally..............................................................................26

         15.3     Indemnification...............................................................................27

         15.4     Remedies......................................................................................27

         15.5     Successors and Assigns........................................................................28

         15.6     Complete Agreement; Amendment.................................................................28

         15.7     Severability..................................................................................28

         15.8     Headings......................................................................................28

         15.9     Governing Law; Consent to Jurisdiction and Venue..............................................28

         15.10    Consent to Jurisdiction and Venue.............................................................28

         15.11    Counterparts..................................................................................29

EXHIBITS:

Exhibit A  -Form of Warrant Certificate...................................................................Exh. A-1

Exhibit B  -Form of Cashless Conversion Notice............................................................Exh. B-1

SCHEDULES:

Schedule A -Capital Stock of the Issuer, Including Shares Subject to
           Outstanding Warrants, Options, Conversion Rights, Etc..........................................Sch. A-1
</TABLE>


                                       ii
<PAGE>   4

THIS WARRANT AGREEMENT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THE WARRANTS
HEREIN HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH
ACT, THE RULES AND REGULATIONS PROMULGATED THEREUNDER, ANY SUCH STATE SECURITIES
LAWS OR THE PROVISIONS OF THIS WARRANT AGREEMENT.

                                WARRANT AGREEMENT


THIS WARRANT AGREEMENT, dated as of July 19, 1999 (this "Agreement"), is entered
into by and between Brigham Exploration Company, a Delaware corporation
("Issuer"), and Bank of Montreal, a Canadian chartered bank (the "Warrant
Holder" or the "Bank of Montreal").

                              W I T N E S S E T H:


         WHEREAS, Brigham Oil & Gas, L.P., a limited partnership formed under
the laws of the State of Delaware (the "Borrower"), the financial institutions
party to the Credit Agreement referred to below (each a "Lender" and
collectively, the "Lenders"), and the Bank of Montreal, as agent for Lenders
under the Credit Agreement (in such capacity, the "Agent"), are parties to that
certain Credit Agreement, dated as of January 26, 1998, as amended by that
certain First Amendment to Credit Agreement, dated as of August 20, 1998, and
that certain Second Amendment to Credit Agreement, dated as of March 26, 1999
(as so amended, the "Credit Agreement"); and

         WHEREAS, the Borrower advised the Lenders and the Agent that it desired
to amend certain provisions of the Credit Agreement, and the Borrower requested
that the Lenders and the Agent agree to various amendments to certain provisions
of the Credit Agreement; and

         WHEREAS, the Lenders and the Agent have agreed to so amend certain
provisions of the Credit Agreement upon the terms and subject to the conditions
and limitations of the Third Amendment to the Credit Agreement dated as of July
19, 1999 (the "Third Amendment");

         WHEREAS, the Issuer has guaranteed the obligations of the Borrower to
the Lenders and the Agent;

         WHEREAS, as a consequence of the contractual relationships between the
Borrower and the Lenders, the Issuer has and will continue to receive
substantial benefits from the Lenders;

         WHEREAS, in order to induce the Lenders to enter into the Third
Amendment, the Issuer has agreed to execute and deliver this Agreement and to
issue to Bank of Montreal the warrants herein described;



                                       1
<PAGE>   5

         NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, the receipt and sufficiency of which is hereby acknowledged,
the parties hereby stipulate and agree as follows:

1.       DEFINITIONS

         As used in this Agreement, the following terms have the respective
         meanings set forth below:

         "Additional Shares of Common Stock" shall mean all shares of Common
         Stock issued by the Issuer after the Closing Date, other than Warrant
         Stock.

         "Affiliate" shall mean as to any Person, any other Person which,
         directly or indirectly, is in control of, is controlled by, or is under
         common control with, such Person. For purposes of this definition,
         "control" (including the terms "controlled by" and "under common
         control with"), as used with respect to any Person, means the power to
         direct or cause the direction of the management and policies of such
         Person, directly or indirectly, whether through the ownership of voting
         securities or by contract or otherwise; and the terms "controlled" and
         "controlling" have the meanings correlative to the foregoing.

         "Appraised Value" shall mean, in respect of any share of Common Stock
         on any date herein specified, the fair saleable value of such share of
         Common Stock (determined without giving effect to the discount for (i)
         a minority interest or (ii) any lack of liquidity of the Common Stock
         or to the fact that the Issuer may have no class of equity registered
         under the Exchange Act) as of the last day of the most recent fiscal
         month to end within 60 days prior to such date specified, based on the
         value of the Issuer, as determined by an investment banking firm
         (selected pursuant to the terms of Section 13 of this Agreement) in
         accordance with such firm's customary practices, divided by the number
         of Outstanding shares of Common Stock, after giving pro forma effect to
         the exercise or conversion of all exercisable or Convertible Securities
         (including the Warrants) for Common Stock and the payment of the
         exercise or conversion price therefor.

         "Book Value" shall mean, in respect of any share of Common Stock on any
         date herein specified, the consolidated book value of the Issuer as of
         the last day of any month immediately preceding such date, divided by
         the number of Outstanding shares of Common Stock, after giving pro
         forma effect to the exercise or conversion of all exercisable or
         Convertible Securities (including the Warrants) for Common Stock and
         the payment of the exercise or conversion price therefor, as determined
         in accordance with GAAP by any firm of independent certified public
         accountants of recognized national standing selected by the Issuer and
         reasonably acceptable to the Required Holders.

         "Business Day" shall mean any day that is not a Saturday or Sunday or a
         day on which banks are required or permitted to be closed in the State
         of New York or California.

         "Cashless Conversion" shall have the meaning set forth in Section
         2.2(b)(ii) hereof.

         "Cashless Conversion Notice" shall have the meaning set forth in
         Section 2.2(b)(ii) hereof.


                                       2
<PAGE>   6

         "Closing Date" shall mean the date hereof.

         "Commission" shall mean the Securities and Exchange Commission, or any
         other federal agency then administering the Securities Act and other
         federal securities laws.

         "Common Stock" shall mean the common stock, $0.01 par value per share,
         of the Issuer, as constituted on the Closing Date, and any capital
         stock into which such Common Stock may thereafter be changed, and shall
         also include (i) capital stock of the Issuer of any other class
         (regardless of how denominated) issued to the holders of shares of
         Common Stock upon any reclassification thereof which is also not
         preferred as to dividends or assets over any other class of stock of
         the Issuer and which is not subject to redemption and (ii) shares of
         common stock of any successor or acquiring corporation (as defined in
         Section 4.8 of this Agreement) received by or distributed to the
         holders of Common Stock of the Issuer in the circumstances contemplated
         by Section 4.8 of this Agreement.

         "Convertible Securities" shall mean evidences of indebtedness, shares
         of stock or other securities which are convertible into or
         exchangeable, with or without payment of additional consideration in
         cash or property, for Additional Shares of Common Stock, either
         immediately or upon the occurrence of a specified date or a specified
         event.

         "Current Market Price" shall mean, in respect of any share of Common
         Stock on any date herein specified, (a) if there shall then be a public
         market for the Common Stock, the average Price per share for the 20
         trading days preceding such date; or (b) at any time that there is no
         public market for the Common Stock, the fair market value per share of
         Common Stock on such date as determined reasonably and in good faith by
         the board of directors of the Issuer (determined without giving effect
         to any discount for a minority interest, any restrictions on
         transferability or any lack of liquidity of the Common Stock or to the
         fact that the Issuer has no class of equity registered under the
         Exchange Act), such fair market value to be determined by reference to
         the cash price that would be paid between a fully informed buyer and
         seller under no compulsion to buy or sell, provided that (i) if Current
         Market Price is being determined in connection with an issuance of
         shares of Common Stock, solely to one or more Affiliates of the Issuer,
         then if so requested by the Required Holders, Current Market Price
         shall be the Appraised Value; and (ii) Current Market Price shall never
         be less than Book Value.

         "Current Warrant Price" shall mean, in respect of a share of Common
         Stock at any date herein specified, two and 25/100 dollars ($2.25) per
         share of Common Stock, subject to adjustment from time to time as
         provided in this Agreement.

         "Demanding Security Holder" shall have the meaning set forth in Section
         9.3.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, as
         amended, or any similar federal statute, and the rules and regulations
         of the Commission thereunder, all as the same shall be in effect from
         time to time.

         "Exercise Period" shall mean the period during which the Warrants are
         exercisable pursuant to Section 2.2.



                                       3
<PAGE>   7

         "Expiration Date" shall mean July 19, 2004.

         "GAAP" shall mean generally accepted accounting principles in the
         United States of America, as from time to time in effect.

         "Material Adverse Effect" shall mean, as to the Issuer, any material
         adverse effect on the business, assets, operations, prospects or
         financial or other condition of the Issuer and its Subsidiaries, taken
         as a whole.

         "NASD" shall mean the National Association of Securities Dealers, Inc.,
         or any successor thereto.

         "Other Property" shall have the meaning set forth in Section 4.8.

         "Outstanding" shall mean, when used with reference to Common Stock, at
         any date as of which the number of shares thereof is to be determined,
         all issued shares of Common Stock, except shares then owned or held by
         or for the account of the Issuer or any Subsidiary, and shall include
         all shares issuable in respect of outstanding scrip or any certificates
         representing fractional interests in shares of Common Stock.

         "Permitted Issuances" shall mean (i) the issuance of shares of Common
         Stock upon exercise of the Warrants, (ii) the issuance of shares
         relating to any benefit plan, stock option plan or any other
         compensation plan offered solely to the Issuer's officers, directors
         and/or employees, (iii) the issuance of shares of Common Stock as
         consideration for the purchase of any property, stock, business or
         securities from any Person who is not an Affiliate of the Issuer or any
         Subsidiary immediately prior to such transaction whether such shares
         are issued directly by the Issuer or a Subsidiary of the Issuer in
         connection with any merger, consolidation or other business
         combination, (iv) if there shall then be a public market for the Common
         Stock, the issuance of shares of Common Stock upon receipt by the
         Issuer of the Current Market Price therefor as described in clause (a)
         of the definition of "Current Market Price" and (v) if there shall then
         be no public market for the Common Stock, the issuance of shares of
         Common Stock, warrants or Convertible Securities on terms that are at
         least as favorable to the Issuer as terms that could be obtained in an
         arm's length transaction with third Persons not Affiliates of the
         Issuer or any Subsidiary and for consideration equal to the fair value
         of such shares as determined in good faith by a majority of
         disinterested members of the board of directors of the Issuer.

         "Person(s)" shall mean any individual, sole proprietorship,
         partnership, joint venture, trust, limited liability company,
         incorporated organization, association, corporation, institution,
         public benefit corporation, entity or government (whether federal,
         state, county, city, municipal or otherwise, including, without
         limitation, any instrumentality, division, agency, body or department
         thereof).

         "Price" means the average of the "high" and "low" prices as reported in
         The Wall Street Journal's listing for such day (corrected for obvious
         typographical errors) or if such shares are not reported in such
         listing, the average of the reported "high" and "low" sales prices on
         the largest national securities exchange (based on the aggregate dollar
         value of


                                       4
<PAGE>   8

         securities listed) on which such shares are listed or traded, or if
         such shares are not listed or traded on any national securities
         exchange, then the average of the reported "high" and "low" sales
         prices for such shares in the over-the-counter market, as reported on
         the National Association of Securities Dealers Automated Quotations
         System, or, if such prices shall not be reported thereon, the average
         of the closing bid and asked prices so reported, or, if such prices
         shall not be reported, then the average of the closing bid and asked
         prices reported by the National Quotations Bureau Incorporated. The
         "average" Price per share for any period shall be determined by
         dividing the sum of the Prices determined for the individual trading
         days in such period by the number of trading days in such period.

         "Registrable Securities" shall mean, at any particular time and as to
         each Warrant Holder, (i) all shares of common stock issuable upon the
         exercise of such Warrant Holder's Warrants and (ii) all of such Warrant
         Holder's issued and outstanding Warrant Stock.

         "Registration Expenses" shall have the meaning set forth in Section 9.5
         of this Agreement.

         "Registration Statement" shall have the meaning set forth in Section
         9.4 of this Agreement.

         "Required Holders" shall mean the Warrant Holders of Warrants
         exercisable for an amount exceeding 50% of the aggregate number of
         shares of Common Stock then purchasable upon exercise of all Warrants,
         whether or not exercisable.

         "Requirement of Law" shall mean, as to any Person, any requirement
         contained in any certificate of incorporation, bylaws, or other
         organizational or governing documents of such Person, and any law,
         treaty, rule or regulation or determination of an arbitrator or a court
         or other governmental authority, in each case applicable to or binding
         such Person or any of the property or to which such Person or any of
         its property is subject.

         "Restricted Common Stock" shall mean shares of Common Stock which are,
         or which upon their issuance on the exercise of a Warrant would be,
         evidenced by a certificate bearing the restrictive legend set forth in
         Section 9.1 of this Agreement.

         "Securities Act" shall mean the Securities Act of 1933, as amended, or
         any similar federal statute, and the rules and regulations of the
         Commission thereunder, all as the same shall be in effect at the time.

         "Subsidiary" shall mean any Person of which an aggregate of more than
         50% of the outstanding sock or other ownership interests having
         ordinary voting power to elect a majority of the board of directors or
         other managers of such Person (irrespective of whether, at the time,
         stock or other ownership interests of any other class or classes of
         such Person shall have or might have voting power by reason of the
         happening of any contingency) is at the time, directly or indirectly,
         owned legally or beneficially by the Issuer and/or one or more
         Subsidiaries of the Issuer.

         "Transfer Notice" shall have the meaning set forth in Section 9.2 of
         this Agreement.


                                       5
<PAGE>   9

         "Warrant Certificate" shall mean a certificate evidencing one or more
         Warrants, substantially in the form of Exhibit A hereto, with such
         changes therein as may be required to reflect any adjustments made
         pursuant to Section 4 of this Agreement.

         "Warrant Holder" shall mean such Person in whose name the Warrants are
         registered on the books of the Issuer maintained for such purpose or
         each Person holding any Warrant Stock. As of the Closing Date, the Bank
         of Montreal is the Warrant Holder hereof.

         "Warrant Price" shall mean, for any exercise of Warrants pursuant to
         Section 2.2 of this Agreement, an amount equal to (i) the number of
         shares of Common Stock being purchased upon such exercise multiplied by
         (ii) the Current Warrant Price for each share of Common Stock as of the
         date of such exercise.

         "Warrant Stock" shall mean the shares of Common Stock purchased by the
         Warrant Holders upon the exercise thereof.

         "Warrants" shall mean the Warrants issued pursuant to this Agreement
         and all Warrants issued upon transfer, division or combination of, or
         in substitution for, such Warrants. All Warrants shall at all times be
         identical as to terms and conditions and date, except as to the number
         of shares of Common Stock for which they may be exercised. A Warrant
         shall entitle the record holder thereof to purchase from the Issuer one
         share of Common Stock (subject to adjustment as provided in Section 4
         of this Agreement).

2.       ISSUANCE AND EXERCISE OF WARRANTS

2.1      Issuance of Warrants. The Issuer hereby agrees to issue to the Warrant
         Holder on the Closing Date, SIX HUNDRED SIXTY-ONE THOUSAND FIVE HUNDRED
         THIRTY-EIGHT (661,538) Warrants. On the Closing Date, the Issuer shall
         deliver to the Warrant Holder Warrant Certificates evidencing the
         Warrants issued to the Warrant Holder.

2.2      Manner of Exercise.

         (a)      The Warrant Holder may, from and after the Closing Date until
                  5:00 p.m., New York City time on the Expiration Date, exercise
                  the Warrants evidenced by a Warrant Certificate, on any
                  Business Day, for all or part of the number of shares of
                  Common Stock purchasable thereunder.

         (b)      In order to exercise the Warrants, in whole or in part, the
                  Warrant Holder shall either:

                  (i)      deliver to the Issuer at its principal office at 6300
                           Bridge Point Parkway, Building 2, Suite 500, Austin,
                           Texas 78730, Attention: President, or at the office
                           or agency designated by the Issuer pursuant to
                           Section 12 of this Agreement (the "Principal
                           Office"), (x) a written notice duly executed by the
                           Warrant Holder or its agent or attorney,
                           substantially in the form of the form of election to
                           purchase appearing at the end of the Warrant
                           Certificate as Exhibit A thereto, of such Warrant
                           Holder's election to exercise the Warrants, which
                           notice shall specify the number of shares of


                                       6
<PAGE>   10

                           Common Stock to be purchased, (y) payment of the
                           Warrant Price in the manner provided below, and (z)
                           the Warrant Certificate or Warrant Certificates
                           evidencing the Warrants. Upon receipt thereof, the
                           Issuer shall, as promptly as practicable, and in any
                           event within three (3) Business Days thereafter,
                           execute or cause to be executed and deliver or cause
                           to be delivered to such Warrant Holder a certificate
                           or certificates representing the aggregate number of
                           full shares of Common Stock issuable upon such
                           exercise, together with cash in lieu of any fraction
                           of a share, as hereinafter provided. The stock
                           certificate or certificates so delivered shall be, to
                           the extent possible, in such denomination or
                           denominations as such Warrant Holder shall request in
                           the notice and shall be registered in the name of the
                           Warrant Holder or, subject to Section 9 of this
                           Agreement, such other name as shall be designated in
                           the notice. The Warrants shall be deemed to have been
                           exercised and such certificate or certificates shall
                           be deemed to have been issued, and such Warrant
                           Holder or any other Person so designated to be named
                           therein shall be deemed to have become a holder of
                           record of such shares for all purposes, as of the
                           date the notice, together with payment of the Warrant
                           Price and the Warrant Certificate or Warrant
                           Certificates, are received by the Issuer as described
                           above and all taxes required to be paid by such
                           Warrant Holder, if any, pursuant to Section 2.3 of
                           this Agreement prior to the issuance of such shares
                           have been paid. If the Warrants evidenced by a
                           Warrant Certificate shall have been exercised, the
                           Issuer shall, at the time of delivery of the
                           certificate or certificates representing the Warrant
                           Stock, deliver to the Warrant Holder a new Warrant
                           Certificate evidencing the rights of the Warrant
                           Holder to purchase the unpurchased shares of Common
                           Stock represented by the old Warrant Certificate,
                           which new Warrant Certificate shall in all other
                           respects be identical to the old Warrant Certificate.
                           Payment of the Warrant Price shall be made in cash in
                           an amount equal to the Warrant Price; or

                  (ii)     deliver to the Issuer on any Business Day at the
                           Principal Office the Cashless Conversion Notice in
                           substantially the form attached hereto as Exhibit B
                           duly executed by the Warrant Holder and setting forth
                           such Warrant Holder's election to receive the number
                           of shares of Common Stock specified in the Cashless
                           Conversion Notice ("Cashless Conversion"). Such
                           presentation and surrender shall be deemed a waiver
                           of the Warrant Holder's obligation to pay all or any
                           portion (as the case may be) of the Warrant Price in
                           connection with such Cashless Conversion. In the
                           event of a Cashless Conversion, the Issuer shall
                           deliver to the Warrant Holder (without payment by the
                           Warrant Holder of any Warrant Price) that number of
                           shares of Common Stock equal to: the number of shares
                           of Common Stock for which the Warrant Holder hereof
                           desires to exercise the Warrants multiplied by a
                           fraction, (x) the numerator of which shall be the
                           Current Market Price on the date of such exercise
                           less the Current Warrant Price on the date of such
                           exercise and (y) the denominator of which shall be
                           the Current Market Price on the date of


                                       7
<PAGE>   11

                           such exercise. The number of shares of Common Stock
                           "into which each Warrant is exercisable" shall be one
                           share, subject to adjustment as provided in Section 4
                           hereof. The Warrant Holder may exercise its Cashless
                           Conversion rights, at any time or from time to time,
                           prior to the Expiration Date. The Cashless Conversion
                           Notice shall also specify a place and date not less
                           than one nor more than 20 Business Days from the date
                           of the Cashless Conversion Notice for the closing of
                           such purchase.

2.3      Payment of Taxes. The Issuer shall pay all expenses in connection with,
         and all transfer taxes and other governmental charges that may be
         imposed with respect to, the issuance or delivery of Warrant Stock. The
         Issuer shall not be required, however, to pay any tax or other charge
         imposed in connection with any transfer involved in the issue of any
         certificate for shares of Warrant Stock issuable upon exercise of
         Warrants in any name other than that of Warrant Holder, and in such
         case the Issuer shall not be required to issue or deliver any stock
         certificate until such tax or other charge has been paid or it has been
         established to the satisfaction of the Issuer that no such tax or other
         charge is due.

2.4      Fractional Shares. The Issuer shall not be required to issue a
         fractional share of Common Stock upon the exercise of Warrants as
         provided in Section 2(b)(i) and (ii). As to any fraction of a share
         which the Warrant Holder would otherwise be entitled to purchase upon
         such exercise, the Issuer shall pay a cash adjustment in respect of
         such fraction in an amount equal to the same fraction of the Current
         Market Price per share of Common Stock on the date of exercise. If the
         determination of Current Market Price for purposes of this Section 2.4
         would otherwise require an appraisal to be made by an investment
         banking firm, then Current Market Price for purposes of this Section
         2.4 only shall mean Book Value per share of Common Stock on the date of
         exercise, unless a determination of Appraised Value shall have been
         made within six months prior to such date in which case such Appraised
         Value shall be utilized for the purposes of determining Current Market
         Price.

2.5      Continued Validity. A Warrant Holder of shares of Warrant Stock (other
         than a holder who acquires such shares after the same have been
         publicly sold pursuant to a Registration Statement under the Securities
         Act) shall continue to be entitled with respect to such shares to all
         rights to which it would have been entitled as Warrant Holder under
         Sections 9, 10 and 15 of this Agreement. The Issuer will, at the time
         of each exercise of Warrants or upon the request of the Warrant Holder
         of the shares of Warrant Stock issued upon the exercise thereof,
         acknowledge in writing, in form reasonably satisfactory to such Warrant
         Holder, its continuing obligation to afford to such Warrant Holder all
         such rights; provided, however, that if such Warrant Holder shall fail
         to make any such request, such failure shall not affect the continuing
         obligation of the Issuer to afford to such Warrant Holder all such
         rights.

3.       TRANSFERS, DIVISION AND COMBINATION

3.1      Transfer. Subject to compliance with Section 9 of this Agreement,
         transfer of Warrants, in whole or in part, shall be registered on the
         books of the Issuer to be maintained for such purposes, upon surrender
         of the Warrant Certificate representing such Warrants at


                                       8
<PAGE>   12

         the principal office of the Issuer referred to in Section 2.2 of this
         Agreement or the office or agency designated by the Issuer pursuant to
         Section 12 of this Agreement, together with a written assignment
         substantially in the form of Exhibit B to the Warrant Certificate and a
         written agreement, in form reasonably satisfactory to the Issuer,
         setting forth the new Warrant Holder's agreement to be bound by all of
         the terms of this Agreement each duly executed by the Warrant Holder or
         its agent or attorney, and funds sufficient to pay any transfer taxes
         payable by such Warrant Holder upon the making of such transfer. Upon
         such surrender and, if required, such payment, the Issuer shall,
         subject to Section 9 of this Agreement, execute and deliver a new
         Warrant Certificate or Warrant Certificates in the name of the assignee
         or assignees and in the denomination specified in such instrument of
         assignment, and shall issue to the assignor a new Warrant Certificate
         or Warrant Certificates evidencing the portion of the old Warrant
         Certificate not so assigned, and the old Warrant Certificate shall
         promptly be canceled. A Warrant, if properly assigned in compliance
         with Section 9 of this Agreement, may be exercised by a new Warrant
         Holder for the purchase of shares of Warrant Stock without having a new
         Warrant Certificate or new Warrant Certificates issued.

3.2      Division and Combination. Subject to the provisions of Section 9 of
         this Agreement, any Warrant Certificate may be divided or combined with
         other Warrant Certificates upon presentation thereof at the aforesaid
         office or agency of the Issuer, together with a written notice
         specifying the names and denominations in which new Warrant
         Certificates are to be issued, signed by a Warrant Holder or its agent
         or attorney. Subject to compliance with Section 3.1 of this Agreement
         as to any transfer which may be involved in such division or
         combination, the Issuer shall execute and deliver a new Warrant
         Certificate or Warrant Certificates in exchange for the Warrant
         Certificate or Warrant Certificates to be divided or combined in
         accordance with such notice.

3.3      Expenses. The Issuer shall prepare, issue and deliver at its own
         expense (other than transfer taxes) the new Warrant Certificate or
         Warrant Certificates provided for under this Section 3.

3.4      Maintenance of Books. The Issuer agrees to maintain, at its aforesaid
         office or agency, books for the registration of, and the registration
         of transfer of, the Warrants.

4.       ADJUSTMENTS

         The number of shares of Warrant Stock for which Warrants are
         exercisable, and the price at which such shares may be purchased upon
         exercise of Warrants, shall be subject to adjustment from time to time
         as set forth in this Section 4. The Issuer shall give each Warrant
         Holder notice of any event described below which requires an adjustment
         pursuant to this Section 4 within three (3) Business Days after such
         event.

4.1      Stock Dividends, Subdivisions and Combinations. If at any time the
         Issuer shall:

         (a)      take a record of the holders of its Common Stock for the
                  purpose of entitling them to receive a dividend payable in, or
                  other distribution of, Additional Shares of Common Stock,


                                       9
<PAGE>   13

         (b)      subdivide its outstanding shares of Common Stock into a larger
                  number of shares of Common Stock, or

         (c)      combine its outstanding shares of Common Stock into a smaller
                  number of shares of Common Stock,

                  then (i) the number of shares of Common Stock for which a
                  Warrant is exercisable immediately after the occurrence of any
                  such event shall be adjusted to equal the number of shares of
                  Common Stock which a record holder of the same number of
                  shares of Common Stock for which a Warrant is exercisable
                  immediately prior to the occurrence of such event would own or
                  be entitled to receive after the happening of such event, and
                  (ii) the Current Warrant Price shall be adjusted to equal the
                  Current Warrant Price multiplied by a fraction, the numerator
                  of which shall be the number of shares of Common Stock for
                  which a Warrant is exercisable immediately prior to the
                  adjustment and the denominator of which shall be the number of
                  shares for which a Warrant is exercisable immediately after
                  such adjustment.

4.2      Certain Other Distributions. If at any time the Issuer shall take a
         record of the holders of its Common Stock for the purpose of entitling
         them to receive any dividend or other distribution of:

         (a)      cash;

         (b)      any evidences of its indebtedness (other than Convertible
                  Securities), any shares of its stock (other than Additional
                  Shares of Common Stock or Convertible Securities) or any other
                  securities or property of any nature whatsoever (other than
                  cash); or

         (c)      any warrants or other rights to subscribe for or purchase any
                  evidences of its indebtedness (other than Convertible
                  Securities), any shares of its stock (other than Additional
                  Shares of Common Stock or Convertible Securities) or any other
                  securities or property of any nature whatsoever;

                  then (i) the number of shares of Common Stock for which a
                  Warrant is exercisable shall be adjusted to equal the product
                  obtained by multiplying the number of shares of Common Stock
                  for which a Warrant is exercisable immediately prior to such
                  adjustment by a fraction (A) the numerator of which shall be
                  the Current Market Price per share of Common Stock at the date
                  of taking such record and (B) the denominator of which shall
                  be such Current Market Price per share of Common Stock, minus
                  the amount allocable to one share of Common Stock of any such
                  cash so distributable and of the fair value (as determined
                  reasonably and in good faith by the board of directors of the
                  Issuer) of any and all such evidences of indebtedness, shares
                  of stock, other securities or property or warrants or other
                  subscription or purchase rights so distributable, and (ii) the
                  Current Warrant Price shall be adjusted to equal (A) the
                  Current Warrant Price multiplied by the number of shares of
                  Common Stock for which a Warrant is


                                       10
<PAGE>   14

                  exercisable immediately prior to the adjustment divided by (B)
                  the number of shares for which a Warrant is exercisable
                  immediately after such adjustment. A reclassification of the
                  Common Stock (other than a change in par value, or from par
                  value to no par value or from no par value to par value) into
                  shares of Common Stock and shares of any other class of stock
                  shall be deemed a distribution by the Issuer to the holders of
                  its Common Stock of such shares of such other class of stock
                  within the meaning of this Section 4.2 and, if the Outstanding
                  shares of Common Stock shall be changed into a larger or
                  smaller number of shares of Common Stock as a part of such
                  reclassification, such change shall be deemed a subdivision or
                  combination, as the case may be, of the Outstanding shares of
                  Common Stock within the meaning of Section 4.1 of this
                  Agreement.

4.3      Issuance of Additional Shares of Stock.

         (a)      If at any time the Issuer shall (except as hereinafter
                  provided) issue or sell any Additional Shares of Common Stock,
                  other than Permitted Issuances, for consideration in an amount
                  per Additional Share of Common Stock less than the Current
                  Market Price, then the Current Warrant Price shall be adjusted
                  by multiplying the Current Warrant Price by a fraction, the
                  numerator of which shall be (A) an amount equal to the sum of
                  (X) the number of shares of Common Stock Outstanding
                  immediately prior to such issuance or sale multiplied by the
                  Current Market Price immediately prior to the first to occur
                  of (i) board action by the Issuer authorizing such action or
                  (ii) the public announcement of an intent to take such action,
                  plus (Y) the consideration, if any, received by the Issuer
                  upon such issuance or sale, and the denominator of which shall
                  be (B) the total number of shares of Common Stock Outstanding
                  immediately after such issuance or sale multiplied by the
                  Current Market Price as determined in clause (A) above.

         (b)      The provisions of Section 4.3(a) of this Agreement shall not
                  apply to any issuance of Additional Shares of Common Stock for
                  which an adjustment is provided under Sections 4.1 or 4.2 of
                  this Agreement. No adjustment of the number of shares of
                  Common Stock for which a Warrant shall be exercisable shall be
                  made under Section 4.3(a) of this Agreement upon the issuance
                  of any Additional Shares of Common Stock which are issued
                  pursuant to the exercise of any warrants or other subscription
                  or purchase rights or pursuant to the exercise of any
                  conversion or exchange rights in any Convertible Securities if
                  any such adjustment shall previously have been made upon the
                  issuance of such warrants or other rights or upon the issuance
                  of such Convertible Securities (or upon the issuance of any
                  warrant or other rights therefor) pursuant to Section 4.4 or
                  Section 4.5 of this Agreement.

4.4      Issuance of Warrants or Other Rights. If at any time the Issuer shall
         take a record of the holders of its Common Stock for the purpose of
         entitling them to receive a distribution of, or shall in any manner
         (whether directly or by assumption in a merger in which the Issuer is
         the surviving corporation) issue or sell, any warrants or other rights
         to subscribe for or purchase any Additional Shares of Common Stock or
         any Convertible Securities, whether


                                       11
<PAGE>   15

         or not the rights to exchange or convert thereunder are immediately
         exercisable, and if the price per share for which Common Stock is
         issuable upon the exercise of such warrants or other rights or upon
         conversion or exchange of such Convertible Securities shall be less
         than the Current Market Price in effect immediately prior to the time
         of such distribution, issue or sale, then the Current Warrant Price
         shall be adjusted as provided in Section 4.3(a) of this Agreement on
         the basis that (A) the maximum number of Additional Shares of Common
         Stock issuable pursuant to all such warrants or other rights or
         necessary to effect the conversion or exchange of all such Convertible
         Securities shall be deemed to be Outstanding immediately following such
         issuance, (B) the price per share for such Additional Shares of Common
         Stock shall be deemed to be the lowest possible price per share in any
         range of prices per share at which such Additional Shares of Common
         Stock are available to such holders, and (C) the Issuer shall be deemed
         to have received all of the consideration payable therefor, if any, as
         of the date of the actual issuance of such warrants or other rights. No
         further adjustments of the Current Warrant Price shall be made upon the
         actual issuance of such Common Stock or of such other rights or upon
         exercise of such warrants or other rights or upon the actual issuance
         of such Common Stock upon such conversion or exchange of such
         Convertible Securities.

4.5      Issuance of Convertible Securities. If at any time the Issuer shall
         take a record of the holders of its Common Stock for the purpose of
         entitling them to receive a distribution of, or shall in any manner
         (whether directly or by assumption in a merger in which the Issuer is
         the surviving corporation) issue or sell, any Convertible Securities,
         whether or not the rights to exchange or convert thereunder are
         immediately exercisable, and if the price per share for which Common
         Stock is issuable upon such conversion or exchange shall be less than
         the Current Market Price in effect immediately prior to the time of
         such issue or sale of Convertible Securities, then the Current Warrant
         Price shall be adjusted as provided in Section 4.3(a) of this Agreement
         on the basis that (A) the maximum number of Additional Shares of Common
         Stock necessary to effect the conversion or exchange of all such
         Convertible Securities shall be deemed to be Outstanding immediately
         following such issuance, (B) the price per share of such Additional
         Shares of Common Stock shall be deemed to be the lowest possible price
         in any range of prices at which such Additional Shares of Common Stock
         are available to such holders, and (C) the Issuer shall be deemed to
         have received all of the consideration payable therefor, if any, as of
         the date of actual issuance of such Convertible Securities. No
         adjustment of the Current Warrant Price shall be made under this
         Section 4.5 upon the issuance of any Convertible Securities which are
         issued pursuant to the exercise of any warrants or other subscription
         or purchase rights therefor if any such adjustments shall previously
         have been made upon the issuance of such warrants or other rights
         pursuant to Section 4.4 of this Agreement. No further adjustments of
         the Current Warrant Price shall be made upon the actual issue of such
         Common Stock upon conversion or exchange of such Convertible Securities
         and, if any issue or sale of such Convertible Securities is made upon
         exercise of any warrant or other right to purchase any such Convertible
         Securities for which adjustments of the Current Warrant Price have been
         or are to be made pursuant to other provisions of this Section 4, no
         further adjustments of the Current Warrant Price shall be made by
         reason of such issue or sale.


                                       12
<PAGE>   16

4.6      Superseding Adjustment. If, at any time after any adjustment of the
         Current Warrant Price shall have been made pursuant to Section 4.4 or
         Section 4.5 of this Agreement as the result of any issuance of
         warrants, options, rights or Convertible Securities, and such warrants,
         options or rights, or the right of conversion or exchange in such other
         Convertible Securities, shall expire, and all or a portion of such
         warrants, options or rights, or the right of conversion or exchange
         with respect to all or a portion of such other Convertible Securities,
         as the case may be, shall not have been exercised, then such previous
         adjustment shall be rescinded and annulled and, if applicable, the
         Current Warrant Price shall be recalculated as if all such expired and
         unexercised warrants, options, rights or Convertible Securities had
         never been issued.

4.7      Other Provisions Applicable to Adjustments Under This Section. The
         following provisions shall be applicable to the making of adjustments
         of the number of shares of Common Stock for which a Warrant is
         exercisable provided for in this Section 4:

         (a)      Computation of Consideration. To the extent that any
                  Additional Shares of Common Stock shall be issued for cash
                  consideration, the consideration received by the Issuer
                  therefor shall be the amount of the cash received by the
                  Issuer therefor, or, if such Additional Shares of Common Stock
                  are sold to underwriters or dealers for public offering
                  without a subscription offering, the initial public offering
                  price (in any such case subtracting any amounts paid or
                  receivable for accrued interest or accrued dividends, but not
                  subtracting any compensation, discounts or expenses paid or
                  incurred by the Issuer for and in the underwriting of, or
                  otherwise in connection with, the issuance thereof). To the
                  extent that such issuance shall be for a consideration other
                  than cash, then, except as herein otherwise expressly
                  provided, the amount of such consideration shall be deemed to
                  be the fair value of such consideration at the time of such
                  issuance as determined reasonably and in good faith by a
                  majority of the disinterested members of the board of
                  directors of the Issuer.

         (b)      When Adjustments to Be Made. The adjustments required by this
                  Section 4 shall be made whenever and as often as any specified
                  event requiring an adjustment shall occur, except that any
                  adjustment to the number of shares for which the Warrants are
                  exercisable that would otherwise be required may be postponed
                  (except in the case of a subdivision or combination of shares
                  of the Common Stock, as provided for in Section 4.1 of this
                  Agreement) up to, but not beyond, the date and time of
                  exercise of any Warrants if such adjustment either by itself
                  or with other adjustments not previously made adds or
                  subtracts less than 1% to the number of shares of Common Stock
                  for which the Warrants initially issued pursuant to this
                  Agreement are exercisable immediately prior to the making of
                  such adjustment. Any adjustment representing a change of less
                  than such minimum amount (except as aforesaid) which is
                  postponed shall be carried forward and made as soon as such
                  adjustment, together with other adjustments required by this
                  Section 4 and not previously made, would result in a minimum
                  adjustment or on the date of exercise. For the purpose of any
                  adjustment, any specified event shall be deemed to have
                  occurred at the close of business on the date of its
                  occurrence.



                                       13
<PAGE>   17

         (c)      Fractional Interests. In computing adjustments under this
                  Section 4, fractional interests in Common Stock resulting from
                  an issuance of additional Warrants to any Warrant Holder
                  pursuant to this Section 4 shall be taken into account to the
                  nearest 1/10th of a share, subject to Section 2.4 of this
                  Agreement.

         (d)      When Adjustment Not Required. If the Issuer shall take a
                  record of the holders of its Common Stock for the purpose of
                  entitling them to receive a dividend or distribution or
                  subscription or purchase rights and shall, thereafter and
                  before the distribution to stockholders thereof, legally
                  abandon its plan to pay or deliver such dividend,
                  distribution, subscription or purchase rights, no adjustment
                  shall be required by reason of the taking of such record and
                  any such adjustment previously made in respect thereof shall
                  be rescinded and annulled.

         (e)      Escrow of Warrant Stock. If after any property becomes
                  distributable pursuant to this Section 4 by reason of the
                  taking of any record of the holders of Common Stock, but prior
                  to the occurrence of the event for which such record is taken,
                  any Warrant Holder exercises Warrants, any Additional Shares
                  of Common Stock issuable upon exercise of such Warrant by
                  reason of such adjustment shall be deemed the last shares of
                  Common Stock for which such Warrant is exercised
                  (notwithstanding any other provision to the contrary herein),
                  and such shares or other property shall be held in escrow for
                  a Warrant Holder by the Issuer to be issued to such Warrant
                  Holder upon and to the extent that the event actually takes
                  place, upon payment of the balance, if any, of the Warrant
                  Price for such Warrant at such date (after taking into account
                  any overpayment of the Warrant Price made at any time of the
                  initial Warrant exercise). Notwithstanding any other provision
                  to the contrary herein, if the event for which such record was
                  taken fails to occur or is rescinded, then such escrowed
                  shares shall be canceled by the Issuer and escrowed property
                  returned.

4.8      Reorganization, Reclassification, Merger, Consolidation or Disposition
         of Assets. In the event the Issuer shall reorganize its capital,
         reclassify its capital stock, consolidate or merge with and into
         another corporation or entity (where the Issuer is not the surviving
         corporation or where there is a change in or distribution with respect
         to the Common Stock of the Issuer), or sell, transfer or otherwise
         dispose of all or substantially all its property, assets or business to
         another corporation or entity and, pursuant to the terms of such
         reorganization, reclassification, merger, consolidation or disposition
         of assets, shares of common stock of the successor or acquiring
         corporation or entity, or any cash, shares of stock or other securities
         or property of any nature whatsoever (including warrants or other
         subscription or purchase rights) in addition to or in lieu of common
         stock of the successor or acquiring corporation or entity ("Other
         Property"), are to be received by or distributed to the holders of
         Common Stock of the Issuer, then the Issuer shall, as a condition
         precedent to such transaction, cause effective provisions to be made so
         that each Warrant Holder shall have the right thereafter to receive,
         upon exercise of a warrant, solely the number of shares of "common
         stock of the successor or acquiring corporation" or of the Issuer, if
         it is the surviving corporation, and Other Property receivable upon or
         as a result of such reorganization, reclassification, merger,
         consolidation or disposition of assets, by a holder of the number of
         shares of Common


                                       14
<PAGE>   18

         Stock for which a Warrant is exercisable immediately prior to such
         event. In case of any such reorganization, reclassification, merger,
         consolidation or disposition of assets, such provisions shall include
         the express assumption by the successor or acquiring corporation or
         entity (if other than the Issuer) of the due and punctual observance
         and performance of each and every covenant and condition of this
         Agreement to be performed and observed by the Issuer and all the
         obligations and liabilities hereunder, subject to such modifications as
         may be deemed appropriate (as determined by resolution of the board of
         directors of the Issuer) to provide for adjustments of shares of the
         Common Stock for which a Warrant is exercisable which shall be as
         nearly equivalent as practicable to the adjustments provided for in
         this Section 4. For purposes of this Section 4.8, "common stock of the
         successor or acquiring corporation" shall include stock of such
         corporation of any class which is not preferred as to dividends or
         assets over any other class of stock or other securities of such
         corporation or entity and which is not subject to redemption and shall
         also include any evidences of indebtedness, shares of stock or other
         securities which are convertible into or exchangeable for any such
         stock or other securities, either immediately or upon the arrival of a
         specified date or the happening of a specified event, and any warrants
         or other rights to subscribe for or purchase any such stock or
         securities. The foregoing provisions of this Section 4.8 shall
         similarly apply to successive reorganizations, reclassifications,
         mergers, consolidations or disposition of assets.

5.       NOTICES TO WARRANT HOLDERS

5.1      Notice of Adjustments. Whenever the number of shares of Common Stock
         for which a Warrant is exercisable, or whenever the price at which a
         share of such Common Stock may be purchased upon exercise of the
         Warrants, shall be adjusted pursuant to Section 4, the Issuer shall
         forthwith prepare a certificate to be executed by the chief financial
         officer of the Issuer setting forth, in reasonable detail, the event
         requiring the adjustment and the method by which such adjustment was
         calculated (including a description of the basis on which the board of
         directors of the Issuer determined the fair value of any evidences of
         indebtedness, shares of stock, other securities or property or warrants
         or other subscription or purchase rights referred to in Section 4 of
         this Agreement), specifying the number of shares of Common Stock for
         which a Warrant is exercisable and (if such adjustment was made
         pursuant to Section 4.8 of this Agreement) describing the number and
         kind of any other shares of stock or Other Property for which a Warrant
         is exercisable, and any change in the purchase price or prices thereof,
         after giving effect to such adjustment or change. The Issuer shall
         promptly cause a signed copy of such certificate to be delivered to
         each Warrant Holder in accordance with Section 15.2 of this Agreement.
         The Issuer shall keep at its office or agency designated pursuant to
         Section 12 of this Agreement copies of all such certificates and cause
         the same to be available for inspection at said office during normal
         business hours by any Warrant Holder or any prospective purchaser of a
         Warrant designated by a Warrant Holder thereof.

5.2      Notice of Certain Corporate Action. Each Warrant Holder shall be
         entitled to the same rights to receive notice of corporate action as
         any holder of Common Stock.


                                       15
<PAGE>   19

6.       REPRESENTATIONS AND WARRANTIES

         The Issuer makes the following representations and warranties, each and
         all of which shall be true and correct as of the date of execution and
         delivery of this Agreement and shall survive the execution and delivery
         of this Agreement:

         (a)      Due Organization; Etc. The Issuer is a corporation duly
                  organized validly existing and in good standing under the laws
                  of the State of Delaware, and has the power and authority to
                  execute and deliver this Agreement and the Warrant
                  Certificates, to issue the Warrants and to perform its
                  obligations under this Agreement and the Warrant Certificates.

         (b)      Due Authorization; No Violation. The execution, delivery and
                  performance by the Issuer of this Agreement and the Warrant
                  Certificates, the issuance of the Warrants and the issuance of
                  the Warrant Stock upon exercise of the Warrants have been duly
                  authorized by all necessary corporate action and do not and
                  will not violate, or result in a breach of, or constitute a
                  default under or require any consent under, or result in the
                  creation of any lien or security interest upon the assets of
                  the Issuer pursuant to, any Requirement of Law or any
                  contractual obligation binding upon the Issuer.

         (c)      Due Execution; Etc. This Agreement has been duly executed and
                  delivered by the Issuer and constitutes a legal, valid and
                  enforceable obligation of the Issuer. When the Warrants and
                  the Warrant Certificates have been issued as contemplated
                  hereby, (i) the Warrants and the Warrant Certificates will
                  constitute legal, valid, binding and enforceable obligations
                  of the Issuer and (ii) the Warrant Stock, when issued upon
                  exercise of the Warrants in accordance with the terms hereof,
                  will be duly authorized, validly issued, fully paid and
                  non-assessable shares of Common Stock with no personal
                  liability attaching to the ownership thereof.

         (d)      Capitalization. The total number of shares of all classes of
                  stock that the Issuer shall on the Closing Date have authority
                  to issue is 40,000,000 shares, consisting of (i) 30,000,000
                  shares of Common Stock, par value $0.01 per share, of which,
                  after giving effect to the transactions contemplated herein
                  and all other issuances of capital stock of the Issuer on or
                  prior to the Closing Date, 14,428,621 shares of Common Stock
                  will be issued and outstanding and 661,538 shares of Common
                  Stock will be reserved for future issuance pursuant to this
                  Agreement and (ii) 10,000,000 shares of Preferred Stock, par
                  value $0.01 per share, none of which are presently
                  outstanding. Schedule A sets forth a complete list of the
                  outstanding capital stock of the Issuer, including any
                  options, warrants or rights to purchase the capital stock of
                  the Issuer. The delivery hereunder by the Issuer to the
                  Warrant Holder of the Warrants issued on the Closing Date will
                  transfer and convey to the Warrant Holder good and marketable
                  title to such Warrants and, upon exercise of such Warrants in
                  accordance with this Agreement, good and marketable title to
                  the Common Stock purchased upon such exercise, free and clear
                  of all preemptive rights, liens, charges and encumbrances,
                  except for


                                       16
<PAGE>   20

                  restrictions on transfer referred to in this Agreement, or
                  arising under the Federal and state securities laws. Except as
                  otherwise disclosed on Schedule A, the Issuer does not have
                  outstanding any stock or securities convertible into or
                  exchangeable for any shares of its stock, nor, except as so
                  set forth, does it have outstanding any agreements, rights or
                  options entitling any person to subscribe for or to purchase
                  any capital stock or securities convertible into or
                  exchangeable for any of its shares of stock.

         (e)      Full Disclosure. No information contained in this Agreement,
                  the financial statements referred to in the Credit Agreement
                  or any written statement furnished by or on behalf of the
                  Issuer pursuant to the terms of this Agreement to the Warrant
                  Holder contains any untrue statement of a material fact or
                  omits to state a material fact necessary to make the
                  statements contained herein or therein not misleading in light
                  of the circumstances under which made.

         (f)      Warrant Price. The Issuer has taken all corporate action, and
                  obtained all necessary authorizations or exemptions from any
                  public regulatory body or bodies or governmental entity or
                  entities having jurisdiction thereof, as may be necessary in
                  order that the Issuer may validly and legally issue fully paid
                  and non-assessable shares of Common Stock upon to exercise of
                  the warrants at the Warrant Price, as the same may be adjusted
                  pursuant hereto.

         (g)      Other Representations and Warranties. The Issuer hereby
                  affirms and reaffirms for the express benefit of the Warrant
                  Holders that the representations and warranties made by the
                  Issuer in that certain Guaranty Agreement dated as of January
                  26, 1998, as amended, are true and correct, as if made in
                  favor of the Warrant Holder on the date hereof.

7.       CERTAIN COVENANTS

7.1      No Impairment. The Issuer shall not by any action including, without
         limitation, amending its certificate of incorporation or through any
         reorganization, transfer of assets, consolidation, merger, dissolution,
         issue or sale of securities or any other voluntary action, avoid or
         seek to avoid the observance or performance of any of the terms of this
         Agreement, but will at all times in good faith assist in the carrying
         out of all such terms and in the taking of all such actions as may be
         necessary or appropriate to protect the rights of each Warrant Holder
         against impairment. Without limiting the generality of the foregoing,
         the Issuer will use reasonable good faith efforts to obtain all such
         authorizations, exemptions or consents from any public regulatory body
         having jurisdiction thereof as may be necessary to enable it to perform
         its obligations under this Agreement.

         Upon the request of a Warrant Holder, the Issuer will, at any time
         during the period this Agreement is in effect, acknowledge in writing,
         in form satisfactory to such Warrant Holder, the continuing validity of
         this Agreement and the obligations of the Issuer hereunder.


                                       17
<PAGE>   21

7.2      Reservation and Authorization of Common Stock; Registration with, or
         Approval of, any Governmental Authority. From and after the Closing
         Date, the Issuer shall at all times reserve and keep available for
         issue upon the exercise of Warrants such number of its authorized but
         unissued shares of Common Stock as will be sufficient to permit the
         exercise in full of all outstanding Warrants. All shares of Common
         Stock which shall be so issuable, when issued upon exercise of any
         Warrants and payment therefor in accordance with the terms of this
         Agreement, shall be duly and validly issued and fully paid and
         non-assessable, and not subject to preemptive rights.

         Before taking any action which would result in an adjustment in the
         number of shares of Common Stock for which a Warrant is exercisable or
         in the Current Warrant Price, the Issuer shall obtain all such
         authorizations or exemptions thereof, or consents thereto, as may be
         necessary from any public regulatory body or bodies or governmental
         entity or entities having jurisdiction thereof.

         If any shares of Common Stock required to be reserved for issuance upon
         exercise of Warrants require registration or qualification with any
         governmental authority under any federal or state law (otherwise than
         as provided in Section 9 of this Agreement) before such shares may be
         so issued, the Issuer will in good faith and as expeditiously as
         possible and at its expense endeavor to cause such shares to be duly
         registered.

8.       TAKING OF RECORD; STOCK AND WARRANT TRANSFER BOOKS

         In the case of all dividends or other distributions by the Issuer to
         the holders of its Common Stock with respect to which any provision of
         Section 4 of this Agreement refers to the taking of a record of such
         holders, the Issuer will in each such case take such a record as of the
         close of business on a Business Day. The Issuer will not at any time,
         except upon dissolution, liquidation or winding up of the Issuer, close
         its stock transfer books or Warrant transfer books so as to result in
         preventing or delaying the exercise or transfer of any Warrants.

9.       RESTRICTIONS ON TRANSFERABILITY

         The Warrants and the Warrant Stock shall not be transferred before
         satisfaction of the conditions specified in this Section 9, which
         conditions are intended to ensure compliance with the provisions of the
         Securities Act and applicable state securities laws with respect to the
         transfer of any Warrant or any Warrant Stock. Each Warrant Holder, by
         entering into this Agreement and accepting the Warrants, agrees to be
         bound by the provisions of this Section 9.

9.1      Restrictive Legend. Except as otherwise provided in this Section 9,
         each certificate representing Warrants or Warrant Stock, shall be
         stamped or otherwise imprinted with a legend in substantially the
         following form:

         "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY
         APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN
         THE ABSENCE OF SUCH REGISTRATION OR AN


                                       18
<PAGE>   22

         EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS
         AND PRIVILEGES SPECIFIED IN A WARRANT AGREEMENT, DATED AS OF JULY 19,
         1999, BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDERS OF
         SECURITIES NAMED THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY
         OF BRIGHAM EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO
         THE HOLDER HEREOF UPON WRITTEN REQUEST, AND THE HOLDER OF THIS
         CERTIFICATE AGREES TO BE BOUND THEREBY."

9.2      Notice of Proposed Transfers; Requests for Registration. Prior to any
         transfer of any Warrants or any shares of Restricted Common Stock, the
         Warrant Holder of such Warrants or Restricted Common Stock shall give
         five days prior written notice to the Issuer of such Warrant Holder's
         intention to effect such transfer (a "Transfer Notice"). Each Warrant
         Holder agrees that it will not sell, transfer or otherwise dispose of
         Warrants or any shares of Restricted Common Stock, in whole or in part,
         except pursuant to an effective registration statement under the
         Securities Act or an exemption from registration thereunder. Each
         certificate, if any, evidencing such shares of Restricted Common Stock
         issued upon such transfer shall bear the restrictive legend set forth
         in Section 9.1, and each Warrant Certificate issued upon such transfer
         shall bear the restrictive legend set forth in Section 9.1 of this
         Agreement, unless in the opinion of the transferee's or Warrant
         Holder's counsel delivered to the Issuer in connection with such
         transfer such legend is not required in order to ensure compliance with
         the Securities Act.

         The Warrant Holders of Warrants and Warrant Stock shall have the right
         to request registration of such Warrant Stock pursuant to Section 9.3
         of this Agreement.

9.3      Incidental Registration. If the Issuer at any time proposes to file on
         its behalf and/or on behalf of any of its security holders (the
         "Demanding Security Holders") a Registration Statement under the
         Securities Act on any form (other than a Registration Statement (i)
         filed pursuant to demand under the Company's Registration Rights
         Agreement with Joint Energy Development Investments II Limited
         Partnership, a Delaware limited partnership, and Enron Capital & Trade
         Resources Corp., a Delaware corporation, dated August 20, 1998, as
         amended, or (ii) on Form S-8 or any similar or successor form or any
         other registration statement relating to an offering of securities
         solely to the Issuer's existing security holders or employees) to
         register the offer and sale of its Common Stock for cash, it will give
         written notice to all Warrant Holders of Warrants or Warrant Stock at
         least twenty (20) days before the anticipated date of initial filing
         with the Commission of such Registration Statement, which notice shall
         set forth the Issuer's intention to effect such a registration, the
         class or series and number of equity securities proposed to be
         registered and the intended method of disposition of the securities
         proposed to be registered by the Issuer. The notice shall offer to
         include in such filing all of the Warrant Holder's Registrable
         Securities.

         Each Warrant Holder desiring to have Registrable Securities registered
         under this Section 9.3 shall advise the Issuer in writing within
         fifteen (15) days after the date of receipt of such offer from the
         Issuer, setting forth the amount of such Registrable


                                       19
<PAGE>   23

         Securities for which registration is requested. The Issuer shall
         thereupon include in such filing the number of shares of Registrable
         Securities for which registration is so requested, subject to the next
         sentence, and shall use its best efforts to effect registration under
         the Securities Act of such securities. If the managing underwriter of a
         proposed public offering shall advise the Issuer in writing that, in
         its opinion, the distribution of the Registrable Securities requested
         to be included in the registration concurrently with the securities
         being registered by the Issuer or any Demanding Security Holder would
         materially and adversely affect the distribution of such securities by
         the Issuer or such Demanding Security Holders, then all selling
         security holders (but not the Issuer or the Demanding Security Holders)
         shall reduce the amount of securities each intended to distribute
         through such offering on a pro rata basis to the greatest aggregate
         amount which, in the opinion of such managing underwriter, would not
         materially and adversely affect the distribution of such securities.

         Nothing in this Section 9.3 shall preclude the Issuer from
         discontinuing the registration of its securities being effected on its
         behalf under this Section 9.3 at any time prior to the effective date
         of the registration relating thereto. Notwithstanding any provision
         herein, the rights of the Warrant Holder under this Section 9.3 are
         subject to the express limitations contained in registration rights
         agreements in effect on the date hereof between the Issuer and other
         parties; provided, however, that the Issuer shall not on or after the
         date of this Agreement enter into any registration rights agreement
         with respect to its securities that conflict with the registration
         rights granted to the Warrant Holder herein.

9.4      Registration Procedures. If the Issuer is required by the provisions of
         this Section 9 to use its best efforts to effect the registration of
         any of its securities under the Securities Act, the Issuer will, as
         expeditiously as possible:

         (a)      prepare and file with the Commission a registration statement
                  with respect to such securities (a "Registration Statement")
                  and use its best efforts to cause such Registration Statement
                  to become and remain effective for the period described in
                  paragraph (b) below;

         (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 and to comply with the
                  provisions of the Securities Act with respect to the sale or
                  other disposition of all securities covered by such
                  Registration Statement until the earlier of such time as all
                  of such securities have been disposed of in a public offering
                  or the expiration of 90 days;

         (c)      furnish to such selling security holders such number of copies
                  of a summary prospectus or other prospectus, including a
                  preliminary prospectus, in conformity with the requirements of
                  the Securities Act, and such other documents, as such selling
                  security holders may reasonably request;


                                       20
<PAGE>   24

         (d)      use its best efforts to register or qualify the securities
                  covered by such Registration Statement under such other
                  securities or blue sky laws of such jurisdictions within the
                  United States as each holder of such securities shall request
                  (provided, however, the Issuer shall not be obligated to
                  qualify as a foreign corporation to do business under the laws
                  of any jurisdiction in which it is not then qualified or to
                  file any general consent to service or process), and do such
                  other reasonable acts and things as may be required of it to
                  enable such holder to consummate the disposition in such
                  jurisdiction of the securities covered by such Registration
                  Statement;

         (e)      enter into customary agreements (including an underwriting
                  agreement in customary form) and take such other actions as
                  are reasonably required in order to expedite or facilitate the
                  disposition of such Registrable Securities; and

         (f)      otherwise use its best efforts to comply with all applicable
                  rules and regulations of the Commission, and make available to
                  its security holders, as soon as reasonably practicable, but
                  not later than 18 months after the effective date of the
                  Registration Statement, an earnings statement covering the
                  period of at least 12 months beginning with the first full
                  month after the effective date of such Registration Statement,
                  which earnings statements shall satisfy the provisions of
                  Section 11(a) of the Securities Act.

                  It shall be a condition precedent to the obligation of the
                  Issuer to take any action pursuant to this Section 9 in
                  respect of the securities which are to be registered at the
                  request of any Warrant Holder of Registrable Securities that
                  such Warrant Holder shall furnish to the Issuer such
                  information regarding the securities held by such Warrant
                  Holder and the intended method of disposition thereof as the
                  Issuer shall reasonably request and as shall be required in
                  connection with the action taken by the Issuer.

9.5      Expenses. All expenses incurred in complying with this Section 9,
         including, without limitation, all registration and filing fees
         (including all expenses incident to filing with the NASD), printing
         expenses, fees and disbursements of counsel for the Issuer, the
         reasonable fees and expenses of one counsel for the selling security
         holders (selected by the Person holding the plurality of the securities
         being registered), expenses of any special audits incident to or
         required by any such registration and expenses of complying with the
         securities or blue sky laws of any jurisdictions pursuant to Section
         9.4(d) of this Agreement (all of such expenses shall be collectively
         referred to herein as "Registration Expenses"), shall be paid by the
         Issuer; provided, however, the Issuer shall not be responsible for any
         discount or commission or cost reimbursement to any underwriter in
         respect of the securities sold by such Warrant Holder of Registrable
         Securities.

9.6      Indemnification and Contribution.

         (a)      In the event of any registration of any of the Registrable
                  Securities under the Securities Act pursuant to this Section
                  9, the Issuer shall indemnify and hold harmless each Warrant
                  Holder of such Registrable Securities, such Warrant


                                       21
<PAGE>   25

                  Holder's directors and officers, each Affiliate of such
                  Warrant Holder, and each other Person (including each
                  underwriter) who participated in the offering of such
                  Registrable Securities and each other Person, if any, who
                  controls such Warrant Holder or such participating Person, if
                  any, who controls such Warrant Holder or such participating
                  Person within the meaning of the Securities Act, against any
                  losses, claims, damages or liabilities, joint or several, to
                  which such Warrant Holder or any such director or officer or
                  participating Person or Affiliate or controlling Person may
                  become subject under the Securities Act or any other statute
                  or at common law, insofar as such losses, claims, damages or
                  liabilities (or actions in respect thereof) arise out of or
                  are based upon (i) any alleged untrue statement of any
                  material fact contained, on the effective date thereof, in any
                  Registration Statement under which such securities were
                  registered under the Securities Act, any preliminary
                  prospectus or final prospectus contained therein, or any
                  amendment or supplement thereto, or (ii) any alleged omission
                  to state therein a material fact required to be stated therein
                  or necessary to make the statements therein, in light of the
                  circumstances under which they were made, not misleading, and
                  shall reimburse such Warrant Holder or such director, officer
                  or participating Person or Affiliate or controlling Person for
                  any legal or any other expenses reasonably incurred by such
                  Warrant Holder or such director, officer or participating
                  Person or Affiliate or controlling Person in connection with
                  investigating or defending any such loss, claim, damage,
                  liability or action; provided, however, that the Issuer shall
                  not be liable in any such case to the extent that any such
                  loss, claim, damage or liability arises out of or is based
                  upon any alleged untrue statement or alleged omission made in
                  such Registration Statement, preliminary prospectus,
                  prospectus or amendment or supplement in reliance upon and in
                  conformity with written information furnished to the Issuer by
                  such Warrant Holder specifically for use therein and, in the
                  case of any non-underwritten offering, to the extent that any
                  such losses, claims, damages, liabilities or expenses arise
                  out of or are based upon the fact that a current copy of the
                  prospectus was not sent or given to the Person asserting any
                  such losses, claims, damages, liabilities or expenses at or
                  prior to the written confirmation of the sale of the
                  securities to such Person if it is determined that it was the
                  responsibility of such Warrant Holder to provide such Person
                  with a current copy of the prospectus and such current copy of
                  the prospectus would have cured the defect giving rise to such
                  losses, claims, damages, liabilities or expenses. Such
                  indemnity shall remain in full force and effect regardless of
                  any investigation made by or on behalf of such Warrant Holder
                  or such director, officer or participating Person or Affiliate
                  or controlling Person, and shall survive the transfer of such
                  securities by such Warrant Holder.

         (b)      Each Warrant Holder of any Registrable Securities, by
                  acceptance thereof, agrees to indemnify and hold harmless the
                  Issuer, its directors and officers and each other Person, if
                  any, who controls the Issuer within the meaning of the
                  Securities Act against any losses, claims, damages or
                  liabilities, joint or several, to which the Issuer or any such
                  director or officer or any such Person may become subject
                  under the Securities Act or any other statute or at common
                  law, insofar as such losses, claims, damages or liabilities
                  (or actions in respect thereof) arise out of or


                                       22
<PAGE>   26

                  are based upon (i) information in writing provided to the
                  Issuer by such Warrant Holder of such Registrable Securities
                  contained, on the effective date thereof, in any Registration
                  Statement under which securities were registered under the
                  Securities Act at the request of such Warrant Holder, any
                  preliminary prospectus or final prospectus contained therein,
                  or any amendment or supplement thereto or (ii) the fact that a
                  current copy of the prospectus was not sent to the Person
                  asserting such losses, claims, damages, liabilities or
                  expenses at or prior to the written confirmation of the sale
                  of the securities with respect to such Person if it is
                  determined that it was the responsibility of such Warrant
                  Holder to provide such Person with a current copy of the
                  prospectus and such current copy would have cured the defect
                  giving rise to such losses, claims, damages, liabilities or
                  expenses; provided, however, that such Warrant Holder's
                  obligation under this Section 9.6(b) to indemnify and hold
                  harmless the Issuer shall in no event exceed the lesser of (x)
                  the damage attributable solely to the inclusion of such
                  written information in such Registration Statement,
                  preliminary prospectus, final prospectus, or amendment or
                  supplement suffered by the Person or Persons whose claims gave
                  rise to such losses, claims, damages or liabilities and (y)
                  the net proceeds received by such Warrant Holder from the sale
                  of Registrable Securities giving rise to such indemnification.

         (c)      If the indemnification provided for in this Section 9 from the
                  indemnifying party is unavailable to an indemnified party
                  hereunder in respect of any losses, claims, damages,
                  liabilities or expenses referred to herein, then the
                  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, claims, damages,
                  liabilities or expenses in such proportion as is appropriate
                  to reflect the relative fault of the indemnifying party and
                  indemnified parties in connection with the actions which
                  resulted in such losses, claims, damages, liabilities or
                  expenses, as well as any other relevant equitable
                  considerations. The relative fault of such indemnifying party
                  and indemnified parties shall be determined by reference to,
                  among other things, whether any action in question, including
                  any untrue or alleged untrue statement of a material fact or
                  omission or alleged omission to state a material fact, has
                  been made by, or related to information supplied by, such
                  indemnifying party or indemnified parties, and the parties'
                  relative intent, knowledge, access to information and
                  opportunity to correct or prevent such action. The amount paid
                  or payable by a party under this Section 9 as a result of the
                  losses, claims, damages, liabilities and expenses referred to
                  above shall be deemed to include any legal or other fees or
                  expenses reasonably incurred by such party in connection with
                  any investigation or proceeding.

                           The parties hereto agree that it would not be just
                  and equitable if contribution pursuant to this Section 9.6(c)
                  were determined by pro rata allocation or by any other method
                  of allocation which does not take account of the equitable
                  considerations referred to in the immediately preceding
                  paragraph. Notwithstanding the provisions of this subsection
                  (c), no Warrant Holder shall be required to contribute any
                  amount in excess of the total amount received by it upon the
                  sale of its securities pursuant to the Registration Statement
                  to which the


                                       23
<PAGE>   27

                  losses, claims, damages, liabilities and expenses referred to
                  above relate. 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 was not
                  guilty of such fraudulent misrepresentation. The obligations
                  of each of the Warrant Holders under this subsection (c) to
                  contribute are several and not joint.

         (d)      Conduct of Indemnification Proceedings. Any person or entity
                  entitled to indemnification hereunder shall (i) give prompt
                  written notice to the indemnifying party after the receipt by
                  the indemnified party of a written notice of the commencement
                  of any action, suit, proceeding or investigation or threat
                  thereof made in writing for which such indemnified party will
                  claim indemnification or contribution pursuant to this
                  Agreement; provided, however, that the failure of any
                  indemnified party to give notice as provided herein shall not
                  relieve the indemnifying party of its obligations under
                  Section 9.6 hereof, except to the extent that the indemnifying
                  party is actually prejudiced by such failure to give notice,
                  and (ii) unless in such indemnified party's reasonable
                  judgment a conflict of interest may exist between such
                  indemnified and indemnifying parties with respect to such
                  claim, permit such indemnifying party to assume the defense of
                  such claim with counsel reasonably satisfactory to the
                  indemnified party. If the indemnifying party is entitled to,
                  and does, assume the defense of such claim, the indemnified
                  party shall have the right to employ separate counsel and to
                  participate in the defense thereof, but the fees and expenses
                  of such counsel shall be borne by the indemnified party.
                  Whether or not such defense is assumed by the indemnifying
                  party, the indemnifying party shall not be subject to any
                  liability for any settlement made without its consent (but
                  such consent will not be unreasonably withheld). No
                  indemnifying party shall be permitted to consent to the entry
                  of any judgment or to enter into any settlement that does not
                  include as an unconditional term thereof the giving by the
                  claimant or plaintiff to such indemnified party of a release
                  from all liability in respect of such claim or litigation. An
                  indemnifying party who is not entitled to, or elects not to,
                  assume the defense of a claim shall not be obligated to pay
                  the fees and expenses of more than one counsel in any one
                  jurisdiction for all parties indemnified by such indemnifying
                  party with respect to such claim, unless in the reasonable
                  judgment of any indemnified party a conflict of interest may
                  exist between such indemnified party and any other of such
                  indemnified parties with respect to such claim, in which event
                  the indemnifying party shall be obligated to pay the fees and
                  expenses of such additional counsel or counsels.

9.7      Termination of Restrictions. Notwithstanding the foregoing provisions
         of this Section 9, the restrictions imposed by this Section 9 upon the
         transferability of the Warrants, the Warrant Stock and the Restricted
         Common Stock (or Common Stock issuable upon the exercise of the
         Warrants) and the legend requirement of Section 9.1 of this Agreement
         shall terminate as to any particular Warrant or share of Warrant Stock
         or Restricted Common Stock (or Warrant Stock) (i) when and so long as
         such security shall have been registered under the Securities Act and
         disposed of pursuant thereto, or (ii) when the Warrant Holder thereof
         shall have delivered to the Issuer the written opinion of counsel to
         such Warrant Holder, stating that such legend is not required in order
         to ensure


                                       24
<PAGE>   28

         compliance with the Securities Act. Whenever the restrictions imposed
         by this Section 9 shall terminate as to any Warrants or any Restricted
         Common Stock, as hereinabove provided, the Warrant Holder thereof shall
         be entitled to receive from the Issuer, at the expense of the Issuer, a
         new Warrant Certificate or a new certificate representing such Common
         Stock, as the case may be, not bearing the restrictive legend set forth
         in Section 9.1 of this Agreement.

9.8      Listing on Securities Exchange. If at any time the Issuer shall list
         any shares of Common Stock on any securities exchange, it will, at its
         expense, use its best efforts to list thereon, maintain and, when
         necessary, increase such listing of, all shares of Common Stock issued
         or, to the extent permissible under the applicable securities exchange
         rules, issuable upon the exercise of the Warrants so long as any shares
         of Common Stock shall be so listed during the Exercise Period.

10.      SUPPLYING INFORMATION

         The Issuer shall cooperate with each Warrant Holder of a Warrant and
         each Warrant Holder of Restricted Common Stock in supplying such
         information as may be reasonably necessary for such Warrant Holder to
         complete and file any information reporting forms presently or
         hereafter required by the Commission as a condition to the availability
         of an exemption from the Securities Act for the sale of any Warrant or
         Restricted Common Stock.

11.      LOSS OR MUTILATION

         Upon receipt by the Issuer from any Warrant Holder of evidence
         reasonably satisfactory to it of the ownership of and the loss, theft,
         destruction or mutilation of a certificate representing Warrants or
         Warrant Stock and indemnity reasonably satisfactory to it (it being
         understood that the written agreement of the Warrant Holder or an
         Affiliate thereof shall be sufficient indemnity) and in case of
         mutilation upon surrender and cancellation hereof or thereof, the
         Issuer will execute and deliver in lieu hereof or thereof a new Warrant
         or new stock certificate as the case may be, of like tenor to such
         Warrant Holder; provided, in the case of mutilation, no indemnity shall
         be required if the certificate representing Warrants or Warrant Stock
         in identifiable form is surrendered to the Issuer for cancellation.

12.      OFFICE OF THE ISSUER

         As long as any of the Warrants remain outstanding, the Issuer shall
         maintain an office or agency (which may be the principal executive
         officers of the Issuer) where the Warrants may be presented for
         exercise, registration or transfer, division or combination as provided
         in this Agreement.

13.      APPRAISAL

         The determination of the Appraised Value per share of Common Stock
         shall be made by an investment banking firm of nationally recognized
         standing mutually agreed to by the Issuer and the Required Holders. If
         the investment banking firm selected by the Issuer is


                                       25
<PAGE>   29

         not acceptable to the Required Holders and the Issuer and the Required
         Holders cannot agree on a mutually acceptable investment banking firm,
         then the Required Holders and the Issuer shall each choose one such
         investment banking firm and the respective chosen firms shall agree on
         another investment banking firm which shall make the determination. The
         Issuer shall retain, at its sole cost, such investment banking firm as
         may be necessary for the determination of Appraised Value required by
         the terms of this Agreement.

14.      LIMITATION OF LIABILITY; NO RIGHTS AS STOCKHOLDER

         No provision hereof, in the absence of affirmative action by any
         Warrant Holder to purchase shares of Common Stock, and no enumeration
         herein of the rights or privileges of any Warrant Holder, shall give
         rise to any liability of such Warrant Holder for the purchase price of
         any Common Stock or as a stockholder of the Issuer, whether such
         liability is asserted by the Issuer or by creditors of the Issuer.
         Except as may otherwise be provided by law or by separate agreement
         between a Warrant Holder and the Issuer, no Warrant Holder, as such,
         shall be entitled to vote or be deemed the holder of Common Stock or
         any other securities (other than Warrants) of the Issuer which may at
         any time be issuable on the exercise hereof, nor shall anything
         contained herein be construed to confer upon any Warrant Holder the
         rights of a stockholder of the Issuer or the right to vote for the
         election of directors or upon any matters submitted to stockholders at
         any meeting thereof, or to give or withhold consent to any corporate
         action or to receive notice of meetings or other actions affecting
         stockholders (except as provided herein), or to receive dividends or
         otherwise, until the Warrants shall have been exercised in accordance
         with the terms and conditions hereof.

15.      MISCELLANEOUS

15.1     Non-waiver and Expenses. No course of dealing or any delay or failure
         to exercise any right hereunder on the part of any Warrant Holder shall
         operate as a waiver of such right or otherwise prejudice such Warrant
         Holder's rights, powers or remedies. If the Issuer fails to comply with
         any provision of this Agreement, the Issuer shall pay to the applicable
         Warrant Holders such amounts as shall be sufficient to cover any costs
         and expenses including, but not limited to, reasonable attorneys' fees,
         including those of appellate proceedings, incurred by the Warrant
         Holders in enforcing any of its rights, powers or remedies hereunder.

15.2     Notice Generally. Any notice, demand, request, consent, approval,
         declaration, delivery or other communication hereunder to be made
         pursuant to the provisions of this Agreement shall be sufficiently
         given or made if in writing and either delivered in person with receipt
         acknowledged or sent by registered or certified mail, return receipt
         requested, postage prepaid, telex, telecopier or overnight air courier
         guaranteeing next day delivery, addressed as follows:



                                       26
<PAGE>   30

         (a)      If to the Bank of Montreal, as Warrant Holder, at:

                           Address:       700 Louisiana, Ste. 4400
                                          Houston, Texas 77002
                           Attention:     Thomas E. McGraw
                           Telecopier No. (713) 223-0477

         (b)      If to the Issuer at:

                           Brigham Exploration Company
                           6300 Bridge Point Parkway
                           Building 2, Suite 500
                           Austin, Texas 78730
                           Attention: President
                           Telecopier No.: (512) 427-3300

                  or at such other address as may be substituted by notice given
                  as herein provided. The giving of any notice required
                  hereunder may be waived in writing by the party entitled to
                  receive such notice. Every notice, demand, request, consent,
                  approval, declaration, delivery or other communication
                  hereunder shall be deemed to have been duly given or served on
                  the date on which personally delivered, with receipt
                  acknowledged, or three (3) Business Days after the same shall
                  have been deposited in the United States mail.

15.3     Indemnification. Except to the extent otherwise provided in Section 9.6
         of this Agreement, the Issuer agrees to indemnify and hold harmless
         each Warrant Holder and its officers, directors, employees, agents,
         attorneys and Affiliates (each an "Indemnified Party") from and against
         any liabilities, obligations, losses, damages, penalties, actions,
         judgments, suits, claims, costs, attorneys' fees, expenses and
         disbursements of any kind which may be imposed upon, incurred by or
         asserted against such Indemnified Party relating to or arising out of
         (i) such Warrant Holder's exercise of the Warrants and/or ownership of
         any shares of Warrant Stock issued in consequence thereof, or (ii) any
         litigation to which such Warrant Holder is made a party in its capacity
         as a stockholder or Warrant Holder of the Issuer; provided, however,
         that the Issuer will not be liable hereunder to the extent that any
         liabilities, obligations, losses, damages, penalties, actions,
         judgments, suits, claims, costs, attorneys' fees, expenses or
         disbursements (A) arise solely from any violation by such Warrant
         Holder of any law or regulation applicable to it or (B) are found in a
         final non-appealable judgment by a court to have resulted from such
         Warrant Holder's bad faith or willful misconduct or violation of law.
         The procedures to be followed for claims of indemnification under this
         Section 15.3 shall be as set forth in Section 9.6(d) of this Agreement.

15.4     Remedies. Each Warrant Holder of Warrants and Warrant Stock, in
         addition to being entitled to exercise all rights granted by law,
         including recovery of damages, will be entitled to specific performance
         of its rights under Section 9 of this Agreement. The Issuer agrees that
         monetary damages would not be adequate compensation for any loss
         incurred by reason of a breach by it of the provisions of Section 9 of
         this Agreement, and


                                       27
<PAGE>   31

         hereby agrees to waive any defense to the contrary in any action for
         specific performance that a remedy at law would be adequate.

15.5     Successors and Assigns. Subject to the provisions of Sections 3.1 and 9
         of this Agreement, this Agreement and the rights evidenced hereby shall
         inure to the benefit of and be binding upon the successor of the Issuer
         and the successors and assigns of any Warrant Holder. The provisions of
         this Agreement are intended to be for the benefit of all Warrant
         Holders from time to time of the Warrants and Warrant Stock, and shall
         be enforceable by any such Warrant Holder.

15.6     Complete Agreement; Amendment. This Agreement and the Warrant
         Certificates constitute the complete agreement among the parties with
         respect to the subject matter hereof. This Agreement may be modified or
         amended or the provisions hereof waived only with the written consent
         of the Issuer and the Required Holders, provided that no Warrant may be
         modified or amended to reduce the number of shares of Common Stock for
         which such Warrant is exercisable or to increase the price at which
         such shares may be purchased upon exercise of such Warrant (before
         giving effect to any adjustment as provided herein) or to accelerate
         the Expiration Date without the prior written consent of the Warrant
         Holder thereof, and any amendment of Section 9 of this Agreement shall
         also require the written consent of Warrant Holders of Warrants and/or
         Warrant Stock representing more than 50% of the total of (i) all shares
         of Warrant Stock then subject to purchase upon exercise of all Warrants
         then Outstanding, and (ii) all shares of Warrant Stock then
         Outstanding.

15.7     Severability. Wherever possible, each provision of this Agreement shall
         be interpreted in such manner as to be effective and valid under
         applicable law, but if any provision of this Agreement shall be
         prohibited by or invalid under applicable law, such provision shall be
         ineffective to the extent of such prohibition or invalidity, without
         invalidating the remainder of such provision or the remaining
         provisions of this Agreement.

15.8     Headings. The headings used in this Agreement are for the convenience
         of reference only and shall not, for any purpose, be deemed a part of
         this Agreement.

15.9     Governing Law; Consent to Jurisdiction and Venue. In all respects,
         including all matters of construction, validity and performance, this
         Agreement and the obligations arising hereunder shall be governed by,
         and construed and enforced in accordance with, the laws of the State of
         Texas applicable to contracts made and performed in such state, without
         regard to the principles thereof regarding conflict of laws, and any
         applicable laws of the United States of America.

15.10    Consent to Jurisdiction and Venue.

         (a)      THE ISSUER AND EACH WARRANT HOLDER HEREBY EXPRESSLY SUBMITS TO
                  THE JURISDICTION OF THE COURTS OF THE STATE OF TEXAS OR THE
                  UNITED STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF
                  TEXAS. FINAL JUDGMENT AGAINST SUCH PARTY IN ANY SUCH SUIT
                  SHALL BE CONCLUSIVE, AND MAY BE


                                       28
<PAGE>   32

                  ENFORCED IN ANY OTHER JURISDICTIONS BY SUIT ON THE JUDGMENT OR
                  AS OTHERWISE PERMITTED BY APPLICABLE LAW, A CERTIFIED OR TRUE
                  COPY OF WHICH SHALL BE CONCLUSIVE EVIDENCE OF THE FACTS AND OF
                  THE AMOUNT OF ANY INDEBTEDNESS OR LIABILITY OF SUCH PARTY
                  THEREIN DESCRIBED; PROVIDED, HOWEVER, EACH PARTY MAY AT ITS
                  OPTION BRING SUIT, OR INSTITUTE OTHER JUDICIAL PROCEEDINGS
                  AGAINST THE OTHER PARTY OR ANY OF ITS ASSETS, IN THE COURTS OF
                  ANY COUNTRY OR PLACE WHERE SUCH PARTY OR SUCH ASSETS MAY BE
                  FOUND.

         (b)      THE ISSUER AND EACH WARRANT HOLDER HEREBY IRREVOCABLY WAIVES
                  ANY OBJECTION WHICH IT MAY NOW OR HEREAFTER HAVE TO THE LAYING
                  OF VENUE OF ANY SUIT, ACTION OR PROCEEDING BROUGHT IN ANY
                  COURTS OF THE STATE OF TEXAS OR THE UNITED STATES DISTRICT
                  COURT FOR THE SOUTHERN DISTRICT OF TEXAS AND HEREBY FURTHER
                  IRREVOCABLY WAIVES ANY CLAIM THAT ANY SUCH SUIT, ACTION OR
                  PROCEEDING BROUGHT IN ANY SUCH COURT HAS BEEN BROUGHT IN AN
                  INCONVENIENT FORUM.

15.11    Counterparts: This Agreement may be executed in two or more
         counterparts, each of which shall be deemed an original, but all of
         which together shall constitute one and the same instrument.


                                       29
<PAGE>   33

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed as of the date first above written.



                                    BRIGHAM EXPLORATION COMPANY, as Issuer


                                    By:
                                       ----------------------------------------
                                    Printed Name:
                                                 ------------------------------
                                    Title:
                                          -------------------------------------


                                    BANK OF MONTREAL, as Warrant Holder


                                    By:
                                       ----------------------------------------
                                    Printed Name:
                                                 ------------------------------
                                    Title:
                                          -------------------------------------


                                       30
<PAGE>   34
                                                                    EXHIBIT A TO
                                                               Warrant Agreement



                          (FORM OF WARRANT CERTIFICATE)



THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES LAWS,
AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN
EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND
PRIVILEGES SPECIFIED IN THE WARRANT AGREEMENT, DATED AS OF JULY 19, 1999,
BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDER OF SECURITIES NAMED
THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM EXPLORATION
COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN
REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES TO BE BOUND THEREBY.

No. ___

                               WARRANT CERTIFICATE

This Warrant Certificate certifies that the Bank of Montreal, a Canadian
chartered bank, or registered assigns thereof, is the holder of 661,538 warrants
(the "Warrants") to purchase shares of common stock of Brigham Exploration
Company, a Delaware corporation (the "Company"). Each Warrant entitles the
holder, but only subject to the conditions set forth herein and in the Warrant
Agreement referred to below, to purchase from the Company before 5:00 p.m., New
York City time, on the Expiration Date, as such term is defined in the Warrant
Agreement, one fully paid and non-assessable share of common stock of the
Company ("Warrant Stock") at a price (the "Exercise Price") of two and 25/100
dollars ($2.25) per share of Warrant Stock payable as set forth in the Warrant
Agreement. The number of shares of Warrant Stock for which each Warrant is
exercisable and the Exercise Price are each subject to adjustment prior to the
Expiration Date upon the occurrence of certain events as set forth in the
Warrant Agreement.

The Company may deem and treat the registered holders of the Warrants evidenced
hereby as the absolute owner thereof (notwithstanding any notation of ownership
or other writing hereon made by anyone), for the purpose of any exercise hereof
and of any distribution to the holders hereof, and for all other purposes.

Warrant Certificates, when surrendered at the office of the Company by the
registered holder hereof in person or by a legal representative duly authorized
in writing, may be exchanged, in the


                                    EXH. A-1
<PAGE>   35
manner and subject to the limitations provided in the Warrant Agreement, but
without payment of any service charge, for another Warrant Certificate or
Warrant Certificates of like tenor evidencing in the aggregate a like number of
Warrants.

Upon due presentment for registration of transfer of this Warrant Certificate at
the office of the Company at 6300 Bridge Point Parkway, Building 2, Suite 500,
Austin, Texas 78730, Attention: President, or such other address as the Company
may specify in writing to the registered holder of the Warrants evidenced
hereby, a new Warrant Certificate or Warrant Certificates of like tenor and
evidencing in the aggregate a like number of Warrants shall be issued to the
transferee in exchange for this Warrant Certificate to the transferee(s) and, if
less than all the Warrants evidenced hereby are to be transferred, the
registered holder hereof, subject to the limitations provided in the Warrant
Agreement, without charge except for any tax or other governmental charge
imposed in connection therewith.

The Warrant Certificate is one of the Warrant Certificates referred to in the
Warrant Agreement, dated as of July 19, 1999, between the Company and the
initial holder of Warrants party thereto (the "Warrant Agreement"). Said Warrant
Agreement is hereby incorporated by reference in and made a part of this
instrument and is hereby referred to for a description of the rights, limitation
of rights, obligations, duties and immunities thereunder of the Company and the
holders, and in the event of any conflict between the terms of this Warrant
Certificate and the provisions of the Warrant Agreement, the provisions of the
Warrant Agreement shall control.

IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be duly
executed and its corporate seal to be impressed hereon and attached by its
secretary.

Dated: ____________________________, 1999.


                                    BRIGHAM EXPLORATION COMPANY


                                    By:
                                       ----------------------------------------
                                    Printed Name:
                                                 ------------------------------
                                    Title:
                                          -------------------------------------


(CORPORATE SEAL)

ATTEST:


- --------------------------------------
Secretary


                                    EXH. A-2
<PAGE>   36
                                                                    Exhibit A To
                                                             Warrant Certificate


                                SUBSCRIPTION FORM

                 [To be executed only upon exercise of Warrants]


The undersigned registered owner of this Warrant Certificate irrevocably
exercises Warrants for the purchase of shares of Common Stock of [     ] and
herewith makes payment therefor

         $_____   in cash

all at the price and on the terms and conditions specified in the Warrant
Certificate and the Warrant Agreement, and requests that certificates for the
shares of Common Stock hereby purchased (and any securities or other property
issuable upon such exercise) be issued in the name of ____________________ and
delivered to _____________________________ whose address is ___________________
________________________________ and, if such shares of Common Stock shall not
include all of the shares of Common Stock issuable as provided in the Warrant
Certificate, that a new Warrant Certificate of like tenor and date for the
balance of the shares of Common Stock issuable thereunder be delivered to the
undersigned.



- ----------------------------------------------
(Name of Registered Owner)



- ----------------------------------------------
(Signature of Registered Owner)



- ----------------------------------------------
(Street Address)



- ----------------------------------------------
(City)            (State)           (Zip Code)


                                    EXH. A-3
<PAGE>   37
                                                                    Exhibit B To
                                                             Warrant Certificate


                                 ASSIGNMENT FORM


FOR VALUE RECEIVED the undersigned registered owner of the attached Warrant
Certificate hereby sells, assigns and transfers unto the assignee named below
all of the rights of the undersigned under this Warrant Certificate, with
respect to the number of shares of Common Stock set forth below:

Name and Address of Assignee:
                             ----------------------------

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

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

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

No. of Shares of
Common Stock ______

and does hereby irrevocably constitute and appoint ____________________________
attorney-in-fact to register such transfer on the books of [    ] maintained for
that purpose, with full power of substitution in the premises.

Dated:
      -------------------------------

Name:
     --------------------------------

Signature:
          ---------------------------

Witness:
        -----------------------------

The assignee named above hereby agrees to purchase and take the attached Warrant
Certificate pursuant to and in accordance with the terms and conditions of the
Warrant Agreement, dated as of ______________, 1999, between [    ] and the
initial Holder named therein and agrees to be bound thereby.

Dated:
      -------------------------------

Name:
     --------------------------------

Signature:
          ---------------------------


                         EXH. B-1 to Warrant Certificate
<PAGE>   38
                                                                    EXHIBIT B TO
                                                               Warrant Agreement



                      [FORM OF CASHLESS CONVERSION NOTICE]

             (To be executed upon a cashless exercise of a Warrant.)

         The undersigned hereby irrevocably elects to exercise the Cashless
Conversion, represented by this Warrant Certificate, to purchase ____ shares of
Common Stock and herewith tenders in payment for such shares this Warrant
Certificate, all in accordance with the terms hereof. The undersigned requests
that a certificate for such shares be registered in the name of _______________
_______________________________________________ whose address is ______________
________________________________________________ and that such certificate (or
any payment in lieu thereof) be delivered to ______________________________
whose address is ___________________________________.


Dated:
      -----------------------            --------------------------------------
                                         (Signature must conform in all respects
                                         to name of holder as specified on the
                                         face of the Warrant.)


         And if said number of shares shall not be all the shares exchangeable
or purchasable under the within Warrant, a new Warrant of like tenor is to be
issued in the name of the undersigned for the balance remaining of the shares
purchasable thereunder.


                                    EXH. B-1
<PAGE>   39
                                   SCHEDULE A


<TABLE>
<CAPTION>
                          Shares of                   Stock Options
                           Common                      Outstanding
                            Stock         -----------------------------------------         Warrants
                         Outstanding      Vested         Unvested           Total         Outstanding
                         -----------      -------        ---------        ---------       -----------
<S>                      <C>              <C>            <C>              <C>             <C>
As of July 19, 1999      14,309,071       267,104        1,307,383        1,574,487        1,000,000

     Issued 7/20/99         119,550
     Forfeited 7/30/99                                     (10,500)         (10,500)
     Forfeited 8/16/99                                    (263,888)        (263,888)
     Issued 8/17/99          89,165                        105,000          105,000
                         ----------       -------        ---------        ---------        ---------
As of August 18, 1999*   14,517,786       267,104        1,137,995        1,405,099        1,000,000
                         ----------       -------        ---------        ---------        ---------
</TABLE>


                                    SCH. A-1

<PAGE>   1
                                                                   EXHIBIT 10.5


                                                                  Execution Copy

THIS WARRANT AGREEMENT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THE WARRANTS
HEREIN HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH
ACT, THE RULES AND REGULATIONS PROMULGATED THEREUNDER, ANY SUCH STATE SECURITIES
LAWS OR THE PROVISIONS OF THIS WARRANT AGREEMENT.



                                WARRANT AGREEMENT


                                     for the


                            Purchase of Common Stock

                                 By and Between



                           BRIGHAM EXPLORATION COMPANY

                                       and

                                SOCIETE GENERALE,
                                Southwest Agency



                                   Dated as of

                                  July 19, 1999





<PAGE>   2
                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                               Page
<S>                                                                                                            <C>
1.       DEFINITIONS.............................................................................................2

2.       ISSUANCE AND EXERCISE OF WARRANTS.......................................................................6

         2.1      Issuance of Warrants...........................................................................6

         2.2      Manner of Exercise.............................................................................6

         2.3      Payment of Taxes...............................................................................8

         2.4      Fractional Shares..............................................................................8

         2.5      Continued Validity.............................................................................8

3.       TRANSFERS, DIVISION AND COMBINATION.....................................................................8

         3.1      Transfer.......................................................................................8

         3.2      Division and Combination.......................................................................9

         3.3      Expenses.......................................................................................9

         3.4      Maintenance of Books...........................................................................9

4.       ADJUSTMENTS.............................................................................................9

         4.1      Stock Dividends, Subdivisions and Combinations.................................................9

         4.2      Certain Other Distributions...................................................................10

         4.3      Issuance of Additional Shares of Stock........................................................11

         4.4      Issuance of Warrants or Other Rights..........................................................11

         4.5      Issuance of Convertible Securities............................................................12

         4.6      Superseding Adjustment........................................................................13

         4.7      Other Provisions Applicable to Adjustments Under This Section.................................13

         4.8      Reorganization, Reclassification, Merger, Consolidation or Disposition of Assets..............14

5.       NOTICES TO WARRANT HOLDERS.............................................................................15

         5.1      Notice of Adjustments.........................................................................15

         5.2      Notice of Certain Corporate Action............................................................16

6.       REPRESENTATIONS AND WARRANTIES.........................................................................16

7.       CERTAIN COVENANTS......................................................................................17

         7.1      No Impairment.................................................................................17

         7.2      Reservation and Authorization of Common Stock; Registration with, or Approval of, any
                  Governmental Authority........................................................................18

8.       TAKING OF RECORD; STOCK AND WARRANT TRANSFER BOOKS.....................................................18
</TABLE>


                                       i

<PAGE>   3
<TABLE>
<S>                                                                                                            <C>
9.       RESTRICTIONS ON TRANSFERABILITY........................................................................18

         9.1      Restrictive Legend............................................................................18

         9.2      Notice of Proposed Transfers; Requests for Registration.......................................19

         9.3      Incidental Registration.......................................................................19

         9.4      Registration Procedures.......................................................................20

         9.5      Expenses......................................................................................21

         9.6      Indemnification and Contribution..............................................................22

         9.7      Termination of Restrictions...................................................................24

         9.8      Listing on Securities Exchange................................................................25

10.      SUPPLYING INFORMATION..................................................................................25

11.      LOSS OR MUTILATION.....................................................................................25

12.      OFFICE OF THE ISSUER...................................................................................25

13.      APPRAISAL..............................................................................................26

14.      LIMITATION OF LIABILITY; NO RIGHTS AS STOCKHOLDER......................................................26

15.      MISCELLANEOUS..........................................................................................26

         15.1     Non-waiver and Expenses.......................................................................26

         15.2     Notice Generally..............................................................................26

         15.3     Indemnification...............................................................................27

         15.4     Remedies......................................................................................27

         15.5     Successors and Assigns........................................................................28

         15.6     Complete Agreement; Amendment.................................................................28

         15.7     Severability..................................................................................28

         15.8     Headings......................................................................................28

         15.9     Governing Law; Consent to Jurisdiction and Venue..............................................28

         15.10    Consent to Jurisdiction and Venue.............................................................28

         15.11    Counterparts..................................................................................29


EXHIBITS:

Exhibit A  -Form of Warrant Certificate...................................................................Exh. A-1

Exhibit B  -Form of Cashless Conversion Notice............................................................Exh. B-1

SCHEDULES:


Schedule A -Capital Stock of the Issuer, Including Shares Subject to
            Outstanding Warrants, Options, Conversion Rights, Etc.........................................Sch. A-1
</TABLE>


                                       ii
<PAGE>   4

THIS WARRANT AGREEMENT AND THE SECURITIES ISSUABLE UPON EXERCISE OF THE WARRANTS
HEREIN HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR
THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE TRANSFERRED IN VIOLATION OF SUCH
ACT, THE RULES AND REGULATIONS PROMULGATED THEREUNDER, ANY SUCH STATE SECURITIES
LAWS OR THE PROVISIONS OF THIS WARRANT AGREEMENT.

                                WARRANT AGREEMENT


THIS WARRANT AGREEMENT, dated as of July 19, 1999 (this "Agreement"), is entered
into by and between Brigham Exploration Company, a Delaware corporation
("Issuer"), and Societe Generale, Southwest Agency, a bank organized under the
laws of the Republic of France acting through its Southwest Agency (the "Warrant
Holder" or "Societe Generale").

                              W I T N E S S E T H:


         WHEREAS, Brigham Oil & Gas, L.P., a limited partnership formed under
the laws of the State of Delaware (the "Borrower"), the financial institutions
party to the Credit Agreement referred to below (each a "Lender" and
collectively, the "Lenders"), and the Bank of Montreal, as agent for Lenders
under the Credit Agreement (in such capacity, the "Agent"), are parties to that
certain Credit Agreement, dated as of January 26, 1998, as amended by that
certain First Amendment to Credit Agreement, dated as of August 20, 1998, and
that certain Second Amendment to Credit Agreement, dated as of March 26, 1999
(as so amended, the "Credit Agreement"); and

         WHEREAS, the Borrower advised the Lenders and the Agent that it desired
to amend certain provisions of the Credit Agreement, and the Borrower requested
that the Lenders and the Agent agree to various amendments to certain provisions
of the Credit Agreement; and

         WHEREAS, the Lenders and the Agent have agreed to so amend certain
provisions of the Credit Agreement upon the terms and subject to the conditions
and limitations of the Third Amendment to the Credit Agreement dated as of July
19, 1999 (the "Third Amendment");

         WHEREAS, the Issuer has guaranteed the obligations of the Borrower to
the Lenders and the Agent;

         WHEREAS, as a consequence of the contractual relationships between the
Borrower and the Lenders, the Issuer has and will continue to receive
substantial benefits from the Lenders;

         WHEREAS, in order to induce the Lenders to enter into the Third
Amendment, the Issuer has agreed to execute and deliver this Agreement and to
issue to Societe Generale the warrants herein described;


                                       1
<PAGE>   5

         NOW, THEREFORE, in consideration of the premises and mutual covenants
contained herein, the receipt and sufficiency of which is hereby acknowledged,
the parties hereby stipulate and agree as follows:

1.       DEFINITIONS

         As used in this Agreement, the following terms have the respective
         meanings set forth below:

         "Additional Shares of Common Stock" shall mean all shares of Common
         Stock issued by the Issuer after the Closing Date, other than Warrant
         Stock.

         "Affiliate" shall mean as to any Person, any other Person which,
         directly or indirectly, is in control of, is controlled by, or is under
         common control with, such Person. For purposes of this definition,
         "control" (including the terms "controlled by" and "under common
         control with"), as used with respect to any Person, means the power to
         direct or cause the direction of the management and policies of such
         Person, directly or indirectly, whether through the ownership of voting
         securities or by contract or otherwise; and the terms "controlled" and
         "controlling" have the meanings correlative to the foregoing.

         "Appraised Value" shall mean, in respect of any share of Common Stock
         on any date herein specified, the fair saleable value of such share of
         Common Stock (determined without giving effect to the discount for (i)
         a minority interest or (ii) any lack of liquidity of the Common Stock
         or to the fact that the Issuer may have no class of equity registered
         under the Exchange Act) as of the last day of the most recent fiscal
         month to end within 60 days prior to such date specified, based on the
         value of the Issuer, as determined by an investment banking firm
         (selected pursuant to the terms of Section 13 of this Agreement) in
         accordance with such firm's customary practices, divided by the number
         of Outstanding shares of Common Stock, after giving pro forma effect to
         the exercise or conversion of all exercisable or Convertible Securities
         (including the Warrants) for Common Stock and the payment of the
         exercise or conversion price therefor.

         "Book Value" shall mean, in respect of any share of Common Stock on any
         date herein specified, the consolidated book value of the Issuer as of
         the last day of any month immediately preceding such date, divided by
         the number of Outstanding shares of Common Stock, after giving pro
         forma effect to the exercise or conversion of all exercisable or
         Convertible Securities (including the Warrants) for Common Stock and
         the payment of the exercise or conversion price therefor, as determined
         in accordance with GAAP by any firm of independent certified public
         accountants of recognized national standing selected by the Issuer and
         reasonably acceptable to the Required Holders.

         "Business Day" shall mean any day that is not a Saturday or Sunday or a
         day on which banks are required or permitted to be closed in the State
         of New York or California.

         "Cashless Conversion" shall have the meaning set forth in Section
         2.2(b)(ii) hereof.

         "Cashless Conversion Notice" shall have the meaning set forth in
         Section 2.2(b)(ii) hereof.


                                       2
<PAGE>   6

         "Closing Date" shall mean the date hereof.

         "Commission" shall mean the Securities and Exchange Commission, or any
         other federal agency then administering the Securities Act and other
         federal securities laws.

         "Common Stock" shall mean the common stock, $0.01 par value per share,
         of the Issuer, as constituted on the Closing Date, and any capital
         stock into which such Common Stock may thereafter be changed, and shall
         also include (i) capital stock of the Issuer of any other class
         (regardless of how denominated) issued to the holders of shares of
         Common Stock upon any reclassification thereof which is also not
         preferred as to dividends or assets over any other class of stock of
         the Issuer and which is not subject to redemption and (ii) shares of
         common stock of any successor or acquiring corporation (as defined in
         Section 4.8 of this Agreement) received by or distributed to the
         holders of Common Stock of the Issuer in the circumstances contemplated
         by Section 4.8 of this Agreement.

         "Convertible Securities" shall mean evidences of indebtedness, shares
         of stock or other securities which are convertible into or
         exchangeable, with or without payment of additional consideration in
         cash or property, for Additional Shares of Common Stock, either
         immediately or upon the occurrence of a specified date or a specified
         event.

         "Current Market Price" shall mean, in respect of any share of Common
         Stock on any date herein specified, (a) if there shall then be a public
         market for the Common Stock, the average Price per share for the 20
         trading days preceding such date; or (b) at any time that there is no
         public market for the Common Stock, the fair market value per share of
         Common Stock on such date as determined reasonably and in good faith by
         the board of directors of the Issuer (determined without giving effect
         to any discount for a minority interest, any restrictions on
         transferability or any lack of liquidity of the Common Stock or to the
         fact that the Issuer has no class of equity registered under the
         Exchange Act), such fair market value to be determined by reference to
         the cash price that would be paid between a fully informed buyer and
         seller under no compulsion to buy or sell, provided that (i) if Current
         Market Price is being determined in connection with an issuance of
         shares of Common Stock, solely to one or more Affiliates of the Issuer,
         then if so requested by the Required Holders, Current Market Price
         shall be the Appraised Value; and (ii) Current Market Price shall never
         be less than Book Value.

         "Current Warrant Price" shall mean, in respect of a share of Common
         Stock at any date herein specified, two and 25/100 dollars ($2.25) per
         share of Common Stock, subject to adjustment from time to time as
         provided in this Agreement.

         "Demanding Security Holder" shall have the meaning set forth in Section
         9.3.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, as
         amended, or any similar federal statute, and the rules and regulations
         of the Commission thereunder, all as the same shall be in effect from
         time to time.

         "Exercise Period" shall mean the period during which the Warrants are
         exercisable pursuant to Section 2.2.


                                       3
<PAGE>   7

         "Expiration Date" shall mean July 19, 2004.

         "GAAP" shall mean generally accepted accounting principles in the
         United States of America, as from time to time in effect.

         "Material Adverse Effect" shall mean, as to the Issuer, any material
         adverse effect on the business, assets, operations, prospects or
         financial or other condition of the Issuer and its Subsidiaries, taken
         as a whole.

         "NASD" shall mean the National Association of Securities Dealers, Inc.,
         or any successor thereto.

         "Other Property" shall have the meaning set forth in Section 4.8.

         "Outstanding" shall mean, when used with reference to Common Stock, at
         any date as of which the number of shares thereof is to be determined,
         all issued shares of Common Stock, except shares then owned or held by
         or for the account of the Issuer or any Subsidiary, and shall include
         all shares issuable in respect of outstanding scrip or any certificates
         representing fractional interests in shares of Common Stock.

         "Permitted Issuances" shall mean (i) the issuance of shares of Common
         Stock upon exercise of the Warrants, (ii) the issuance of shares
         relating to any benefit plan, stock option plan or any other
         compensation plan offered solely to the Issuer's officers, directors
         and/or employees, (iii) the issuance of shares of Common Stock as
         consideration for the purchase of any property, stock, business or
         securities from any Person who is not an Affiliate of the Issuer or any
         Subsidiary immediately prior to such transaction whether such shares
         are issued directly by the Issuer or a Subsidiary of the Issuer in
         connection with any merger, consolidation or other business
         combination, (iv) if there shall then be a public market for the Common
         Stock, the issuance of shares of Common Stock upon receipt by the
         Issuer of the Current Market Price therefor as described in clause (a)
         of the definition of "Current Market Price" and (v) if there shall then
         be no public market for the Common Stock, the issuance of shares of
         Common Stock, warrants or Convertible Securities on terms that are at
         least as favorable to the Issuer as terms that could be obtained in an
         arm's length transaction with third Persons not Affiliates of the
         Issuer or any Subsidiary and for consideration equal to the fair value
         of such shares as determined in good faith by a majority of
         disinterested members of the board of directors of the Issuer.

         "Person(s)" shall mean any individual, sole proprietorship,
         partnership, joint venture, trust, limited liability company,
         incorporated organization, association, corporation, institution,
         public benefit corporation, entity or government (whether federal,
         state, county, city, municipal or otherwise, including, without
         limitation, any instrumentality, division, agency, body or department
         thereof).

         "Price" means the average of the "high" and "low" prices as reported in
         The Wall Street Journal's listing for such day (corrected for obvious
         typographical errors) or if such shares are not reported in such
         listing, the average of the reported "high" and "low" sales prices on
         the largest national securities exchange (based on the aggregate dollar
         value of


                                       4
<PAGE>   8

         securities listed) on which such shares are listed or traded, or if
         such shares are not listed or traded on any national securities
         exchange, then the average of the reported "high" and "low" sales
         prices for such shares in the over-the-counter market, as reported on
         the National Association of Securities Dealers Automated Quotations
         System, or, if such prices shall not be reported thereon, the average
         of the closing bid and asked prices so reported, or, if such prices
         shall not be reported, then the average of the closing bid and asked
         prices reported by the National Quotations Bureau Incorporated. The
         "average" Price per share for any period shall be determined by
         dividing the sum of the Prices determined for the individual trading
         days in such period by the number of trading days in such period.

         "Registrable Securities" shall mean, at any particular time and as to
         each Warrant Holder, (i) all shares of common stock issuable upon the
         exercise of such Warrant Holder's Warrants and (ii) all of such Warrant
         Holder's issued and outstanding Warrant Stock.

         "Registration Expenses" shall have the meaning set forth in Section 9.5
         of this Agreement.

         "Registration Statement" shall have the meaning set forth in Section
         9.4 of this Agreement.

         "Required Holders" shall mean the Warrant Holders of Warrants
         exercisable for an amount exceeding 50% of the aggregate number of
         shares of Common Stock then purchasable upon exercise of all Warrants,
         whether or not exercisable.

         "Requirement of Law" shall mean, as to any Person, any requirement
         contained in any certificate of incorporation, bylaws, or other
         organizational or governing documents of such Person, and any law,
         treaty, rule or regulation or determination of an arbitrator or a court
         or other governmental authority, in each case applicable to or binding
         such Person or any of the property or to which such Person or any of
         its property is subject.

         "Restricted Common Stock" shall mean shares of Common Stock which are,
         or which upon their issuance on the exercise of a Warrant would be,
         evidenced by a certificate bearing the restrictive legend set forth in
         Section 9.1 of this Agreement.

         "Securities Act" shall mean the Securities Act of 1933, as amended, or
         any similar federal statute, and the rules and regulations of the
         Commission thereunder, all as the same shall be in effect at the time.

         "Subsidiary" shall mean any Person of which an aggregate of more than
         50% of the outstanding sock or other ownership interests having
         ordinary voting power to elect a majority of the board of directors or
         other managers of such Person (irrespective of whether, at the time,
         stock or other ownership interests of any other class or classes of
         such Person shall have or might have voting power by reason of the
         happening of any contingency) is at the time, directly or indirectly,
         owned legally or beneficially by the Issuer and/or one or more
         Subsidiaries of the Issuer.

         "Transfer Notice" shall have the meaning set forth in Section 9.2 of
         this Agreement.



                                       5
<PAGE>   9

         "Warrant Certificate" shall mean a certificate evidencing one or more
         Warrants, substantially in the form of Exhibit A hereto, with such
         changes therein as may be required to reflect any adjustments made
         pursuant to Section 4 of this Agreement.

         "Warrant Holder" shall mean such Person in whose name the Warrants are
         registered on the books of the Issuer maintained for such purpose or
         each Person holding any Warrant Stock. As of the Closing Date, the
         Societe Generale is the Warrant Holder hereof.

         "Warrant Price" shall mean, for any exercise of Warrants pursuant to
         Section 2.2 of this Agreement, an amount equal to (i) the number of
         shares of Common Stock being purchased upon such exercise multiplied by
         (ii) the Current Warrant Price for each share of Common Stock as of the
         date of such exercise.

         "Warrant Stock" shall mean the shares of Common Stock purchased by the
         Warrant Holders upon the exercise thereof.

         "Warrants" shall mean the Warrants issued pursuant to this Agreement
         and all Warrants issued upon transfer, division or combination of, or
         in substitution for, such Warrants. All Warrants shall at all times be
         identical as to terms and conditions and date, except as to the number
         of shares of Common Stock for which they may be exercised. A Warrant
         shall entitle the record holder thereof to purchase from the Issuer one
         share of Common Stock (subject to adjustment as provided in Section 4
         of this Agreement).

2.       ISSUANCE AND EXERCISE OF WARRANTS

2.1      Issuance of Warrants. The Issuer hereby agrees to issue to the Warrant
         Holder on the Closing Date, THREE HUNDRED THIRTY-EIGHT THOUSAND FOUR
         HUNDRED SIXTY-TWO (338,462) Warrants. On the Closing Date, the Issuer
         shall deliver to the Warrant Holder Warrant Certificates evidencing the
         Warrants issued to the Warrant Holder.

2.2      Manner of Exercise.

         (a)      The Warrant Holder may, from and after the Closing Date until
                  5:00 p.m., New York City time on the Expiration Date, exercise
                  the Warrants evidenced by a Warrant Certificate, on any
                  Business Day, for all or part of the number of shares of
                  Common Stock purchasable thereunder.

         (b)      In order to exercise the Warrants, in whole or in part, the
                  Warrant Holder shall either:

                  (i)      deliver to the Issuer at its principal office at 6300
                           Bridge Point Parkway, Building 2, Suite 500, Austin,
                           Texas 78730, Attention: President, or at the office
                           or agency designated by the Issuer pursuant to
                           Section 12 of this Agreement (the "Principal
                           Office"), (x) a written notice duly executed by the
                           Warrant Holder or its agent or attorney,
                           substantially in the form of the form of election to
                           purchase appearing at the end of the Warrant
                           Certificate as Exhibit A thereto, of such Warrant
                           Holder's election to


                                       6
<PAGE>   10

                           exercise the Warrants, which notice shall specify the
                           number of shares of Common Stock to be purchased, (y)
                           payment of the Warrant Price in the manner provided
                           below, and (z) the Warrant Certificate or Warrant
                           Certificates evidencing the Warrants. Upon receipt
                           thereof, the Issuer shall, as promptly as
                           practicable, and in any event within three (3)
                           Business Days thereafter, execute or cause to be
                           executed and deliver or cause to be delivered to such
                           Warrant Holder a certificate or certificates
                           representing the aggregate number of full shares of
                           Common Stock issuable upon such exercise, together
                           with cash in lieu of any fraction of a share, as
                           hereinafter provided. The stock certificate or
                           certificates so delivered shall be, to the extent
                           possible, in such denomination or denominations as
                           such Warrant Holder shall request in the notice and
                           shall be registered in the name of the Warrant Holder
                           or, subject to Section 9 of this Agreement, such
                           other name as shall be designated in the notice. The
                           Warrants shall be deemed to have been exercised and
                           such certificate or certificates shall be deemed to
                           have been issued, and such Warrant Holder or any
                           other Person so designated to be named therein shall
                           be deemed to have become a holder of record of such
                           shares for all purposes, as of the date the notice,
                           together with payment of the Warrant Price and the
                           Warrant Certificate or Warrant Certificates, are
                           received by the Issuer as described above and all
                           taxes required to be paid by such Warrant Holder, if
                           any, pursuant to Section 2.3 of this Agreement prior
                           to the issuance of such shares have been paid. If the
                           Warrants evidenced by a Warrant Certificate shall
                           have been exercised, the Issuer shall, at the time of
                           delivery of the certificate or certificates
                           representing the Warrant Stock, deliver to the
                           Warrant Holder a new Warrant Certificate evidencing
                           the rights of the Warrant Holder to purchase the
                           unpurchased shares of Common Stock represented by the
                           old Warrant Certificate, which new Warrant
                           Certificate shall in all other respects be identical
                           to the old Warrant Certificate. Payment of the
                           Warrant Price shall be made in cash in an amount
                           equal to the Warrant Price; or

                  (ii)     deliver to the Issuer on any Business Day at the
                           Principal Office the Cashless Conversion Notice in
                           substantially the form attached hereto as Exhibit B
                           duly executed by the Warrant Holder and setting forth
                           such Warrant Holder's election to receive the number
                           of shares of Common Stock specified in the Cashless
                           Conversion Notice ("Cashless Conversion"). Such
                           presentation and surrender shall be deemed a waiver
                           of the Warrant Holder's obligation to pay all or any
                           portion (as the case may be) of the Warrant Price in
                           connection with such Cashless Conversion. In the
                           event of a Cashless Conversion, the Issuer shall
                           deliver to the Warrant Holder (without payment by the
                           Warrant Holder of any Warrant Price) that number of
                           shares of Common Stock equal to: the number of shares
                           of Common Stock for which the Warrant Holder hereof
                           desires to exercise the Warrants multiplied by a
                           fraction, (x) the numerator of which shall be the
                           Current Market Price on the date of such exercise
                           less the Current Warrant Price on the date of such
                           exercise and (y) the


                                       7
<PAGE>   11

                           denominator of which shall be the Current Market
                           Price on the date of such exercise. The number of
                           shares of Common Stock "into which each Warrant is
                           exercisable" shall be one share, subject to
                           adjustment as provided in Section 4 hereof. The
                           Warrant Holder may exercise its Cashless Conversion
                           rights, at any time or from time to time, prior to
                           the Expiration Date. The Cashless Conversion Notice
                           shall also specify a place and date not less than one
                           nor more than 20 Business Days from the date of the
                           Cashless Conversion Notice for the closing of such
                           purchase.

2.3      Payment of Taxes. The Issuer shall pay all expenses in connection with,
         and all transfer taxes and other governmental charges that may be
         imposed with respect to, the issuance or delivery of Warrant Stock. The
         Issuer shall not be required, however, to pay any tax or other charge
         imposed in connection with any transfer involved in the issue of any
         certificate for shares of Warrant Stock issuable upon exercise of
         Warrants in any name other than that of Warrant Holder, and in such
         case the Issuer shall not be required to issue or deliver any stock
         certificate until such tax or other charge has been paid or it has been
         established to the satisfaction of the Issuer that no such tax or other
         charge is due.

2.4      Fractional Shares. The Issuer shall not be required to issue a
         fractional share of Common Stock upon the exercise of Warrants as
         provided in Section 2(b)(i) and (ii). As to any fraction of a share
         which the Warrant Holder would otherwise be entitled to purchase upon
         such exercise, the Issuer shall pay a cash adjustment in respect of
         such fraction in an amount equal to the same fraction of the Current
         Market Price per share of Common Stock on the date of exercise. If the
         determination of Current Market Price for purposes of this Section 2.4
         would otherwise require an appraisal to be made by an investment
         banking firm, then Current Market Price for purposes of this Section
         2.4 only shall mean Book Value per share of Common Stock on the date of
         exercise, unless a determination of Appraised Value shall have been
         made within six months prior to such date in which case such Appraised
         Value shall be utilized for the purposes of determining Current Market
         Price.

2.5      Continued Validity. A Warrant Holder of shares of Warrant Stock (other
         than a holder who acquires such shares after the same have been
         publicly sold pursuant to a Registration Statement under the Securities
         Act) shall continue to be entitled with respect to such shares to all
         rights to which it would have been entitled as Warrant Holder under
         Sections 9, 10 and 15 of this Agreement. The Issuer will, at the time
         of each exercise of Warrants or upon the request of the Warrant Holder
         of the shares of Warrant Stock issued upon the exercise thereof,
         acknowledge in writing, in form reasonably satisfactory to such Warrant
         Holder, its continuing obligation to afford to such Warrant Holder all
         such rights; provided, however, that if such Warrant Holder shall fail
         to make any such request, such failure shall not affect the continuing
         obligation of the Issuer to afford to such Warrant Holder all such
         rights.

3.       TRANSFERS, DIVISION AND COMBINATION

3.1      Transfer. Subject to compliance with Section 9 of this Agreement,
         transfer of Warrants, in whole or in part, shall be registered on the
         books of the Issuer to be maintained for


                                       8
<PAGE>   12

         such purposes, upon surrender of the Warrant Certificate representing
         such Warrants at the principal office of the Issuer referred to in
         Section 2.2 of this Agreement or the office or agency designated by the
         Issuer pursuant to Section 12 of this Agreement, together with a
         written assignment substantially in the form of Exhibit B to the
         Warrant Certificate and a written agreement, in form reasonably
         satisfactory to the Issuer, setting forth the new Warrant Holder's
         agreement to be bound by all of the terms of this Agreement each duly
         executed by the Warrant Holder or its agent or attorney, and funds
         sufficient to pay any transfer taxes payable by such Warrant Holder
         upon the making of such transfer. Upon such surrender and, if required,
         such payment, the Issuer shall, subject to Section 9 of this Agreement,
         execute and deliver a new Warrant Certificate or Warrant Certificates
         in the name of the assignee or assignees and in the denomination
         specified in such instrument of assignment, and shall issue to the
         assignor a new Warrant Certificate or Warrant Certificates evidencing
         the portion of the old Warrant Certificate not so assigned, and the old
         Warrant Certificate shall promptly be canceled. A Warrant, if properly
         assigned in compliance with Section 9 of this Agreement, may be
         exercised by a new Warrant Holder for the purchase of shares of Warrant
         Stock without having a new Warrant Certificate or new Warrant
         Certificates issued.

3.2      Division and Combination. Subject to the provisions of Section 9 of
         this Agreement, any Warrant Certificate may be divided or combined with
         other Warrant Certificates upon presentation thereof at the aforesaid
         office or agency of the Issuer, together with a written notice
         specifying the names and denominations in which new Warrant
         Certificates are to be issued, signed by a Warrant Holder or its agent
         or attorney. Subject to compliance with Section 3.1 of this Agreement
         as to any transfer which may be involved in such division or
         combination, the Issuer shall execute and deliver a new Warrant
         Certificate or Warrant Certificates in exchange for the Warrant
         Certificate or Warrant Certificates to be divided or combined in
         accordance with such notice.

3.3      Expenses. The Issuer shall prepare, issue and deliver at its own
         expense (other than transfer taxes) the new Warrant Certificate or
         Warrant Certificates provided for under this Section 3.

3.4      Maintenance of Books. The Issuer agrees to maintain, at its aforesaid
         office or agency, books for the registration of, and the registration
         of transfer of, the Warrants.

4.       ADJUSTMENTS

         The number of shares of Warrant Stock for which Warrants are
         exercisable, and the price at which such shares may be purchased upon
         exercise of Warrants, shall be subject to adjustment from time to time
         as set forth in this Section 4. The Issuer shall give each Warrant
         Holder notice of any event described below which requires an adjustment
         pursuant to this Section 4 within three (3) Business Days after such
         event.

4.1      Stock Dividends, Subdivisions and Combinations. If at any time the
         Issuer shall:


                                       9
<PAGE>   13

         (a)      take a record of the holders of its Common Stock for the
                  purpose of entitling them to receive a dividend payable in, or
                  other distribution of, Additional Shares of Common Stock,

         (b)      subdivide its outstanding shares of Common Stock into a larger
                  number of shares of Common Stock, or

         (c)      combine its outstanding shares of Common Stock into a smaller
                  number of shares of Common Stock,

                  then (i) the number of shares of Common Stock for which a
                  Warrant is exercisable immediately after the occurrence of any
                  such event shall be adjusted to equal the number of shares of
                  Common Stock which a record holder of the same number of
                  shares of Common Stock for which a Warrant is exercisable
                  immediately prior to the occurrence of such event would own or
                  be entitled to receive after the happening of such event, and
                  (ii) the Current Warrant Price shall be adjusted to equal the
                  Current Warrant Price multiplied by a fraction, the numerator
                  of which shall be the number of shares of Common Stock for
                  which a Warrant is exercisable immediately prior to the
                  adjustment and the denominator of which shall be the number of
                  shares for which a Warrant is exercisable immediately after
                  such adjustment.

4.2      Certain Other Distributions. If at any time the Issuer shall take a
         record of the holders of its Common Stock for the purpose of entitling
         them to receive any dividend or other distribution of:

         (a)      cash;

         (b)      any evidences of its indebtedness (other than Convertible
                  Securities), any shares of its stock (other than Additional
                  Shares of Common Stock or Convertible Securities) or any other
                  securities or property of any nature whatsoever (other than
                  cash); or

         (c)      any warrants or other rights to subscribe for or purchase any
                  evidences of its indebtedness (other than Convertible
                  Securities), any shares of its stock (other than Additional
                  Shares of Common Stock or Convertible Securities) or any other
                  securities or property of any nature whatsoever;

                  then (i) the number of shares of Common Stock for which a
                  Warrant is exercisable shall be adjusted to equal the product
                  obtained by multiplying the number of shares of Common Stock
                  for which a Warrant is exercisable immediately prior to such
                  adjustment by a fraction (A) the numerator of which shall be
                  the Current Market Price per share of Common Stock at the date
                  of taking such record and (B) the denominator of which shall
                  be such Current Market Price per share of Common Stock, minus
                  the amount allocable to one share of Common Stock of any such
                  cash so distributable and of the fair value (as determined
                  reasonably and in good faith by the board of directors of the
                  Issuer) of any and all such evidences of indebtedness, shares
                  of stock, other securities or property or


                                       10
<PAGE>   14

                  warrants or other subscription or purchase rights so
                  distributable, and (ii) the Current Warrant Price shall be
                  adjusted to equal (A) the Current Warrant Price multiplied by
                  the number of shares of Common Stock for which a Warrant is
                  exercisable immediately prior to the adjustment divided by (B)
                  the number of shares for which a Warrant is exercisable
                  immediately after such adjustment. A reclassification of the
                  Common Stock (other than a change in par value, or from par
                  value to no par value or from no par value to par value) into
                  shares of Common Stock and shares of any other class of stock
                  shall be deemed a distribution by the Issuer to the holders of
                  its Common Stock of such shares of such other class of stock
                  within the meaning of this Section 4.2 and, if the Outstanding
                  shares of Common Stock shall be changed into a larger or
                  smaller number of shares of Common Stock as a part of such
                  reclassification, such change shall be deemed a subdivision or
                  combination, as the case may be, of the Outstanding shares of
                  Common Stock within the meaning of Section 4.1 of this
                  Agreement.

4.3      Issuance of Additional Shares of Stock.

         (a)      If at any time the Issuer shall (except as hereinafter
                  provided) issue or sell any Additional Shares of Common Stock,
                  other than Permitted Issuances, for consideration in an amount
                  per Additional Share of Common Stock less than the Current
                  Market Price, then the Current Warrant Price shall be adjusted
                  by multiplying the Current Warrant Price by a fraction, the
                  numerator of which shall be (A) an amount equal to the sum of
                  (X) the number of shares of Common Stock Outstanding
                  immediately prior to such issuance or sale multiplied by the
                  Current Market Price immediately prior to the first to occur
                  of (i) board action by the Issuer authorizing such action or
                  (ii) the public announcement of an intent to take such action,
                  plus (Y) the consideration, if any, received by the Issuer
                  upon such issuance or sale, and the denominator of which shall
                  be (B) the total number of shares of Common Stock Outstanding
                  immediately after such issuance or sale multiplied by the
                  Current Market Price as determined in clause (A) above.

         (b)      The provisions of Section 4.3(a) of this Agreement shall not
                  apply to any issuance of Additional Shares of Common Stock for
                  which an adjustment is provided under Sections 4.1 or 4.2 of
                  this Agreement. No adjustment of the number of shares of
                  Common Stock for which a Warrant shall be exercisable shall be
                  made under Section 4.3(a) of this Agreement upon the issuance
                  of any Additional Shares of Common Stock which are issued
                  pursuant to the exercise of any warrants or other subscription
                  or purchase rights or pursuant to the exercise of any
                  conversion or exchange rights in any Convertible Securities if
                  any such adjustment shall previously have been made upon the
                  issuance of such warrants or other rights or upon the issuance
                  of such Convertible Securities (or upon the issuance of any
                  warrant or other rights therefor) pursuant to Section 4.4 or
                  Section 4.5 of this Agreement.

4.4      Issuance of Warrants or Other Rights. If at any time the Issuer shall
         take a record of the holders of its Common Stock for the purpose of
         entitling them to receive a distribution of,


                                       11
<PAGE>   15

         or shall in any manner (whether directly or by assumption in a merger
         in which the Issuer is the surviving corporation) issue or sell, any
         warrants or other rights to subscribe for or purchase any Additional
         Shares of Common Stock or any Convertible Securities, whether or not
         the rights to exchange or convert thereunder are immediately
         exercisable, and if the price per share for which Common Stock is
         issuable upon the exercise of such warrants or other rights or upon
         conversion or exchange of such Convertible Securities shall be less
         than the Current Market Price in effect immediately prior to the time
         of such distribution, issue or sale, then the Current Warrant Price
         shall be adjusted as provided in Section 4.3(a) of this Agreement on
         the basis that (A) the maximum number of Additional Shares of Common
         Stock issuable pursuant to all such warrants or other rights or
         necessary to effect the conversion or exchange of all such Convertible
         Securities shall be deemed to be Outstanding immediately following such
         issuance, (B) the price per share for such Additional Shares of Common
         Stock shall be deemed to be the lowest possible price per share in any
         range of prices per share at which such Additional Shares of Common
         Stock are available to such holders, and (C) the Issuer shall be deemed
         to have received all of the consideration payable therefor, if any, as
         of the date of the actual issuance of such warrants or other rights. No
         further adjustments of the Current Warrant Price shall be made upon the
         actual issuance of such Common Stock or of such other rights or upon
         exercise of such warrants or other rights or upon the actual issuance
         of such Common Stock upon such conversion or exchange of such
         Convertible Securities.

4.5      Issuance of Convertible Securities. If at any time the Issuer shall
         take a record of the holders of its Common Stock for the purpose of
         entitling them to receive a distribution of, or shall in any manner
         (whether directly or by assumption in a merger in which the Issuer is
         the surviving corporation) issue or sell, any Convertible Securities,
         whether or not the rights to exchange or convert thereunder are
         immediately exercisable, and if the price per share for which Common
         Stock is issuable upon such conversion or exchange shall be less than
         the Current Market Price in effect immediately prior to the time of
         such issue or sale of Convertible Securities, then the Current Warrant
         Price shall be adjusted as provided in Section 4.3(a) of this Agreement
         on the basis that (A) the maximum number of Additional Shares of Common
         Stock necessary to effect the conversion or exchange of all such
         Convertible Securities shall be deemed to be Outstanding immediately
         following such issuance, (B) the price per share of such Additional
         Shares of Common Stock shall be deemed to be the lowest possible price
         in any range of prices at which such Additional Shares of Common Stock
         are available to such holders, and (C) the Issuer shall be deemed to
         have received all of the consideration payable therefor, if any, as of
         the date of actual issuance of such Convertible Securities. No
         adjustment of the Current Warrant Price shall be made under this
         Section 4.5 upon the issuance of any Convertible Securities which are
         issued pursuant to the exercise of any warrants or other subscription
         or purchase rights therefor if any such adjustments shall previously
         have been made upon the issuance of such warrants or other rights
         pursuant to Section 4.4 of this Agreement. No further adjustments of
         the Current Warrant Price shall be made upon the actual issue of such
         Common Stock upon conversion or exchange of such Convertible Securities
         and, if any issue or sale of such Convertible Securities is made upon
         exercise of any warrant or other right to purchase any such Convertible
         Securities for which adjustments of the Current Warrant Price have been
         or are to be made pursuant to other provisions of this


                                       12
<PAGE>   16

         Section 4, no further adjustments of the Current Warrant Price shall be
         made by reason of such issue or sale.

4.6      Superseding Adjustment. If, at any time after any adjustment of the
         Current Warrant Price shall have been made pursuant to Section 4.4 or
         Section 4.5 of this Agreement as the result of any issuance of
         warrants, options, rights or Convertible Securities, and such warrants,
         options or rights, or the right of conversion or exchange in such other
         Convertible Securities, shall expire, and all or a portion of such
         warrants, options or rights, or the right of conversion or exchange
         with respect to all or a portion of such other Convertible Securities,
         as the case may be, shall not have been exercised, then such previous
         adjustment shall be rescinded and annulled and, if applicable, the
         Current Warrant Price shall be recalculated as if all such expired and
         unexercised warrants, options, rights or Convertible Securities had
         never been issued.

4.7      Other Provisions Applicable to Adjustments Under This Section. The
         following provisions shall be applicable to the making of adjustments
         of the number of shares of Common Stock for which a Warrant is
         exercisable provided for in this Section 4:

         (a)      Computation of Consideration. To the extent that any
                  Additional Shares of Common Stock shall be issued for cash
                  consideration, the consideration received by the Issuer
                  therefor shall be the amount of the cash received by the
                  Issuer therefor, or, if such Additional Shares of Common Stock
                  are sold to underwriters or dealers for public offering
                  without a subscription offering, the initial public offering
                  price (in any such case subtracting any amounts paid or
                  receivable for accrued interest or accrued dividends, but not
                  subtracting any compensation, discounts or expenses paid or
                  incurred by the Issuer for and in the underwriting of, or
                  otherwise in connection with, the issuance thereof). To the
                  extent that such issuance shall be for a consideration other
                  than cash, then, except as herein otherwise expressly
                  provided, the amount of such consideration shall be deemed to
                  be the fair value of such consideration at the time of such
                  issuance as determined reasonably and in good faith by a
                  majority of the disinterested members of the board of
                  directors of the Issuer.

         (b)      When Adjustments to Be Made. The adjustments required by this
                  Section 4 shall be made whenever and as often as any specified
                  event requiring an adjustment shall occur, except that any
                  adjustment to the number of shares for which the Warrants are
                  exercisable that would otherwise be required may be postponed
                  (except in the case of a subdivision or combination of shares
                  of the Common Stock, as provided for in Section 4.1 of this
                  Agreement) up to, but not beyond, the date and time of
                  exercise of any Warrants if such adjustment either by itself
                  or with other adjustments not previously made adds or
                  subtracts less than 1% to the number of shares of Common Stock
                  for which the Warrants initially issued pursuant to this
                  Agreement are exercisable immediately prior to the making of
                  such adjustment. Any adjustment representing a change of less
                  than such minimum amount (except as aforesaid) which is
                  postponed shall be carried forward and made as soon as such
                  adjustment, together with other adjustments required by this
                  Section 4 and not previously made, would result in a minimum


                                       13
<PAGE>   17

                  adjustment or on the date of exercise. For the purpose of any
                  adjustment, any specified event shall be deemed to have
                  occurred at the close of business on the date of its
                  occurrence.

         (c)      Fractional Interests. In computing adjustments under this
                  Section 4, fractional interests in Common Stock resulting from
                  an issuance of additional Warrants to any Warrant Holder
                  pursuant to this Section 4 shall be taken into account to the
                  nearest 1/10th of a share, subject to Section 2.4 of this
                  Agreement.

         (d)      When Adjustment Not Required. If the Issuer shall take a
                  record of the holders of its Common Stock for the purpose of
                  entitling them to receive a dividend or distribution or
                  subscription or purchase rights and shall, thereafter and
                  before the distribution to stockholders thereof, legally
                  abandon its plan to pay or deliver such dividend,
                  distribution, subscription or purchase rights, no adjustment
                  shall be required by reason of the taking of such record and
                  any such adjustment previously made in respect thereof shall
                  be rescinded and annulled.

         (e)      Escrow of Warrant Stock. If after any property becomes
                  distributable pursuant to this Section 4 by reason of the
                  taking of any record of the holders of Common Stock, but prior
                  to the occurrence of the event for which such record is taken,
                  any Warrant Holder exercises Warrants, any Additional Shares
                  of Common Stock issuable upon exercise of such Warrant by
                  reason of such adjustment shall be deemed the last shares of
                  Common Stock for which such Warrant is exercised
                  (notwithstanding any other provision to the contrary herein),
                  and such shares or other property shall be held in escrow for
                  a Warrant Holder by the Issuer to be issued to such Warrant
                  Holder upon and to the extent that the event actually takes
                  place, upon payment of the balance, if any, of the Warrant
                  Price for such Warrant at such date (after taking into account
                  any overpayment of the Warrant Price made at any time of the
                  initial Warrant exercise). Notwithstanding any other provision
                  to the contrary herein, if the event for which such record was
                  taken fails to occur or is rescinded, then such escrowed
                  shares shall be canceled by the Issuer and escrowed property
                  returned.

4.8      Reorganization, Reclassification, Merger, Consolidation or Disposition
         of Assets. In the event the Issuer shall reorganize its capital,
         reclassify its capital stock, consolidate or merge with and into
         another corporation or entity (where the Issuer is not the surviving
         corporation or where there is a change in or distribution with respect
         to the Common Stock of the Issuer), or sell, transfer or otherwise
         dispose of all or substantially all its property, assets or business to
         another corporation or entity and, pursuant to the terms of such
         reorganization, reclassification, merger, consolidation or disposition
         of assets, shares of common stock of the successor or acquiring
         corporation or entity, or any cash, shares of stock or other securities
         or property of any nature whatsoever (including warrants or other
         subscription or purchase rights) in addition to or in lieu of common
         stock of the successor or acquiring corporation or entity ("Other
         Property"), are to be received by or distributed to the holders of
         Common Stock of the Issuer, then the Issuer shall, as a condition
         precedent to such transaction, cause effective provisions to be made so
         that each Warrant Holder shall have the right thereafter to receive,
         upon exercise of a


                                       14
<PAGE>   18

         warrant, solely the number of shares of "common stock of the successor
         or acquiring corporation" or of the Issuer, if it is the surviving
         corporation, and Other Property receivable upon or as a result of such
         reorganization, reclassification, merger, consolidation or disposition
         of assets, by a holder of the number of shares of Common Stock for
         which a Warrant is exercisable immediately prior to such event. In case
         of any such reorganization, reclassification, merger, consolidation or
         disposition of assets, such provisions shall include the express
         assumption by the successor or acquiring corporation or entity (if
         other than the Issuer) of the due and punctual observance and
         performance of each and every covenant and condition of this Agreement
         to be performed and observed by the Issuer and all the obligations and
         liabilities hereunder, subject to such modifications as may be deemed
         appropriate (as determined by resolution of the board of directors of
         the Issuer) to provide for adjustments of shares of the Common Stock
         for which a Warrant is exercisable which shall be as nearly equivalent
         as practicable to the adjustments provided for in this Section 4. For
         purposes of this Section 4.8, "common stock of the successor or
         acquiring corporation" shall include stock of such corporation of any
         class which is not preferred as to dividends or assets over any other
         class of stock or other securities of such corporation or entity and
         which is not subject to redemption and shall also include any evidences
         of indebtedness, shares of stock or other securities which are
         convertible into or exchangeable for any such stock or other
         securities, either immediately or upon the arrival of a specified date
         or the happening of a specified event, and any warrants or other rights
         to subscribe for or purchase any such stock or securities. The
         foregoing provisions of this Section 4.8 shall similarly apply to
         successive reorganizations, reclassifications, mergers, consolidations
         or disposition of assets.

5.       NOTICES TO WARRANT HOLDERS

5.1      Notice of Adjustments. Whenever the number of shares of Common Stock
         for which a Warrant is exercisable, or whenever the price at which a
         share of such Common Stock may be purchased upon exercise of the
         Warrants, shall be adjusted pursuant to Section 4, the Issuer shall
         forthwith prepare a certificate to be executed by the chief financial
         officer of the Issuer setting forth, in reasonable detail, the event
         requiring the adjustment and the method by which such adjustment was
         calculated (including a description of the basis on which the board of
         directors of the Issuer determined the fair value of any evidences of
         indebtedness, shares of stock, other securities or property or warrants
         or other subscription or purchase rights referred to in Section 4 of
         this Agreement), specifying the number of shares of Common Stock for
         which a Warrant is exercisable and (if such adjustment was made
         pursuant to Section 4.8 of this Agreement) describing the number and
         kind of any other shares of stock or Other Property for which a Warrant
         is exercisable, and any change in the purchase price or prices thereof,
         after giving effect to such adjustment or change. The Issuer shall
         promptly cause a signed copy of such certificate to be delivered to
         each Warrant Holder in accordance with Section 15.2 of this Agreement.
         The Issuer shall keep at its office or agency designated pursuant to
         Section 12 of this Agreement copies of all such certificates and cause
         the same to be available for inspection at said office during normal
         business hours by any Warrant Holder or any prospective purchaser of a
         Warrant designated by a Warrant Holder thereof.


                                       15
<PAGE>   19

5.2      Notice of Certain Corporate Action. Each Warrant Holder shall be
         entitled to the same rights to receive notice of corporate action as
         any holder of Common Stock.

6.       REPRESENTATIONS AND WARRANTIES

         The Issuer makes the following representations and warranties, each and
         all of which shall be true and correct as of the date of execution and
         delivery of this Agreement and shall survive the execution and delivery
         of this Agreement:

         (a)      Due Organization; Etc. The Issuer is a corporation duly
                  organized validly existing and in good standing under the laws
                  of the State of Delaware, and has the power and authority to
                  execute and deliver this Agreement and the Warrant
                  Certificates, to issue the Warrants and to perform its
                  obligations under this Agreement and the Warrant Certificates.

         (b)      Due Authorization; No Violation. The execution, delivery and
                  performance by the Issuer of this Agreement and the Warrant
                  Certificates, the issuance of the Warrants and the issuance of
                  the Warrant Stock upon exercise of the Warrants have been duly
                  authorized by all necessary corporate action and do not and
                  will not violate, or result in a breach of, or constitute a
                  default under or require any consent under, or result in the
                  creation of any lien or security interest upon the assets of
                  the Issuer pursuant to, any Requirement of Law or any
                  contractual obligation binding upon the Issuer.

         (c)      Due Execution; Etc. This Agreement has been duly executed and
                  delivered by the Issuer and constitutes a legal, valid and
                  enforceable obligation of the Issuer. When the Warrants and
                  the Warrant Certificates have been issued as contemplated
                  hereby, (i) the Warrants and the Warrant Certificates will
                  constitute legal, valid, binding and enforceable obligations
                  of the Issuer and (ii) the Warrant Stock, when issued upon
                  exercise of the Warrants in accordance with the terms hereof,
                  will be duly authorized, validly issued, fully paid and
                  non-assessable shares of Common Stock with no personal
                  liability attaching to the ownership thereof.

         (d)      Capitalization. The total number of shares of all classes of
                  stock that the Issuer shall on the Closing Date have authority
                  to issue is 40,000,000 shares, consisting of (i) 30,000,000
                  shares of Common Stock, par value $0.01 per share, of which,
                  after giving effect to the transactions contemplated herein
                  and all other issuances of capital stock of the Issuer on or
                  prior to the Closing Date, 14,428,621 shares of Common Stock
                  will be issued and outstanding and 338,462 shares of Common
                  Stock will be reserved for future issuance pursuant to this
                  Agreement and (ii) 10,000,000 shares of Preferred Stock, par
                  value $0.01 per share, none of which are presently
                  outstanding. Schedule A sets forth a complete list of the
                  outstanding capital stock of the Issuer, including any
                  options, warrants or rights to purchase the capital stock of
                  the Issuer. The delivery hereunder by the Issuer to the
                  Warrant Holder of the Warrants issued on the Closing Date will
                  transfer and convey to the Warrant Holder good and marketable
                  title to such Warrants and,


                                       16
<PAGE>   20

                  upon exercise of such Warrants in accordance with this
                  Agreement, good and marketable title to the Common Stock
                  purchased upon such exercise, free and clear of all preemptive
                  rights, liens, charges and encumbrances, except for
                  restrictions on transfer referred to in this Agreement, or
                  arising under the Federal and state securities laws. Except as
                  otherwise disclosed on Schedule A, the Issuer does not have
                  outstanding any stock or securities convertible into or
                  exchangeable for any shares of its stock, nor, except as so
                  set forth, does it have outstanding any agreements, rights or
                  options entitling any person to subscribe for or to purchase
                  any capital stock or securities convertible into or
                  exchangeable for any of its shares of stock.

         (e)      Full Disclosure. No information contained in this Agreement,
                  the financial statements referred to in the Credit Agreement
                  or any written statement furnished by or on behalf of the
                  Issuer pursuant to the terms of this Agreement to the Warrant
                  Holder contains any untrue statement of a material fact or
                  omits to state a material fact necessary to make the
                  statements contained herein or therein not misleading in light
                  of the circumstances under which made.

         (f)      Warrant Price. The Issuer has taken all corporate action, and
                  obtained all necessary authorizations or exemptions from any
                  public regulatory body or bodies or governmental entity or
                  entities having jurisdiction thereof, as may be necessary in
                  order that the Issuer may validly and legally issue fully paid
                  and non-assessable shares of Common Stock upon to exercise of
                  the warrants at the Warrant Price, as the same may be adjusted
                  pursuant hereto.

         (g)      Other Representations and Warranties. The Issuer hereby
                  affirms and reaffirms for the express benefit of the Warrant
                  Holders that the representations and warranties made by the
                  Issuer in that certain Guaranty Agreement dated as of January
                  26, 1998, as amended, are true and correct, as if made in
                  favor of the Warrant Holder on the date hereof.

7.       CERTAIN COVENANTS

7.1      No Impairment. The Issuer shall not by any action including, without
         limitation, amending its certificate of incorporation or through any
         reorganization, transfer of assets, consolidation, merger, dissolution,
         issue or sale of securities or any other voluntary action, avoid or
         seek to avoid the observance or performance of any of the terms of this
         Agreement, but will at all times in good faith assist in the carrying
         out of all such terms and in the taking of all such actions as may be
         necessary or appropriate to protect the rights of each Warrant Holder
         against impairment. Without limiting the generality of the foregoing,
         the Issuer will use reasonable good faith efforts to obtain all such
         authorizations, exemptions or consents from any public regulatory body
         having jurisdiction thereof as may be necessary to enable it to perform
         its obligations under this Agreement.

         Upon the request of a Warrant Holder, the Issuer will, at any time
         during the period this Agreement is in effect, acknowledge in writing,
         in form satisfactory to such Warrant


                                       17
<PAGE>   21

         Holder, the continuing validity of this Agreement and the obligations
         of the Issuer hereunder.

7.2      Reservation and Authorization of Common Stock; Registration with, or
         Approval of, any Governmental Authority. From and after the Closing
         Date, the Issuer shall at all times reserve and keep available for
         issue upon the exercise of Warrants such number of its authorized but
         unissued shares of Common Stock as will be sufficient to permit the
         exercise in full of all outstanding Warrants. All shares of Common
         Stock which shall be so issuable, when issued upon exercise of any
         Warrants and payment therefor in accordance with the terms of this
         Agreement, shall be duly and validly issued and fully paid and
         non-assessable, and not subject to preemptive rights.

         Before taking any action which would result in an adjustment in the
         number of shares of Common Stock for which a Warrant is exercisable or
         in the Current Warrant Price, the Issuer shall obtain all such
         authorizations or exemptions thereof, or consents thereto, as may be
         necessary from any public regulatory body or bodies or governmental
         entity or entities having jurisdiction thereof.

         If any shares of Common Stock required to be reserved for issuance upon
         exercise of Warrants require registration or qualification with any
         governmental authority under any federal or state law (otherwise than
         as provided in Section 9 of this Agreement) before such shares may be
         so issued, the Issuer will in good faith and as expeditiously as
         possible and at its expense endeavor to cause such shares to be duly
         registered.

8.       TAKING OF RECORD; STOCK AND WARRANT TRANSFER BOOKS

         In the case of all dividends or other distributions by the Issuer to
         the holders of its Common Stock with respect to which any provision of
         Section 4 of this Agreement refers to the taking of a record of such
         holders, the Issuer will in each such case take such a record as of the
         close of business on a Business Day. The Issuer will not at any time,
         except upon dissolution, liquidation or winding up of the Issuer, close
         its stock transfer books or Warrant transfer books so as to result in
         preventing or delaying the exercise or transfer of any Warrants.

9.       RESTRICTIONS ON TRANSFERABILITY

         The Warrants and the Warrant Stock shall not be transferred before
         satisfaction of the conditions specified in this Section 9, which
         conditions are intended to ensure compliance with the provisions of the
         Securities Act and applicable state securities laws with respect to the
         transfer of any Warrant or any Warrant Stock. Each Warrant Holder, by
         entering into this Agreement and accepting the Warrants, agrees to be
         bound by the provisions of this Section 9.

9.1      Restrictive Legend. Except as otherwise provided in this Section 9,
         each certificate representing Warrants or Warrant Stock, shall be
         stamped or otherwise imprinted with a legend in substantially the
         following form:


                                       18
<PAGE>   22

         "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN
         REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY
         APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN
         THE ABSENCE OF SUCH REGISTRATION OR AN EXEMPTION THEREFROM. SUCH
         SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND PRIVILEGES SPECIFIED IN
         A WARRANT AGREEMENT, DATED AS OF JULY 19, 1999, BETWEEN BRIGHAM
         EXPLORATION COMPANY AND THE INITIAL HOLDERS OF SECURITIES NAMED
         THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM
         EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER
         HEREOF UPON WRITTEN REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES
         TO BE BOUND THEREBY."

9.2      Notice of Proposed Transfers; Requests for Registration. Prior to any
         transfer of any Warrants or any shares of Restricted Common Stock, the
         Warrant Holder of such Warrants or Restricted Common Stock shall give
         five days prior written notice to the Issuer of such Warrant Holder's
         intention to effect such transfer (a "Transfer Notice"). Each Warrant
         Holder agrees that it will not sell, transfer or otherwise dispose of
         Warrants or any shares of Restricted Common Stock, in whole or in part,
         except pursuant to an effective registration statement under the
         Securities Act or an exemption from registration thereunder. Each
         certificate, if any, evidencing such shares of Restricted Common Stock
         issued upon such transfer shall bear the restrictive legend set forth
         in Section 9.1, and each Warrant Certificate issued upon such transfer
         shall bear the restrictive legend set forth in Section 9.1 of this
         Agreement, unless in the opinion of the transferee's or Warrant
         Holder's counsel delivered to the Issuer in connection with such
         transfer such legend is not required in order to ensure compliance with
         the Securities Act.

         The Warrant Holders of Warrants and Warrant Stock shall have the right
         to request registration of such Warrant Stock pursuant to Section 9.3
         of this Agreement.

9.3      Incidental Registration. If the Issuer at any time proposes to file on
         its behalf and/or on behalf of any of its security holders (the
         "Demanding Security Holders") a Registration Statement under the
         Securities Act on any form (other than a Registration Statement (i)
         filed pursuant to demand under the Company's Registration Rights
         Agreement with Joint Energy Development Investments II Limited
         Partnership, a Delaware limited partnership, and Enron Capital & Trade
         Resources Corp., a Delaware corporation, dated August 20, 1998, as
         amended, or (ii) on Form S-8 or any similar or successor form or any
         other registration statement relating to an offering of securities
         solely to the Issuer's existing security holders or employees) to
         register the offer and sale of its Common Stock for cash, it will give
         written notice to all Warrant Holders of Warrants or Warrant Stock at
         least twenty (20) days before the anticipated date of initial filing
         with the Commission of such Registration Statement, which notice shall
         set forth the Issuer's intention to effect such a registration, the
         class or series and number of equity securities proposed to be
         registered and the intended method of disposition of the securities
         proposed to be registered by the Issuer. The notice shall offer to
         include in such filing all of the Warrant Holder's Registrable
         Securities.


                                       19
<PAGE>   23

         Each Warrant Holder desiring to have Registrable Securities registered
         under this Section 9.3 shall advise the Issuer in writing within
         fifteen (15) days after the date of receipt of such offer from the
         Issuer, setting forth the amount of such Registrable Securities for
         which registration is requested. The Issuer shall thereupon include in
         such filing the number of shares of Registrable Securities for which
         registration is so requested, subject to the next sentence, and shall
         use its best efforts to effect registration under the Securities Act of
         such securities. If the managing underwriter of a proposed public
         offering shall advise the Issuer in writing that, in its opinion, the
         distribution of the Registrable Securities requested to be included in
         the registration concurrently with the securities being registered by
         the Issuer or any Demanding Security Holder would materially and
         adversely affect the distribution of such securities by the Issuer or
         such Demanding Security Holders, then all selling security holders (but
         not the Issuer or the Demanding Security Holders) shall reduce the
         amount of securities each intended to distribute through such offering
         on a pro rata basis to the greatest aggregate amount which, in the
         opinion of such managing underwriter, would not materially and
         adversely affect the distribution of such securities.

         Nothing in this Section 9.3 shall preclude the Issuer from
         discontinuing the registration of its securities being effected on its
         behalf under this Section 9.3 at any time prior to the effective date
         of the registration relating thereto. Notwithstanding any provision
         herein, the rights of the Warrant Holder under this Section 9.3 are
         subject to the express limitations contained in registration rights
         agreements in effect on the date hereof between the Issuer and other
         parties; provided, however, that the Issuer shall not on or after the
         date of this Agreement enter into any registration rights agreement
         with respect to its securities that conflict with the registration
         rights granted to the Warrant Holder herein.

9.4      Registration Procedures. If the Issuer is required by the provisions of
         this Section 9 to use its best efforts to effect the registration of
         any of its securities under the Securities Act, the Issuer will, as
         expeditiously as possible:

         (a)      prepare and file with the Commission a registration statement
                  with respect to such securities (a "Registration Statement")
                  and use its best efforts to cause such Registration Statement
                  to become and remain effective for the period described in
                  paragraph (b) below;

         (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 and to comply with the
                  provisions of the Securities Act with respect to the sale or
                  other disposition of all securities covered by such
                  Registration Statement until the earlier of such time as all
                  of such securities have been disposed of in a public offering
                  or the expiration of 90 days;

         (c)      furnish to such selling security holders such number of copies
                  of a summary prospectus or other prospectus, including a
                  preliminary prospectus, in conformity


                                       20
<PAGE>   24

                  with the requirements of the Securities Act, and such other
                  documents, as such selling security holders may reasonably
                  request;

         (d)      use its best efforts to register or qualify the securities
                  covered by such Registration Statement under such other
                  securities or blue sky laws of such jurisdictions within the
                  United States as each holder of such securities shall request
                  (provided, however, the Issuer shall not be obligated to
                  qualify as a foreign corporation to do business under the laws
                  of any jurisdiction in which it is not then qualified or to
                  file any general consent to service or process), and do such
                  other reasonable acts and things as may be required of it to
                  enable such holder to consummate the disposition in such
                  jurisdiction of the securities covered by such Registration
                  Statement;

         (e)      enter into customary agreements (including an underwriting
                  agreement in customary form) and take such other actions as
                  are reasonably required in order to expedite or facilitate the
                  disposition of such Registrable Securities; and

         (f)      otherwise use its best efforts to comply with all applicable
                  rules and regulations of the Commission, and make available to
                  its security holders, as soon as reasonably practicable, but
                  not later than 18 months after the effective date of the
                  Registration Statement, an earnings statement covering the
                  period of at least 12 months beginning with the first full
                  month after the effective date of such Registration Statement,
                  which earnings statements shall satisfy the provisions of
                  Section 11(a) of the Securities Act.

                  It shall be a condition precedent to the obligation of the
                  Issuer to take any action pursuant to this Section 9 in
                  respect of the securities which are to be registered at the
                  request of any Warrant Holder of Registrable Securities that
                  such Warrant Holder shall furnish to the Issuer such
                  information regarding the securities held by such Warrant
                  Holder and the intended method of disposition thereof as the
                  Issuer shall reasonably request and as shall be required in
                  connection with the action taken by the Issuer.

9.5      Expenses. All expenses incurred in complying with this Section 9,
         including, without limitation, all registration and filing fees
         (including all expenses incident to filing with the NASD), printing
         expenses, fees and disbursements of counsel for the Issuer, the
         reasonable fees and expenses of one counsel for the selling security
         holders (selected by the Person holding the plurality of the securities
         being registered), expenses of any special audits incident to or
         required by any such registration and expenses of complying with the
         securities or blue sky laws of any jurisdictions pursuant to Section
         9.4(d) of this Agreement (all of such expenses shall be collectively
         referred to herein as "Registration Expenses"), shall be paid by the
         Issuer; provided, however, the Issuer shall not be responsible for any
         discount or commission or cost reimbursement to any underwriter in
         respect of the securities sold by such Warrant Holder of Registrable
         Securities.



                                       21
<PAGE>   25

9.6      Indemnification and Contribution.

         (a)      In the event of any registration of any of the Registrable
                  Securities under the Securities Act pursuant to this Section
                  9, the Issuer shall indemnify and hold harmless each Warrant
                  Holder of such Registrable Securities, such Warrant Holder's
                  directors and officers, each Affiliate of such Warrant Holder,
                  and each other Person (including each underwriter) who
                  participated in the offering of such Registrable Securities
                  and each other Person, if any, who controls such Warrant
                  Holder or such participating Person, if any, who controls such
                  Warrant Holder or such participating Person within the meaning
                  of the Securities Act, against any losses, claims, damages or
                  liabilities, joint or several, to which such Warrant Holder or
                  any such director or officer or participating Person or
                  Affiliate or controlling Person may become subject under the
                  Securities Act or any other statute or at common law, insofar
                  as such losses, claims, damages or liabilities (or actions in
                  respect thereof) arise out of or are based upon (i) any
                  alleged untrue statement of any material fact contained, on
                  the effective date thereof, in any Registration Statement
                  under which such securities were registered under the
                  Securities Act, any preliminary prospectus or final prospectus
                  contained therein, or any amendment or supplement thereto, or
                  (ii) any alleged omission to state therein a material fact
                  required to be stated therein or necessary to make the
                  statements therein, in light of the circumstances under which
                  they were made, not misleading, and shall reimburse such
                  Warrant Holder or such director, officer or participating
                  Person or Affiliate or controlling Person for any legal or any
                  other expenses reasonably incurred by such Warrant Holder or
                  such director, officer or participating Person or Affiliate or
                  controlling Person in connection with investigating or
                  defending any such loss, claim, damage, liability or action;
                  provided, however, that the Issuer shall not be liable in any
                  such case to the extent that any such loss, claim, damage or
                  liability arises out of or is based upon any alleged untrue
                  statement or alleged omission made in such Registration
                  Statement, preliminary prospectus, prospectus or amendment or
                  supplement in reliance upon and in conformity with written
                  information furnished to the Issuer by such Warrant Holder
                  specifically for use therein and, in the case of any
                  non-underwritten offering, to the extent that any such losses,
                  claims, damages, liabilities or expenses arise out of or are
                  based upon the fact that a current copy of the prospectus was
                  not sent or given to the Person asserting any such losses,
                  claims, damages, liabilities or expenses at or prior to the
                  written confirmation of the sale of the securities to such
                  Person if it is determined that it was the responsibility of
                  such Warrant Holder to provide such Person with a current copy
                  of the prospectus and such current copy of the prospectus
                  would have cured the defect giving rise to such losses,
                  claims, damages, liabilities or expenses. Such indemnity shall
                  remain in full force and effect regardless of any
                  investigation made by or on behalf of such Warrant Holder or
                  such director, officer or participating Person or Affiliate or
                  controlling Person, and shall survive the transfer of such
                  securities by such Warrant Holder.

         (b)      Each Warrant Holder of any Registrable Securities, by
                  acceptance thereof, agrees to indemnify and hold harmless the
                  Issuer, its directors and officers and each other Person, if
                  any, who controls the Issuer within the meaning of the
                  Securities Act against any losses, claims, damages or
                  liabilities, joint or several, to which the


                                       22
<PAGE>   26

                  Issuer or any such director or officer or any such Person may
                  become subject under the Securities Act or any other statute
                  or at common law, insofar as such losses, claims, damages or
                  liabilities (or actions in respect thereof) arise out of or
                  are based upon (i) information in writing provided to the
                  Issuer by such Warrant Holder of such Registrable Securities
                  contained, on the effective date thereof, in any Registration
                  Statement under which securities were registered under the
                  Securities Act at the request of such Warrant Holder, any
                  preliminary prospectus or final prospectus contained therein,
                  or any amendment or supplement thereto or (ii) the fact that a
                  current copy of the prospectus was not sent to the Person
                  asserting such losses, claims, damages, liabilities or
                  expenses at or prior to the written confirmation of the sale
                  of the securities with respect to such Person if it is
                  determined that it was the responsibility of such Warrant
                  Holder to provide such Person with a current copy of the
                  prospectus and such current copy would have cured the defect
                  giving rise to such losses, claims, damages, liabilities or
                  expenses; provided, however, that such Warrant Holder's
                  obligation under this Section 9.6(b) to indemnify and hold
                  harmless the Issuer shall in no event exceed the lesser of (x)
                  the damage attributable solely to the inclusion of such
                  written information in such Registration Statement,
                  preliminary prospectus, final prospectus, or amendment or
                  supplement suffered by the Person or Persons whose claims gave
                  rise to such losses, claims, damages or liabilities and (y)
                  the net proceeds received by such Warrant Holder from the sale
                  of Registrable Securities giving rise to such indemnification.

         (c)      If the indemnification provided for in this Section 9 from the
                  indemnifying party is unavailable to an indemnified party
                  hereunder in respect of any losses, claims, damages,
                  liabilities or expenses referred to herein, then the
                  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, claims, damages,
                  liabilities or expenses in such proportion as is appropriate
                  to reflect the relative fault of the indemnifying party and
                  indemnified parties in connection with the actions which
                  resulted in such losses, claims, damages, liabilities or
                  expenses, as well as any other relevant equitable
                  considerations. The relative fault of such indemnifying party
                  and indemnified parties shall be determined by reference to,
                  among other things, whether any action in question, including
                  any untrue or alleged untrue statement of a material fact or
                  omission or alleged omission to state a material fact, has
                  been made by, or related to information supplied by, such
                  indemnifying party or indemnified parties, and the parties'
                  relative intent, knowledge, access to information and
                  opportunity to correct or prevent such action. The amount paid
                  or payable by a party under this Section 9 as a result of the
                  losses, claims, damages, liabilities and expenses referred to
                  above shall be deemed to include any legal or other fees or
                  expenses reasonably incurred by such party in connection with
                  any investigation or proceeding.

                           The parties hereto agree that it would not be just
                  and equitable if contribution pursuant to this Section 9.6(c)
                  were determined by pro rata allocation or by any other method
                  of allocation which does not take account of the equitable
                  considerations referred to in the immediately preceding
                  paragraph.


                                       23
<PAGE>   27

                  Notwithstanding the provisions of this subsection (c), no
                  Warrant Holder shall be required to contribute any amount in
                  excess of the total amount received by it upon the sale of its
                  securities pursuant to the Registration Statement to which the
                  losses, claims, damages, liabilities and expenses referred to
                  above relate. 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 was not
                  guilty of such fraudulent misrepresentation. The obligations
                  of each of the Warrant Holders under this subsection (c) to
                  contribute are several and not joint.

         (d)      Conduct of Indemnification Proceedings. Any person or entity
                  entitled to indemnification hereunder shall (i) give prompt
                  written notice to the indemnifying party after the receipt by
                  the indemnified party of a written notice of the commencement
                  of any action, suit, proceeding or investigation or threat
                  thereof made in writing for which such indemnified party will
                  claim indemnification or contribution pursuant to this
                  Agreement; provided, however, that the failure of any
                  indemnified party to give notice as provided herein shall not
                  relieve the indemnifying party of its obligations under
                  Section 9.6 hereof, except to the extent that the indemnifying
                  party is actually prejudiced by such failure to give notice,
                  and (ii) unless in such indemnified party's reasonable
                  judgment a conflict of interest may exist between such
                  indemnified and indemnifying parties with respect to such
                  claim, permit such indemnifying party to assume the defense of
                  such claim with counsel reasonably satisfactory to the
                  indemnified party. If the indemnifying party is entitled to,
                  and does, assume the defense of such claim, the indemnified
                  party shall have the right to employ separate counsel and to
                  participate in the defense thereof, but the fees and expenses
                  of such counsel shall be borne by the indemnified party.
                  Whether or not such defense is assumed by the indemnifying
                  party, the indemnifying party shall not be subject to any
                  liability for any settlement made without its consent (but
                  such consent will not be unreasonably withheld). No
                  indemnifying party shall be permitted to consent to the entry
                  of any judgment or to enter into any settlement that does not
                  include as an unconditional term thereof the giving by the
                  claimant or plaintiff to such indemnified party of a release
                  from all liability in respect of such claim or litigation. An
                  indemnifying party who is not entitled to, or elects not to,
                  assume the defense of a claim shall not be obligated to pay
                  the fees and expenses of more than one counsel in any one
                  jurisdiction for all parties indemnified by such indemnifying
                  party with respect to such claim, unless in the reasonable
                  judgment of any indemnified party a conflict of interest may
                  exist between such indemnified party and any other of such
                  indemnified parties with respect to such claim, in which event
                  the indemnifying party shall be obligated to pay the fees and
                  expenses of such additional counsel or counsels.

9.7      Termination of Restrictions. Notwithstanding the foregoing provisions
         of this Section 9, the restrictions imposed by this Section 9 upon the
         transferability of the Warrants, the Warrant Stock and the Restricted
         Common Stock (or Common Stock issuable upon the exercise of the
         Warrants) and the legend requirement of Section 9.1 of this Agreement
         shall terminate as to any particular Warrant or share of Warrant Stock
         or Restricted Common Stock (or Warrant Stock) (i) when and so long as
         such security shall have been


                                       24
<PAGE>   28

         registered under the Securities Act and disposed of pursuant thereto,
         or (ii) when the Warrant Holder thereof shall have delivered to the
         Issuer the written opinion of counsel to such Warrant Holder, stating
         that such legend is not required in order to ensure compliance with the
         Securities Act. Whenever the restrictions imposed by this Section 9
         shall terminate as to any Warrants or any Restricted Common Stock, as
         hereinabove provided, the Warrant Holder thereof shall be entitled to
         receive from the Issuer, at the expense of the Issuer, a new Warrant
         Certificate or a new certificate representing such Common Stock, as the
         case may be, not bearing the restrictive legend set forth in Section
         9.1 of this Agreement.

9.8      Listing on Securities Exchange. If at any time the Issuer shall list
         any shares of Common Stock on any securities exchange, it will, at its
         expense, use its best efforts to list thereon, maintain and, when
         necessary, increase such listing of, all shares of Common Stock issued
         or, to the extent permissible under the applicable securities exchange
         rules, issuable upon the exercise of the Warrants so long as any shares
         of Common Stock shall be so listed during the Exercise Period.

10.      SUPPLYING INFORMATION

         The Issuer shall cooperate with each Warrant Holder of a Warrant and
         each Warrant Holder of Restricted Common Stock in supplying such
         information as may be reasonably necessary for such Warrant Holder to
         complete and file any information reporting forms presently or
         hereafter required by the Commission as a condition to the availability
         of an exemption from the Securities Act for the sale of any Warrant or
         Restricted Common Stock.

11.      LOSS OR MUTILATION

         Upon receipt by the Issuer from any Warrant Holder of evidence
         reasonably satisfactory to it of the ownership of and the loss, theft,
         destruction or mutilation of a certificate representing Warrants or
         Warrant Stock and indemnity reasonably satisfactory to it (it being
         understood that the written agreement of the Warrant Holder or an
         Affiliate thereof shall be sufficient indemnity) and in case of
         mutilation upon surrender and cancellation hereof or thereof, the
         Issuer will execute and deliver in lieu hereof or thereof a new Warrant
         or new stock certificate as the case may be, of like tenor to such
         Warrant Holder; provided, in the case of mutilation, no indemnity shall
         be required if the certificate representing Warrants or Warrant Stock
         in identifiable form is surrendered to the Issuer for cancellation.

12.      OFFICE OF THE ISSUER

         As long as any of the Warrants remain outstanding, the Issuer shall
         maintain an office or agency (which may be the principal executive
         officers of the Issuer) where the Warrants may be presented for
         exercise, registration or transfer, division or combination as provided
         in this Agreement.



                                       25
<PAGE>   29

13.      APPRAISAL

         The determination of the Appraised Value per share of Common Stock
         shall be made by an investment banking firm of nationally recognized
         standing mutually agreed to by the Issuer and the Required Holders. If
         the investment banking firm selected by the Issuer is not acceptable to
         the Required Holders and the Issuer and the Required Holders cannot
         agree on a mutually acceptable investment banking firm, then the
         Required Holders and the Issuer shall each choose one such investment
         banking firm and the respective chosen firms shall agree on another
         investment banking firm which shall make the determination. The Issuer
         shall retain, at its sole cost, such investment banking firm as may be
         necessary for the determination of Appraised Value required by the
         terms of this Agreement.

14.      LIMITATION OF LIABILITY; NO RIGHTS AS STOCKHOLDER

         No provision hereof, in the absence of affirmative action by any
         Warrant Holder to purchase shares of Common Stock, and no enumeration
         herein of the rights or privileges of any Warrant Holder, shall give
         rise to any liability of such Warrant Holder for the purchase price of
         any Common Stock or as a stockholder of the Issuer, whether such
         liability is asserted by the Issuer or by creditors of the Issuer.
         Except as may otherwise be provided by law or by separate agreement
         between a Warrant Holder and the Issuer, no Warrant Holder, as such,
         shall be entitled to vote or be deemed the holder of Common Stock or
         any other securities (other than Warrants) of the Issuer which may at
         any time be issuable on the exercise hereof, nor shall anything
         contained herein be construed to confer upon any Warrant Holder the
         rights of a stockholder of the Issuer or the right to vote for the
         election of directors or upon any matters submitted to stockholders at
         any meeting thereof, or to give or withhold consent to any corporate
         action or to receive notice of meetings or other actions affecting
         stockholders (except as provided herein), or to receive dividends or
         otherwise, until the Warrants shall have been exercised in accordance
         with the terms and conditions hereof.

15.      MISCELLANEOUS

15.1     Non-waiver and Expenses. No course of dealing or any delay or failure
         to exercise any right hereunder on the part of any Warrant Holder shall
         operate as a waiver of such right or otherwise prejudice such Warrant
         Holder's rights, powers or remedies. If the Issuer fails to comply with
         any provision of this Agreement, the Issuer shall pay to the applicable
         Warrant Holders such amounts as shall be sufficient to cover any costs
         and expenses including, but not limited to, reasonable attorneys' fees,
         including those of appellate proceedings, incurred by the Warrant
         Holders in enforcing any of its rights, powers or remedies hereunder.

15.2     Notice Generally. Any notice, demand, request, consent, approval,
         declaration, delivery or other communication hereunder to be made
         pursuant to the provisions of this Agreement shall be sufficiently
         given or made if in writing and either delivered in person with receipt
         acknowledged or sent by registered or certified mail, return receipt
         requested, postage prepaid, telex, telecopier or overnight air courier
         guaranteeing next day delivery, addressed as follows:


                                       26
<PAGE>   30

         (a)      If to Societe Generale, as Warrant Holder, at:

                           Address:   1111 Bagby Street
                                      Suite 2020
                                      Houston, Texas 77002
                           Attention: Mark A. Cox
                           Telecopier No. (713) 650-0824

(b)      If to the Issuer at:

                           Brigham Exploration Company
                           6300 Bridge Point Parkway
                           Building 2, Suite 500
                           Austin, Texas 78730
                           Attention: President
                           Telecopier No.: (512) 427-3300

                  or at such other address as may be substituted by notice given
                  as herein provided. The giving of any notice required
                  hereunder may be waived in writing by the party entitled to
                  receive such notice. Every notice, demand, request, consent,
                  approval, declaration, delivery or other communication
                  hereunder shall be deemed to have been duly given or served on
                  the date on which personally delivered, with receipt
                  acknowledged, or three (3) Business Days after the same shall
                  have been deposited in the United States mail.

15.3     Indemnification. Except to the extent otherwise provided in Section 9.6
         of this Agreement, the Issuer agrees to indemnify and hold harmless
         each Warrant Holder and its officers, directors, employees, agents,
         attorneys and Affiliates (each an "Indemnified Party") from and against
         any liabilities, obligations, losses, damages, penalties, actions,
         judgments, suits, claims, costs, attorneys' fees, expenses and
         disbursements of any kind which may be imposed upon, incurred by or
         asserted against such Indemnified Party relating to or arising out of
         (i) such Warrant Holder's exercise of the Warrants and/or ownership of
         any shares of Warrant Stock issued in consequence thereof, or (ii) any
         litigation to which such Warrant Holder is made a party in its capacity
         as a stockholder or Warrant Holder of the Issuer; provided, however,
         that the Issuer will not be liable hereunder to the extent that any
         liabilities, obligations, losses, damages, penalties, actions,
         judgments, suits, claims, costs, attorneys' fees, expenses or
         disbursements (A) arise solely from any violation by such Warrant
         Holder of any law or regulation applicable to it or (B) are found in a
         final non-appealable judgment by a court to have resulted from such
         Warrant Holder's bad faith or willful misconduct or violation of law.
         The procedures to be followed for claims of indemnification under this
         Section 15.3 shall be as set forth in Section 9.6(d) of this Agreement.

15.4     Remedies. Each Warrant Holder of Warrants and Warrant Stock, in
         addition to being entitled to exercise all rights granted by law,
         including recovery of damages, will be entitled to specific performance
         of its rights under Section 9 of this Agreement. The Issuer agrees that
         monetary damages would not be adequate compensation for any loss


                                       27
<PAGE>   31

         incurred by reason of a breach by it of the provisions of Section 9 of
         this Agreement, and hereby agrees to waive any defense to the contrary
         in any action for specific performance that a remedy at law would be
         adequate.

15.5     Successors and Assigns. Subject to the provisions of Sections 3.1 and 9
         of this Agreement, this Agreement and the rights evidenced hereby shall
         inure to the benefit of and be binding upon the successor of the Issuer
         and the successors and assigns of any Warrant Holder. The provisions of
         this Agreement are intended to be for the benefit of all Warrant
         Holders from time to time of the Warrants and Warrant Stock, and shall
         be enforceable by any such Warrant Holder.

15.6     Complete Agreement; Amendment. This Agreement and the Warrant
         Certificates constitute the complete agreement among the parties with
         respect to the subject matter hereof. This Agreement may be modified or
         amended or the provisions hereof waived only with the written consent
         of the Issuer and the Required Holders, provided that no Warrant may be
         modified or amended to reduce the number of shares of Common Stock for
         which such Warrant is exercisable or to increase the price at which
         such shares may be purchased upon exercise of such Warrant (before
         giving effect to any adjustment as provided herein) or to accelerate
         the Expiration Date without the prior written consent of the Warrant
         Holder thereof, and any amendment of Section 9 of this Agreement shall
         also require the written consent of Warrant Holders of Warrants and/or
         Warrant Stock representing more than 50% of the total of (i) all shares
         of Warrant Stock then subject to purchase upon exercise of all Warrants
         then Outstanding, and (ii) all shares of Warrant Stock then
         Outstanding.

15.7     Severability. Wherever possible, each provision of this Agreement shall
         be interpreted in such manner as to be effective and valid under
         applicable law, but if any provision of this Agreement shall be
         prohibited by or invalid under applicable law, such provision shall be
         ineffective to the extent of such prohibition or invalidity, without
         invalidating the remainder of such provision or the remaining
         provisions of this Agreement.

15.8     Headings. The headings used in this Agreement are for the convenience
         of reference only and shall not, for any purpose, be deemed a part of
         this Agreement.

15.9     Governing Law; Consent to Jurisdiction and Venue. In all respects,
         including all matters of construction, validity and performance, this
         Agreement and the obligations arising hereunder shall be governed by,
         and construed and enforced in accordance with, the laws of the State of
         Texas applicable to contracts made and performed in such state, without
         regard to the principles thereof regarding conflict of laws, and any
         applicable laws of the United States of America.

15.10    Consent to Jurisdiction and Venue.

         (a)      THE ISSUER AND EACH WARRANT HOLDER HEREBY EXPRESSLY SUBMITS TO
                  THE JURISDICTION OF THE COURTS OF THE STATE OF TEXAS OR THE
                  UNITED STATES DISTRICT COURT FOR THE SOUTHERN DISTRICT OF
                  TEXAS. FINAL JUDGMENT AGAINST SUCH


                                       28
<PAGE>   32

                  PARTY IN ANY SUCH SUIT SHALL BE CONCLUSIVE, AND MAY BE
                  ENFORCED IN ANY OTHER JURISDICTIONS BY SUIT ON THE JUDGMENT OR
                  AS OTHERWISE PERMITTED BY APPLICABLE LAW, A CERTIFIED OR TRUE
                  COPY OF WHICH SHALL BE CONCLUSIVE EVIDENCE OF THE FACTS AND OF
                  THE AMOUNT OF ANY INDEBTEDNESS OR LIABILITY OF SUCH PARTY
                  THEREIN DESCRIBED; PROVIDED, HOWEVER, EACH PARTY MAY AT ITS
                  OPTION BRING SUIT, OR INSTITUTE OTHER JUDICIAL PROCEEDINGS
                  AGAINST THE OTHER PARTY OR ANY OF ITS ASSETS, IN THE COURTS OF
                  ANY COUNTRY OR PLACE WHERE SUCH PARTY OR SUCH ASSETS MAY BE
                  FOUND.

         (b)      THE ISSUER AND EACH WARRANT HOLDER HEREBY IRREVOCABLY WAIVES
                  ANY OBJECTION WHICH IT MAY NOW OR HEREAFTER HAVE TO THE LAYING
                  OF VENUE OF ANY SUIT, ACTION OR PROCEEDING BROUGHT IN ANY
                  COURTS OF THE STATE OF TEXAS OR THE UNITED STATES DISTRICT
                  COURT FOR THE SOUTHERN DISTRICT OF TEXAS AND HEREBY FURTHER
                  IRREVOCABLY WAIVES ANY CLAIM THAT ANY SUCH SUIT, ACTION OR
                  PROCEEDING BROUGHT IN ANY SUCH COURT HAS BEEN BROUGHT IN AN
                  INCONVENIENT FORUM.

15.11    Counterparts: This Agreement may be executed in two or more
         counterparts, each of which shall be deemed an original, but all of
         which together shall constitute one and the same instrument.


                                       29
<PAGE>   33

         IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be
duly executed as of the date first above written.



                                    BRIGHAM EXPLORATION COMPANY, as Issuer





                                    By:
                                       ----------------------------------------
                                    Printed Name:
                                                 ------------------------------
                                    Title:
                                          -------------------------------------



                                    SOCIETE GENERALE, Southwest Agency,
                                    as Warrant Holder



                                    By:
                                       ----------------------------------------
                                    Printed Name:
                                                 ------------------------------
                                    Title:
                                          -------------------------------------


                                       30
<PAGE>   34
                                                                    EXHIBIT A TO
                                                               Warrant Agreement



                          (FORM OF WARRANT CERTIFICATE)




THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER
THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES LAWS,
AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR AN
EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND
PRIVILEGES SPECIFIED IN THE WARRANT AGREEMENT, DATED AS OF JULY 19, 1999,
BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDER OF SECURITIES NAMED
THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF BRIGHAM EXPLORATION
COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER HEREOF UPON WRITTEN
REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES TO BE BOUND THEREBY.

No. ___

                               WARRANT CERTIFICATE

This Warrant Certificate certifies that Societe Generale, Southwest Agency, or
registered assigns thereof, is the holder of 338,462 warrants (the "Warrants")
to purchase shares of common stock of Brigham Exploration Company, a Delaware
corporation (the "Company"). Each Warrant entitles the holder, but only subject
to the conditions set forth herein and in the Warrant Agreement referred to
below, to purchase from the Company before 5:00 p.m., New York City time, on the
Expiration Date, as such term is defined in the Warrant Agreement, one fully
paid and non-assessable share of common stock of the Company ("Warrant Stock")
at a price (the "Exercise Price") of two and 25/100 dollars ($2.25) per share of
Warrant Stock payable as set forth in the Warrant Agreement. The number of
shares of Warrant Stock for which each Warrant is exercisable and the Exercise
Price are each subject to adjustment prior to the Expiration Date upon the
occurrence of certain events as set forth in the Warrant Agreement.

The Company may deem and treat the registered holders of the Warrants evidenced
hereby as the absolute owner thereof (notwithstanding any notation of ownership
or other writing hereon made by anyone), for the purpose of any exercise hereof
and of any distribution to the holders hereof, and for all other purposes.

Warrant Certificates, when surrendered at the office of the Company by the
registered holder hereof in person or by a legal representative duly authorized
in writing, may be exchanged, in the


                                    EXH. A-1
<PAGE>   35
manner and subject to the limitations provided in the Warrant Agreement, but
without payment of any service charge, for another Warrant Certificate or
Warrant Certificates of like tenor evidencing in the aggregate a like number of
Warrants.

Upon due presentment for registration of transfer of this Warrant Certificate at
the office of the Company at 6300 Bridge Point Parkway, Building 2, Suite 500,
Austin, Texas 78730, Attention: President, or such other address as the Company
may specify in writing to the registered holder of the Warrants evidenced
hereby, a new Warrant Certificate or Warrant Certificates of like tenor and
evidencing in the aggregate a like number of Warrants shall be issued to the
transferee in exchange for this Warrant Certificate to the transferee(s) and, if
less than all the Warrants evidenced hereby are to be transferred, the
registered holder hereof, subject to the limitations provided in the Warrant
Agreement, without charge except for any tax or other governmental charge
imposed in connection therewith.

The Warrant Certificate is one of the Warrant Certificates referred to in the
Warrant Agreement, dated as of July 19, 1999, between the Company and the
initial holder of Warrants party thereto (the "Warrant Agreement"). Said Warrant
Agreement is hereby incorporated by reference in and made a part of this
instrument and is hereby referred to for a description of the rights, limitation
of rights, obligations, duties and immunities thereunder of the Company and the
holders, and in the event of any conflict between the terms of this Warrant
Certificate and the provisions of the Warrant Agreement, the provisions of the
Warrant Agreement shall control.

IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to be duly
executed and its corporate seal to be impressed hereon and attached by its
secretary.

Dated: ____________________________, 1999.


                                    BRIGHAM EXPLORATION COMPANY


                                    By:
                                       ----------------------------------------
                                    Printed Name:
                                                 ------------------------------
                                    Title:
                                          -------------------------------------


(CORPORATE SEAL)

ATTEST:


- --------------------------------------
Secretary


                                    EXH. A-2
<PAGE>   36
                                                                    Exhibit A To
                                                             Warrant Certificate


                                SUBSCRIPTION FORM

                 [To be executed only upon exercise of Warrants]


The undersigned registered owner of this Warrant Certificate irrevocably
exercises Warrants for the purchase of shares of Common Stock of [     ] and
herewith makes payment therefor

         $_____   in cash

all at the price and on the terms and conditions specified in the Warrant
Certificate and the Warrant Agreement, and requests that certificates for the
shares of Common Stock hereby purchased (and any securities or other property
issuable upon such exercise) be issued in the name of ____________________ and
delivered to _____________________________ whose address is
________________________________ and, if such shares of Common Stock shall not
include all of the shares of Common Stock issuable as provided in the Warrant
Certificate, that a new Warrant Certificate of like tenor and date for the
balance of the shares of Common Stock issuable thereunder be delivered to the
undersigned.



- ----------------------------------------------
(Name of Registered Owner)



- ----------------------------------------------
(Signature of Registered Owner)



- ----------------------------------------------
(Street Address)



- ----------------------------------------------
(City)            (State)           (Zip Code)


                                    EXH. A-3
<PAGE>   37
                                                                    Exhibit B To
                                                             Warrant Certificate


                                 ASSIGNMENT FORM


FOR VALUE RECEIVED the undersigned registered owner of the attached Warrant
Certificate hereby sells, assigns and transfers unto the assignee named below
all of the rights of the undersigned under this Warrant Certificate, with
respect to the number of shares of Common Stock set forth below:

Name and Address of Assignee:
                               ---------------------------------

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

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

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

No. of Shares of
Common Stock
             -------

and does hereby irrevocably constitute and appoint ______ attorney-in-fact to
register such transfer on the books of [           ] maintained for that
purpose, with full power of substitution in the premises.

Dated:
      -------------------------------

Name:
     --------------------------------

Signature:
          ---------------------------

Witness:
        -----------------------------


The assignee named above hereby agrees to purchase and take the attached Warrant
Certificate pursuant to and in accordance with the terms and conditions of the
Warrant Agreement, dated as of ______________, 1999, between [          ] and
the initial Holder named therein and agrees to be bound thereby.

Dated:
      -------------------------------

Name:
     --------------------------------

Signature:
          ---------------------------


                         EXH. B-1 to Warrant Certificate
<PAGE>   38

                                                                    EXHIBIT B TO
                                                               Warrant Agreement



                      [FORM OF CASHLESS CONVERSION NOTICE]

             (To be executed upon a cashless exercise of a Warrant.)

         The undersigned hereby irrevocably elects to exercise the Cashless
Conversion, represented by this Warrant Certificate, to purchase ____ shares of
Common Stock and herewith tenders in payment for such shares this Warrant
Certificate, all in accordance with the terms hereof. The undersigned requests
that a certificate for such shares be registered in the name of _______________
_______________________________________________ whose address is ______________
________________________________________________ and that such certificate (or
any payment in lieu thereof) be delivered to ______________________________
whose address is ___________________________________.


Dated:
      -----------------------            --------------------------------------
                                         (Signature must conform in all respects
                                         to name of holder as specified on the
                                         face of the Warrant.)


         And if said number of shares shall not be all the shares exchangeable
or purchasable under the within Warrant, a new Warrant of like tenor is to be
issued in the name of the undersigned for the balance remaining of the shares
purchasable thereunder.


                                    EXH. B-1
<PAGE>   39
                                   SCHEDULE A


<TABLE>
<CAPTION>
                          Shares of                   Stock Options
                           Common                      Outstanding
                            Stock         -----------------------------------------         Warrants
                         Outstanding      Vested         Unvested           Total         Outstanding
                         -----------      -------        ---------        ---------       -----------
<S>                      <C>              <C>            <C>              <C>             <C>
As of July 19, 1999      14,309,071       267,104        1,307,383        1,574,487        1,000,000

     Issued 7/20/99         119,550
     Forfeited 7/30/99                                     (10,500)         (10,500)
     Forfeited 8/16/99                                    (263,888)        (263,888)
     Issued 8/17/99          89,165                        105,000          105,000
                         ----------       -------        ---------        ---------        ---------
As of August 18, 1999*   14,517,786       267,104        1,137,995        1,405,099        1,000,000
                         ----------       -------        ---------        ---------        ---------
</TABLE>


                                    SCH. A-1

<TABLE> <S> <C>

<ARTICLE> 5
<MULTIPLIER> 1,000

<S>                             <C>
<PERIOD-TYPE>                   9-MOS
<FISCAL-YEAR-END>                          DEC-31-1999
<PERIOD-START>                             JAN-01-1999
<PERIOD-END>                               SEP-30-1999
<CASH>                                           3,381
<SECURITIES>                                         0
<RECEIVABLES>                                    5,627
<ALLOWANCES>                                         0
<INVENTORY>                                          0
<CURRENT-ASSETS>                                 9,488
<PP&E>                                         108,311
<DEPRECIATION>                                       0
<TOTAL-ASSETS>                                 122,484
<CURRENT-LIABILITIES>                           16,993
<BONDS>                                              0
                                0
                                          0
<COMMON>                                           145
<OTHER-SE>                                       9,168
<TOTAL-LIABILITY-AND-EQUITY>                     9,313
<SALES>                                         10,855
<TOTAL-REVENUES>                                11,102
<CGS>                                                0
<TOTAL-COSTS>                                    2,364
<OTHER-EXPENSES>                                20,943
<LOSS-PROVISION>                                     0
<INTEREST-EXPENSE>                               9,087
<INCOME-PRETAX>                               (21,292)
<INCOME-TAX>                                         0
<INCOME-CONTINUING>                           (21,292)
<DISCONTINUED>                                       0
<EXTRAORDINARY>                                      0
<CHANGES>                                            0
<NET-INCOME>                                  (21,292)
<EPS-BASIC>                                     (1.52)
<EPS-DILUTED>                                   (1.52)


</TABLE>


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