BRIGHAM EXPLORATION CO
10-K/A, 1999-04-15
CRUDE PETROLEUM & NATURAL GAS
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<PAGE>   1
                                    The following items were the subject of a
                                    Form 12b-25 and are included herein: (1)
                                    financial statements of the Registrant's
                                    subsidiaries whose securities are pledged as
                                    collateral for the Registrant's Senior
                                    Subordinated Secured Notes and (2) the
                                    exhibits filed herewith.

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


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

                                   FORM 10-K/A
                                 AMENDMENT NO. 1
                            -------------------------

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

                        COMMISSION FILE NUMBER: 000-22433

                           BRIGHAM EXPLORATION COMPANY


             (Exact name of Registrant as Specified in its Charter)


                DELAWARE                                75-2692967
     (State or other jurisdiction of                 (I.R.S. Employer
     incorporation or organization)                 Identification No.)
        6300 BRIDGE POINT PARKWAY
          BUILDING 2, SUITE 500                            78730
             AUSTIN, TEXAS                              (Zip Code)
(Address of principal executive offices)

                                 (512) 427-3300
              (Registrant's telephone number, including area code)
                                 ---------------
           Securities registered pursuant to Section 12(b) of the Act:

<TABLE>
<CAPTION>
                                                 NAME OF EACH EXCHANGE ON
           TITLE OF EACH CLASS                       WHICH REGISTERED
           -------------------                   ------------------------
<S>                                              <C>   
                  None                                     None
</TABLE>

           Securities registered pursuant to Section 12(g) of the Act:
                          COMMON STOCK, $.01 PAR VALUE
                                (Title of Class)

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

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

     As of April 13, 1999, the Registrant had outstanding 14,309,071 shares of
Common Stock. The aggregate market value of the Common Stock held by
non-affiliates of the Registrant, based upon the closing sale price of the
Common Stock on April 13, 1999, as reported on The Nasdaq Stock Market(sm), was
approximately $35.8 million.

                       DOCUMENTS INCORPORATED BY REFERENCE

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

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


<PAGE>   2

         Item 14 of Brigham Exploration Company's Annual Report on Form 10-K for
the fiscal year ended December 31, 1998 is hereby amended in order to file the
following items which were the subject of a Form 12b-25 and were omitted from
the Company's Form 10-K as filed with the Securities and Exchange Commission on
March 31, 1999: (1) financial statements of the Registrant's subsidiaries whose
securities are pledged as collateral for the Registrant's Senior Subordinated
Secured Notes and (2) the exhibits (other than 23.1) filed herewith. Item 14 is
set forth herein in its entirety, as amended.


                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                                                 PAGE
                                                                                                                 ----

                                                      PART IV

<S>                                                                                                              <C>
     ITEM 14.  EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K....................................1
     SIGNATURES...................................................................................................7
     INDEX TO FINANCIAL STATEMENTS.............................................................................F1-1
</TABLE>





                                      - i -

<PAGE>   3
                           BRIGHAM EXPLORATION COMPANY

                         1998 ANNUAL REPORT ON FORM 10-K


                                     PART IV

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

(a)  1.     Financial Statements:

            See Index to Financial Statements on page F1-1.

     2.     Financial Statement Schedules:

            See Index to Financial Statements on page F1-1.

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

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


                                      - 1 -

<PAGE>   4
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.1.3        -- Amendment No. 3 to Agreement of Limited Partnership of Brigham                  
                 Oil & Gas, L.P., dated August 24, 1995, by and among Brigham                    
                 Exploration Company, General Atlantic Partners III, L.P.,                       
                 GAP-Brigham Partners, L.P., Harold D. Carter, Craig M. Fleming,                 
                 David T. Brigham and Jon L. Glass (filed as Exhibit 10.1.3 to the               
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.1.4+       -- Amended and Restated Agreement of Limited Partnership of Brigham                
                 Oil & Gas, L.P., dated December 30, 1997 by and among Brigham, Inc.,            
                 Brigham Holdings I, L.L.C. and Brigham Holdings II, L.L.C.                      
                                                                                                 
10.2          -- Agreement of Limited Partnership of Venture Acquisitions, L.P.,                 
                 dated September 23, 1994, by and between Quest Resources, L.L.C. and            
                 RIMCO Energy, Inc. as general partners, and RIMCO Production                    
                 Company, Inc., RIMCO Exploration Partners, L.P. I and RIMCO                     
                 Exploration Partners, L.P. II, as limited partners (filed as Exhibit            
                 10.2 to the Company's Registration Statement on Form S-1                        
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.3          -- Regulations of Quest Resources, L.L.C. (filed as Exhibit 10.3 to                
                 the Company's Registration Statement on Form S-1 (Registration No.              
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.4          -- Management and Ownership Agreement, dated September 23, 1994, by                
                 and among Brigham Oil & Gas, L.P., Brigham Exploration Company,                 
                 General Atlantic Partners III, L.P., Harold D. Carter, Ben M.                   
                 Brigham and GAP-Brigham Partners, L.P. (filed as Exhibit 10.4 to the            
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.5*         -- Consulting Agreement, dated May 1, 1997, by and between Brigham                 
                 Oil & Gas, L.P. and Harold D. Carter (filed as Exhibit 10.4 to the              
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 33-53873), and incorporated herein by reference).                               
                                                                                                 
10.6*         -- Employment Agreement, by and between Brigham Exploration Company                
                 and Ben M. Brigham (filed as Exhibit 10.7 to the Company's                      
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.7*         -- Form of Confidentiality and Noncompete Agreement between the                    
                 Registrant and each of its executive officers (filed as Exhibit 10.8            
                 to the Company's Registration Statement on Form S-1 (Registration               
                 No. 333-22491), and incorporated herein by reference).                          
                                                                                                 
10.8*         -- 1997 Incentive Plan of Brigham Exploration Company (filed as                    
                 Exhibit 10.9 to the Company's Registration Statement on Form S-1                
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.8.1*       -- Form of Option Agreement for certain executive officers (filed as               
                 Exhibit 10.9.1 to the Company's Registration Statement on Form S-1              
                 (Registration No. 333-22491), and incorporated herein by                       
                 reference).                                                                     
                                                                                                 
10.8.2*       -- Option Agreement dated as of March 4, 1997, by and between                      
                 Brigham Exploration Company and Jon L. Glass (filed as Exhibit                  
                 10.9.2 to the Company's Registration Statement on Form S-1                      
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.9*         -- Incentive Bonus Plan dated as of February 28, 1997 of Brigham,                  
                 Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit 10.10 to the                 
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.10         -- Two Bridgepoint Lease Agreement, dated September 30, 1996, by and               
                 between Investors Life Insurance Company of North America and                   
                 Brigham Oil & Gas, L.P.                                                         
</TABLE>


                                      - 2 -

<PAGE>   5
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 (filed as Exhibit 10.14 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.10.1       -- First Amendment to Two Bridge Point Lease Agreement dated April                 
                 11, 1997 between Investors Life Insurance Company of North America              
                 and Brigham Oil & Gas, L.P. (filed as Exhibit 10.9.1 to the                     
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-53873), and incorporated herein by reference).                              
                                                                                                 
10.10.2       -- Second Amendment to Two Bridge Point Lease Agreement dated                      
                 October 13, 1997 between Investors Life Insurance Company of North              
                 America and Brigham Oil & Gas, L.P. (filed as Exhibit 10.9.2 to the             
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-53873), and incorporated herein by reference).                              
                                                                                                 
10.10.3       -- Letter dated April 17, 1998 exercising Right of First Refusal to                
                 Lease "3rd Option Space" (filed as Exhibit 10.9.3 to the Company's              
                 Registration Statement on Form S-1 (Registration No. 333-53873), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.11         -- Anadarko Basin Seismic Operations Agreement, dated February 15,                 
                 1996, by and between Brigham Oil & Gas, L.P. and Veritas                        
                 Geophysical, Ltd. (filed as Exhibit 10.15 to the Company's                      
                 Registration Statement on Form S-1 (Registration No. 333-22491),               
                 and incorporated herein by reference).                                          
                                                                                                 
10.11.1       -- Letter Amendment to Anadarko Basin Seismic Operations Agreement,                
                 dated June 10, 1996, between Brigham Oil & Gas, L.P. and Veritas                
                 Geophysical, Ltd. (filed as Exhibit 10.15.1 to the Company's                    
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.12         -- Expense Allocation and Participation Agreement, dated April 1,                  
                 1996, between Brigham Oil & Gas, L.P. and Gasco Limited Partnership.            
                 (filed as Exhibit 10.16 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by              
                 reference).                                                                     
                                                                                                 
10.12.1       -- Amendment to Expense Allocation and Participation Agreement,                    
                 dated October 21, 1996, between Brigham Oil & Gas, L.P. and Gasco               
                 Limited Partnership (filed as Exhibit 10.16.1 to the Company's                  
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.13         -- Expense Allocation and Participation Agreement, dated April 1,                  
                 1996, between Brigham Oil & Gas, L.P. and Middle Bay Oil Company,               
                 Inc. (filed as Exhibit 10.17 to the Company's Registration Statement            
                 on Form S-1 (Registration No. 333-22491), and incorporated herein              
                 by reference).                                                                  
                                                                                                 
10.13.1       -- Amendment to Expense Allocation and Participation Agreement,                    
                 dated September 26, 1996, between Brigham Oil & Gas, L.P. and Middle            
                 Bay Oil Company, Inc. (filed as Exhibit 10.17.1 to the Company's                
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.13.2       -- Letter Amendment to Expense Allocation and Participation                        
                 Agreement, dated May 20, 1996, between Brigham Oil & Gas, L.P. and              
                 Middle Bay Oil Company, Inc. (filed as Exhibit 10.17.2 to the                   
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.14         -- Anadarko Basin Joint Participation Agreement, dated May 1, 1996,                
                 by and among Stephens Production Company and Brigham Oil & Gas, L.P.            
                 (filed as Exhibit 10.18 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by              
                 reference).                                                                     
                                                                                                 
10.15         -- Anadarko Basin Joint Participation Agreement, dated May 1, 1996,                
                 by and between Vintage Petroleum, Inc. and Brigham Oil & Gas, L.P.              
                 (filed as Exhibit 10.19 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.16         -- Processing Alliance Agreement, dated July 20, 1993, between                     
                 Veritas Seismic Ltd. and Brigham Oil & Gas, L.P. (filed as Exhibit              
                 10.20 to the Company's Registration                                             
</TABLE>


                                      - 3 -

<PAGE>   6
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 Statement on Form S-1 (Registration No. 333-22491), and incorporated            
                 herein by reference).                                                           
                                                                                                 
10.16.1       -- Letter Amendment to Processing Alliance Agreement, dated November               
                 3, 1994, between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.               
                 (filed as Exhibit 10.20.1 to the Company's Registration Statement on            
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.17         -- Agreement and Assignment of Interest, West Bradley Project, dated               
                 September 1, 1995, by and between Aspect Resources Limited Liability            
                 Company and Brigham Oil & Gas, L.P. (filed as Exhibit 10.21 to the              
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.18         -- Agreement and Assignment of Interests in lands located in Grady                 
                 County, Oklahoma, West Bradley Project, dated December 1, 1995, by             
                 and between Aspect Resources Limited Liability Company, Brigham Oil             
                 & Gas, L.P. and Venture Acquisitions, L.P. (filed as Exhibit 10.22              
                 to the Company's Registration Statement on Form S-1 (Registration               
                 No. 333-22491), and incorporated herein by reference).                          
                                                                                                 
10.19         -- Agreement and Assignment of Interests, West Bradley Project,                    
                 dated December 1, 1995, by and between Aspect Resources Limited                 
                 Liability Company and Brigham Oil & Gas, L.P. (filed as Exhibit                 
                 10.23 to the Company's Registration Statement on Form S-1                       
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.20         -- Geophysical Exploration Agreement, Hardeman Project, Hardeman and               
                 Wilbarger Counties, Texas and Jackson County, Oklahoma, dated March             
                 15, 1993 by and among General Atlantic Resources, Inc., Maynard Oil             
                 Company, Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ               
                 Exploration, Ltd., Cheyenne Petroleum Company, Antrim Resources,                
                 Inc., and Brigham Oil & Gas, L.P. (filed as Exhibit 10.24 to the                
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.21         -- Agreement and Partial Assignment of Interests in OK13-P Prospect                
                 Area, Jackson County, Oklahoma (Hardeman Project), dated August 1,              
                 1995, by and between Brigham Oil & Gas, L.P. and Aspect Resources               
                 Limited Liability Company (filed as Exhibit 10.25 to the Company's              
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.22         -- Agreement and Partial Assignment of Interests in Q140-E Prospect                
                 Area, Hardeman County, Texas (Hardeman Project), dated August 1,                
                 1995, by and between Brigham Oil & Gas, L.P. and Aspect Resources               
                 Limited Liability Company (filed as Exhibit 10.26 to the Company's              
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.23         -- Agreement and Partial Assignment of Interests in Hankins #1                     
                 Chappel Prospect Agreement, Jackson County, Oklahoma (Hardeman                  
                 Project), dated March 21, 1996, by and between Brigham Oil & Gas,               
                 L.P., NGR, Ltd. and Aspect Resources Limited Liability Company                  
                 (filed as Exhibit 10.27 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.24         -- Form of Indemnity Agreement between the Registrant and each of                  
                 its executive officers (filed as Exhibit 10.28 to the Company's                 
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.25         -- Registration Rights Agreement dated February 26, 1997 by and                    
                 among Brigham Exploration Company, General Atlantic Partners III                
                 L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P. II, RIMCO                
                 Partners L.P. III, and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne            
                 L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and            
                 Jon L. Glass (filed as Exhibit 10.29 to the Company's Registration              
                 Statement on Form S-1 (Registration No. 333-22491), and incorporated            
                 herein by reference).                                                           
</TABLE>



                                      - 4 -

<PAGE>   7

<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
10.26         -- 1997 Director Stock Option Plan (filed as Exhibit 10.30 to the                  
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.27         -- Form of Employee Stock Ownership Agreement (filed as Exhibit                    
                 10.31 to the Company's Registration Statement on Form S-1                       
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.28         -- Agreement and Assignment of Interest in Geophysical Exploration                 
                 Agreement, Esperson Dome Project, dated November 1, 1994, by and                
                 between Brigham Oil & Gas, L.P. and Vaquero Gas Company (filed as               
                 Exhibit 10.33 to the Company's Registration Statement on Form S-1               
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.29         -- Geophysical Exploration Agreement, Southwest Danbury Project,                   
                 Brazoria County, Texas, dated as of July 1, 1996, by and among                  
                 UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit 10.34 to             
                 the Company's Registration Statement on Form S-1 (Registration No.              
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.30         -- Geophysical Exploration Agreement, Welder Project, Duval County,                
                 Texas, dated as of October 1, 1996, by and among UNEXCO, Inc. and               
                 Brigham Oil & Gas, L.P. (filed as Exhibit 10.35 to the Company's                
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.31         -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion Parish,               
                 Louisiana, among Brigham Oil & Gas, L.P., Tigre Energy Corporation              
                 and Resource Investors Management Company (filed as Exhibit 10.36 to            
                 the Company's Registration Statement on Form S-1 (Registration No.              
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.31.1       -- Letter relating to Proposed Trade Structure, RIMCO/Tigre Project,               
                 dated January 31, 1997, from Resource Investors Management Company              
                 to Brigham Oil & Gas, L.P. (filed as Exhibit 10.36 to the Company's             
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.32         -- Anadarko Basin Seismic Operations Agreement II, dated as of April               
                 1, 1997, by and between Brigham Oil & Gas, L.P. (filed as Exhibit               
                 10.37 to the Company's Registration Statement on Form S-1                       
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.32.1       -- Letter Amendment to Anadarko Basin Seismic Operations Agreement                 
                 II, dated March 20, 1997, between Brigham Oil & Gas, L.P. and                   
                 Veritas DGC Land, Inc. (filed as Exhibit 10.37 to the Company's                 
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.33         -- Expense Allocation and Participation Agreement II, dated April 1,               
                 1997, between Brigham Oil & Gas, L.P., and Gasco Limited Partnership            
                 (filed as Exhibit 10.31 to the Company's Quarterly Report on Form               
                 10-Q for the quarter ended June 30, 1997, and incorporated herein by            
                 reference).                                                                     
                                                                                                 
10.36         -- Credit Agreement dated as of January 26, 1998 among Brigham Oil &               
                 Gas, L.P., Bank of Montreal, as Agent, and the lenders signatory                
                 thereto (filed as Exhibit 10.36 to the Company's Annual Report on               
                 Form 10-K for the year ended December 31, 1997, and incorporated                
                 herein by reference).                                                           
                                                                                                 
10.36.1+      -- First Amendment to Credit Agreement dated as of August 20, 1998                 
                 among Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and the              
                 lenders signatory thereto.                                                      
                                                                                                 
10.36.2++     -- Second Amendment to Credit Agreement dated as of March 26, 1999                 
                 among Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and the              
                 lenders signatory thereto.                                                      
                                                                                                 
10.37         -- Guaranty Agreement dated January 26, 1998 by Brigham Exploration                
                 Company in favor of Bank of Montreal, as Agent, and each of the                 
                 Lenders party to the Credit                                                     
</TABLE>


                                      - 5 -

<PAGE>   8
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 Agreement (filed as Exhibit 10.33.1 to the Company's Registration               
                 Statement on Form S-1 (Registration No. 333-53873), and incorporated            
                 herein by reference).                                                           
                                                                                                 
10.37.1       -- First Amendment to Guaranty Agreement dated as of March 30, 1998                
                 between Brigham Exploration Company and Bank of Montreal, as Agent              
                 for the Lenders party to the Credit Agreement (filed as Exhibit                 
                 10.33.2 to the Company's Registration Statement on Form S-1                     
                 (Registration No. 333-53873), and incorporated herein by reference).            
                                                                                                 
10.37.2+      -- Second Amendment to Guaranty Agreement dated as of August 20,                   
                 1998 between Brigham Exploration Company and Bank of Montreal, as               
                 Agent for the Lenders party to the Credit Agreement.                            
                                                                                                 
10.37.3++     -- Third Amendment to Guaranty Agreement dated as of March 26, 1999                
                 between Brigham Exploration Company and Bank of Montreal, as Agent              
                 for the Lenders party to the Credit Agreement.                                  
                                                                                                 
10.38+        -- Securities Purchase Agreement dated as of August 20, 1998 among                 
                 Brigham Exploration Company, Enron Capital & Trade Resources Corp.              
                 and Joint Energy Development Investments II Limited Partnership.                
                                                                                                 
10.39+        -- Registration Rights Agreement dated as of August 20, 1998, by and               
                 among Brigham Exploration Company, Enron Capital & Trade Resources              
                 Corp. and Joint Energy Development Investments II Limited                       
                 Partnership.                                                                    
                                                                                                 
10.39.1++     -- Amendment to Registration Rights Agreement dated as of March 26,                
                 1999, by and among Brigham Exploration Company, Enron Capital &                 
                 Trade Resources Corp., ECT Merchant Investments Corp. and Joint                 
                 Energy Development Investments II Limited Partnership.                          
                                                                                                 
10.40+        -- Form of Guaranty for subsidiaries.                                              
                                                                                                 
10.41++       -- Exchange Agreement dated as of March 30, 1999 by and between                    
                 Brigham Exploration Company and Veritas DGC Land, Inc.                          
                                                                                                 
10.42++       -- Registration Rights Agreement dated as of March 30, 1999 by and                 
                 between Brigham Exploration Company and Veritas DGC Land, Inc.                  
                                                                                                 
21+           -- Subsidiaries of the Registrant.                                                 
                                                                                                 
23.1++        -- Consent of Pricewaterhouse Coopers LLP, independent public                      
                 accountants.                                                                    
                                                                                                 
23.2+         -- Consent of Cawley, Gillespie & Associates, Inc., independent                    
                 petroleum engineers.                                                            
                                                                                                 
27+           -- Financial Data Schedule.                                                        
</TABLE>      



- ----------
*      Management contract or compensatory plan.
+      Previously filed
++     Filed herewith.


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

       None.


                                      - 6 -

<PAGE>   9

                                    SIGNATURE

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


                                      BRIGHAM EXPLORATION COMPANY


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





                                      - 7 -

<PAGE>   10



                          INDEX TO FINANCIAL STATEMENTS


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


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

Financial statements for the wholly owned subsidiaries whose securities are
pledged as collateral for the Senior Subordinated Notes are included in the
Financial Statements of Brigham Exploration Company Subsidiaries. The financial
statements for Brigham Oil & Gas L.P. for the year ended December 31, 1996,
whose partnerhsip interests are pledged as collateral for the Notes, are
substantially the same as those presented in the Consolidated Financial
Statements of Brigham Exploration Company.



                                      F1-1
<PAGE>   11


                        REPORT OF INDEPENDENT ACCOUNTANTS


To the Board of Directors
and Stockholders of Brigham Exploration Company

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



PricewaterhouseCoopers LLP

Houston, Texas
March 30, 1999



                                      F1-2


<PAGE>   12

                           BRIGHAM EXPLORATION COMPANY

                           CONSOLIDATED BALANCE SHEETS
                                 (in thousands)

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

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

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

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

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

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



        See accompanying notes to the consolidated financial statements.

                                      F1-3

<PAGE>   13

                           BRIGHAM EXPLORATION COMPANY

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

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

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

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

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

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

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

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

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



        See accompanying notes to the consolidated financial statements.

                                      F1-4


<PAGE>   14

                          BRIGHAM EXPLORATION COMPANY

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


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

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

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

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

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

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

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


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

<PAGE>   15

                          BRIGHAM EXPLORATION COMPANY

                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                                 (in thousands)

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

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

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

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

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

        See accompanying notes to the consolidated financial statements.

                                      F1-6
<PAGE>   16





                           BRIGHAM EXPLORATION COMPANY

                 NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS


1.   ORGANIZATION AND NATURE OF OPERATIONS

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

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

2.   SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

Basis of Accounting

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

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

Principles of Consolidation

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


                                      F1-7

<PAGE>   17



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Cash and Cash Equivalents

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

Property and Equipment

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

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

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

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

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

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


                                      F1-8

<PAGE>   18



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

Revenue Recognition

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

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

Derivative Instruments

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

Stock Based Compensation

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

Federal and State Income Taxes

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

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


                                      F1-9

<PAGE>   19



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Unaudited Pro Forma Information

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

Comprehensive Income

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

Recent Pronouncements

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

3.   ACQUISITION

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

                                      F1-10

<PAGE>   20



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Pro Forma Information

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


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

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

4.   PROPERTY AND EQUIPMENT

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

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


                                     F1-11
<PAGE>   21
                          BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)

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

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

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

5.   NOTES PAYABLE AND SENIOR SUBORDINATED NOTES PAYABLE

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

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

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


                                      F1-12

<PAGE>   22



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

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

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

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

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

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

                                      F1-13

<PAGE>   23


                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


6.   CAPITAL LEASE OBLIGATIONS

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

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

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


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

7.   INCOME TAXES

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


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

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

                                      F1-14

<PAGE>   24



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



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

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


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

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

8.   NET INCOME (LOSS) PER SHARE

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

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

                                      F1-15

<PAGE>   25



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

Litigation

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

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

Lease Commitments

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


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

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

Factors Which May Affect Future Operations

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

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

                                      F1-16

<PAGE>   26



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

10.  SEGMENT INFORMATION

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

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

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

11.  FINANCIAL INSTRUMENTS

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

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

                                      F1-17

<PAGE>   27



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

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

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

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

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

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

12.  EMPLOYEE BENEFIT PLANS

Retirement Savings Plan

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

                                      F1-18

<PAGE>   28

                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


Stock Compensation

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

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

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

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


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

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

                                      F1-19

<PAGE>   29



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

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

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

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

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


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

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

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


                                      F1-20

<PAGE>   30



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



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


13.  RELATED PARTY TRANSACTIONS

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

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

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

14.  SUBSEQUENT EVENT

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



                                     F1-21

<PAGE>   31



                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


15.  NATURAL GAS AND OIL EXPLORATION AND PRODUCTION ACTIVITIES

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

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


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

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

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

Costs Incurred and Capitalized Costs

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

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

                                     F1-22
<PAGE>   32


                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)


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

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

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

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


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

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

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

Natural Gas and Oil Reserve Data

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

                                      F1-23

<PAGE>   33


                           BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



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

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

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

Standardized Measure of Discounted Future Net Cash Inflows and Changes Therein

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


                                      F1-24

<PAGE>   34
                          BRIGHAM EXPLORATION COMPANY

          NOTES TO THE CONSOLIDATED FINANCIAL STATEMENTS - (CONTINUED)



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

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

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

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

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


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

                                     F1-25

<PAGE>   35


                       REPORT OF INDEPENDENT ACCOUNTANTS


To the Board of Directors
 and Stockholders of Brigham Exploration Company

In our opinion, the accompanying balance sheets and the related statements of
operations, of cash flows and of changes in equity present fairly, in all
material respects, the financial position of Brigham Oil & Gas, L.P., and
Brigham, Inc. at December 31, 1998 and 1997, and the results of their operations
and their cash flows for each of the two years in the period ended December 31,
1998, in conformity with generally accepted accounting principles. Additionally,
in our opinion, the accompanying balance sheets and the related statements of
operations, of cash flows and of changes in equity present fairly, in all
material respects, the financial position of Brigham Holdings I, LLC and Brigham
Holdings II, LLC at December 31, 1998 and for the year then ended, in conformity
with generally accepted accounting principles. These financial statements are
the responsibility of management; our responsibility is to express an opinion on
these financial statements based on our audits. We conducted our audits of these
statements in accordance with generally accepted auditing standards which
require that we plan and perform the audit to obtain reasonable assurance about
whether the financial statements are free of material misstatement. An audit
includes examining, on a test basis, evidence supporting the amounts and
disclosures in the financial statements, assessing the accounting principles
used and significant estimates made by management, and evaluating the overall
financial statement presentation. We believe that our audits provide a
reasonable basis for the opinion expressed above.





PricewaterhouseCoopers LLP

Houston, Texas
April 14, 1999




                                      F2-1
<PAGE>   36

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                                 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           --          --
Other noncurrent assets                                                        1,409       1,409           --          --
                                                                           ---------   ---------    ---------   ---------
                                                                           $ 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 financial statements.

                                      F2-2
<PAGE>   37

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                                 BALANCE SHEETS
                             AS OF DECEMBER 31, 1997
                                 (in thousands)

<TABLE>
<CAPTION>
                                                         BRIGHAM
                                                          OIL &      BRIGHAM,
                                                         GAS, L.P.     INC.
<S>                                                       <C>        <C>     
                                     ASSETS
Current assets:
     Cash and cash equivalents                            $  1,701   $  1,701
     Accounts receivable                                     4,909      4,909
     Prepaid expenses                                          280        280
                                                          --------   --------
                Total current assets                         6,890      6,890
                                                          --------   --------

Natural gas and oil properties, at cost, net                84,294     84,294
Other property and equipment, at cost, net                   1,239      1,239
Drilling advances paid                                          78         78
Other noncurrent assets                                         18         18
                                                          --------   --------
                                                          $ 92,519   $ 92,519
                                                          ========   ========

                             LIABILITIES AND EQUITY
Current liabilities:
     Accounts payable                                     $ 11,892   $ 11,892
     Accrued drilling costs                                  2,406      2,406
     Participant advances received                             489        489
     Other current liabilities                                 726        726
                                                          --------   --------
                Total current liabilities                   15,513     15,513
                                                          --------   --------

Notes payable                                               32,000     32,000
Other noncurrent liabilities                                   507        507
Deferred income tax liability                                   --      5,088
Intercompany accounts payable                                  834        834

Minority interest                                               --     29,910

Equity
     Partners' capital                                      43,665         --
     Common stock, $1.00 par value, 1,000 shares
                     authorized, issued and outstanding         --          1
     Additional paid-in capital                                 --     13,732
     Accumulated deficit                                        --     (5,066)
                                                          --------   --------
                Total equity                                43,665      8,667
                                                          --------   --------
                                                          $ 92,519   $ 92,519
                                                          ========   ========
</TABLE>

  Natural gas and oil properties are accounted for using the full cost method.




               See accompanying notes to the financial statements.



                                      F2-3
<PAGE>   38

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                            STATEMENTS OF OPERATIONS
                      FOR THE YEAR ENDED 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>          
Revenues:
     Natural gas and oil sales                          $      13,799     $      13,799    $          --     $          --
     Workstation revenue                                          390               390               --                --
                                                        -------------     -------------    -------------     -------------
                                                               14,189            14,189               --                --
                                                        -------------     -------------    -------------     -------------
Costs and expenses:
     Lease operating                                            2,172             2,172               --                --
     Production taxes                                             850               850               --                --
     General and administrative                                 4,650             4,661               11                11
     Depletion of natural gas and oil properties                8,410             8,410               --                --
     Depreciation and amortization                                413               413               --                --
     Capitalized ceiling impairment                            24,847            24,847               --                --
     Amortization of stock compensation                           372               372               --                --
                                                        -------------     -------------    -------------     -------------
                                                               41,714            41,725               11                11
                                                        -------------     -------------    -------------     -------------
           Operating loss                                     (27,525)          (27,536)             (11)              (11)
                                                        -------------     -------------    -------------     -------------

Other income (expense):
     Interest income                                              136               136               --                --
     Interest expense                                          (4,993)           (4,993)              --                --
     Interest expense - intercompany                           (1,707)           (1,707)              --            (1,707)
                                                        -------------     -------------    -------------     -------------
                                                               (6,564)           (6,564)              --            (1,707)
                                                        -------------     -------------    -------------     -------------

Minority interest in net loss                                      --           (23,351)              --                --
                                                        -------------     -------------    -------------     -------------
Net loss before income taxes                                  (34,089)          (10,749)             (11)           (1,718)

Income tax expense                                                 --             5,088               --                --
Equity in net loss of investee                                     --                --          (23,351)           (8,690)
                                                        -------------     -------------    -------------     -------------
     Net loss                                           $     (34,089)    $      (5,661)   $     (23,362)    $     (10,408)
                                                        =============     =============    =============     ============= 
</TABLE>





               See accompanying notes to the financial statements.



                                      F2-4
<PAGE>   39

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                            STATEMENTS OF OPERATIONS
                      FOR THE YEAR ENDED DECEMBER 31, 1997
                                 (in thousands)

<TABLE>
<CAPTION>
                                                  BRIGHAM
                                                   OIL &      BRIGHAM,
                                                  GAS, L.P.     INC.
<S>                                                <C>        <C>    
Revenues:
     Natural gas and oil sales                     $ 9,184    $ 9,184
     Workstation revenue                               637        637
                                                   -------    -------
                                                     9,821      9,821
                                                   -------    -------
Costs and expenses:
     Lease operating                                 1,151      1,151
     Production taxes                                  549        549
     General and administrative                      3,570      3,570
     Depletion of natural gas and oil properties     2,743      2,743
     Depreciation and amortization                     306        306
     Amortization of stock compensation                388        388
                                                   -------    -------
                                                     8,707      8,707
                                                   -------    -------
             Operating income                        1,114      1,114
                                                   -------    -------

Other income (expense):
     Interest income                                   145        145
     Interest expense                               (1,017)    (1,017)
     Interest expense - related party                 (173)      (173)
                                                   -------    -------
                                                    (1,045)    (1,045)
                                                   -------    -------

Minority interest in net income                         --         47
                                                   -------    -------
Net income before income taxes                          69         22

Income tax benefit                                      --     (5,088)
                                                   -------    -------
     Net income (loss)                             $    69    $(5,066)
                                                   =======    =======
</TABLE>





               See accompanying notes to the financial statements.




                                      F2-5
<PAGE>   40

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                            STATEMENTS OF CASH FLOWS
                      FOR THE YEAR ENDED 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>       
Cash flows from operating activities:
     Net loss                                                            $ (34,089)   $  (5,661)   $ (23,362)   $ (10,408)
     Adjustments to reconcile net loss to cash
     provided by operating activities:
         Depletion of natural gas and oil properties                         8,410        8,410           --           --
         Depreciation and amortization                                         413          413           --           --
         Capitalized ceiling impairment                                     24,847       24,847           --           --
         Amortization of stock compensation                                    372          372           --           --
         Amortization of deferred loan fees and debt issuance costs            593          593           --           --
         Minority interest in net loss                                          --      (23,351)          --           --
         Equity in net loss of investee                                         --           --       23,351        8,690
         Changes in working capital and other items:
            Increase in accounts receivable                                 (3,029)      (3,029)          --           --
            Increase in prepaid expenses                                       (10)         (10)          --           --
            Increase in accounts payable                                     7,991        7,991           --           --
            Increase in participant advances received                          275          275           --           --
            Increase in other current liabilities                              862          862           --           --
            Decrease in deferred income tax liability                           --       (5,088)          --           --
            Increase in intercompany accounts payable                           --           --           --        1,707
            Other noncurrent assets                                              6            6           --           --
            Other noncurrent liabilities                                     7,004        7,004           --           --
                                                                         ---------    ---------    ---------    ---------
                                                                            13,645       13,634          (11)         (11)
                                                                         ---------    ---------    ---------    ---------
Cash flows from investing activities:
     Natural gas and oil properties                                        (84,056)     (84,056)          --           --
     Other property and equipment                                             (868)        (868)          --           --
     Investment in subsidiaries and intercompany advances                      (42)         (17)      (5,154)     (42,285)
     Change in drilling advances paid                                         (153)        (153)          --           --
                                                                         ---------    ---------    ---------    ---------
                                                                           (85,119)     (85,094)      (5,154)     (42,285)
                                                                         ---------    ---------    ---------    ---------
Cash flows from financing activities:
     Capital contribution received                                           7,548        7,548        5,170        2,302
     Increase in intercompany notes payable                                 40,000       40,000           --       40,000
     Increase in notes payable                                             105,800      105,800           --           --
     Repayment of notes payable                                            (78,800)     (78,800)          --           --
     Principal payments on capital lease obligations                          (236)        (236)          --           --
     Deferred loan fees                                                     (1,990)      (1,990)          --           --
                                                                         ---------    ---------    ---------    ---------
                                                                            72,322       72,322        5,170       42,302
                                                                         ---------    ---------    ---------    ---------

Net increase in cash and cash equivalents                                      848          862            5            6

Cash and cash equivalents, beginning of year                                 1,701        1,701           --           --
                                                                         ---------    ---------    ---------    ---------
Cash and cash equivalents, end of year                                   $   2,549    $   2,563    $       5    $       6
                                                                         =========    =========    =========    =========

Supplemental disclosure of cash flow information:
     Cash paid during the year for interest                              $   4,878    $   4,878    $      --    $      -- 

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 financial statements.



                                      F2-6
<PAGE>   41

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                            STATEMENTS OF CASH FLOWS
                      FOR THE YEAR ENDED DECEMBER 31, 1997
                                 (in thousands)

<TABLE>
<CAPTION>
                                                                            BRIGHAM
                                                                             OIL &           BRIGHAM,
                                                                           GAS, L.P.           INC.
<S>                                                                      <C>             <C>          
Cash flows from operating activities:
     Net income (loss)                                                   $         69    $     (5,066)
     Adjustments to reconcile net income (loss) to cash
     provided by operating activities:
         Depletion of natural gas and oil properties                            2,743           2,743
         Depreciation and amortization                                            306             306
         Amortization of stock compensation                                       388             388
         Minority interest in net income                                           --              47
         Changes in working capital and other items:
            Increase in accounts receivable                                    (2,213)         (2,213)
            Increase in prepaid expenses                                         (128)           (128)
            Increase in accounts payable                                        8,955           8,955
            Decrease in participant advances received                            (648)           (648)
            Increase in other current liabilities                                  50              50
            Increase in deferred interest payable - related party                  53              53
            Increase in deferred income tax liability                              --           5,088
            Other noncurrent assets                                               281             281
            Other noncurrent liabilities                                          (50)            (50)
                                                                         ------------    ------------
                                                                                9,806           9,806
                                                                         ------------    ------------
Cash flows from investing activities:
     Natural gas and oil properties                                           (57,170)        (57,170)
     Proceeds from the sale of natural gas and oil properties                      74              74
     Other property and equipment                                                (545)           (545)
     Change in drilling advances paid                                             341             341
                                                                         ------------    ------------
                                                                              (57,300)        (57,300)
                                                                         ------------    ------------
Cash flows from financing activities:
     Capital contribution received                                             23,927          23,927
     Increase in notes payable                                                 37,250          37,250
     Repayment of notes payable                                               (13,250)        (13,250)
     Principal payments on capital lease obligations                             (179)           (179)
                                                                         ------------    ------------
                                                                               47,748          47,748
                                                                         ------------    ------------

Net increase in cash and cash equivalents                                         254             254

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

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

Supplemental disclosure of noncash investing and financing activities:
     Capital lease asset additions                                       $        403    $        403
     Intercompany capital contributions                                  $     16,425    $         --
     Increase resulting from the Exchange and the Offering
         in ownership interest in the Partnership                        $         --    $     13,703
</TABLE>

               See accompanying notes to the financial statements.



                                      F2-7
<PAGE>   42

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

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

<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, 1997             --   $        --   $        --   $        --    $    43,665    $    43,665
     Capital contribution            --            --            --            --          7,548          7,548
     Net loss                                      --            --            --        (34,089)       (34,089)
                            -----------   -----------   -----------   -----------    -----------    -----------
     Balance,
       December 31, 1998             --   $        --   $        --   $        --    $    17,124    $    17,124
                            ===========   ===========   ===========   ===========    ===========    ===========

BRIGHAM INC. 
     Balance,
       December 31, 1997          1,000   $         1   $    13,732   $    (5,066)   $        --    $     8,667
     Capital contribution            --            --         2,377            --             --          2,377
     Net loss                        --            --            --        (5,661)            --         (5,661)
                            -----------   -----------   -----------   -----------    -----------    -----------
     Balance,
       December 31, 1998          1,000   $         1   $    16,109   $   (10,727)   $        --    $     5,383
                            ===========   ===========   ===========   ===========    ===========    ===========

BRIGHAM HOLDING I, LLC
     Balance,
       December 31, 1997             --   $        --   $        --   $        --    $        --    $        -- 
     Partnership interest
       contributed                   --            --            --            --         29,911         29,911
     Capital contribution            --            --            --            --          5,170          5,170
     Net loss                        --            --            --            --        (23,362)       (23,362)
                            -----------   -----------   -----------   -----------    -----------    -----------
     Balance,
       December 31, 1998             --   $        --   $        --   $        --    $    11,719    $    11,719
                            ===========   ===========   ===========   ===========    ===========    ===========

BRIGHAM HOLDINGS II, LLC
     Balance,
       December 31, 1997             --   $        --   $        --   $        --    $        --    $        -- 
     Partnership interest
       contributed                   --            --            --            --         13,318         13,318
     Capital contribution            --            --            --            --          2,302          2,302
     Net loss                        --            --            --            --        (10,408)       (10,408)
                            -----------   -----------   -----------   -----------    -----------    -----------
     Balance,
       December 31, 1998             --   $        --   $        --   $        --    $     5,212    $     5,212
                            ===========   ===========   ===========   ===========    ===========    ===========
</TABLE>

              See accompanying notes to the financial statements.





                                     F2-8
<PAGE>   43

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                        STATEMENTS OF CHANGES IN EQUITY
                                 (in thousands)

<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, 1996                          --   $         --   $         --   $         --    $      3,244   $      3,244
     Capital contribution from
       Brigham Exploration
       Company at consummation
       of Exchange                                --             --             --             --          16,425         16,425
     Capital contribution from
       Brigham Exploration
       Company of proceeds
       from Offering                              --             --             --             --          23,927         23,927
     Net income                                   --             --             --             --              69             69
                                        ------------   ------------   ------------   ------------    ------------   ------------
     Balance,
       December 31, 1997 should be                --   $         --   $         --   $         --    $     43,665   $     43,665
                                        ============   ============   ============   ============    ============   ============
       

BRIGHAM INC. 
     Balance,
       December 31, 1996                       1,000   $          1   $         29   $         --    $         --   $         30
     Increase in equity due to
       change in ownership in the
       Partnership resulting from the
       Exchange and the Offering                  --             --         13,703             --              --         13,703
     Net loss                                     --             --             --         (5,066)             --         (5,066)
                                        ------------   ------------   ------------   ------------    ------------   ------------
     Balance,
       December 31, 1997                       1,000   $          1   $     13,732   $     (5,066)   $         --   $      8,667
                                        ============   ============   ============   ============    ============   ============
</TABLE>



              See accompanying notes to the financial statements.




                                      F2-9
<PAGE>   44

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                        NOTES TO THE FINANCIAL STATEMENTS


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.

     Pursuant to an exchange agreement dated February 26, 1997 (the "Exchange
Agreement") and upon the initial filing on February 27, 1997 of a registration
statement with the Securities and Exchange Commission (the "SEC") for the public
offering of common stock (the "Offering"), the shareholders of Brigham, Inc.
transferred all of the outstanding stock of Brigham, Inc. to the Company in
exchange for 3,859,821 shares of common stock of the Company. Pursuant to the
Exchange Agreement, the Partnership's other general partner and the limited
partners also transferred all of their partnership interests to the Company in
exchange for 3,314,286 shares of common stock of the Company. Furthermore, the
holders of the Partnership's subordinated convertible notes transferred these
notes to the Company in exchange for 1,754,464 shares of common stock. These
transactions are referred to as "the Exchange." In completing the Exchange, the
Company issued 8,928,571 shares of common stock to the stockholders of Brigham,
Inc., the partners of the Partnership and the holder of the Partnership's
subordinated notes payable. In May 1997, the Company sold 3,325,000 shares of
its common stock in the Offering at a price of $8.00 per share. As a result of
the Exchange and the Offering, the Company owns a 68.5% partnership interest in
the Partnership and all of the outstanding shares of Brigham, Inc. Brigham, Inc.
owns the remainder of the Partnership interest in the Partnership. The proceeds
of the Offering were contributed to the Partnership by the Company.

     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 Holdings I, a newly formed Nevada LLC and
wholly owned subsidiary of the Company whose only asset is its investment in the
Partnership.




                                     F2-10
<PAGE>   45


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)


2.   SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

Basis of Accounting

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

Principles of Consolidation

     The accompanying financial statements include the accounts of the
Partnership, Brigham, Inc., Holdings I and Holdings II (collectively referred to
as the "Subsidiaries"). Holdings II accounts for its interest in the Partnership
under the equity method. Brigham, Inc. consolidates its interests in the
Partnership and Holdings II as a result of its general partner interest in the
Partnership and its 100% ownership of Holdings II. Holdings I accounts for its
68.5% investment in the Partnership under the equity method and its ownership in
the Partnership is reflected as the minority interest in the consolidated
results of Brigham, Inc. All entities are either directly or indirectly
wholly-owned subsidiaries of the Company. All significant intercompany accounts
and transactions have been eliminated.

     Substantially all of the Subsidiaries' assets are held by and all
operations conducted through the Partnership and its subsidiaries. All
references in these financial statements to assets held by the Partnership and
transactions entered into by the Partnership are applicable to Brigham, Inc.
through its consolidation of the Partnership.      

Cash and Cash Equivalents

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

Property and Equipment

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

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

     All costs directly associated with the acquisition and evaluation of
unproved properties are initially excluded from the Amortizable Base. Upon the
interpretation by the Partnership of the 3-D seismic data associated with
unproved properties, the geological and geophysical costs related to acreage
that is not specifically identified as



                                     F2-11
<PAGE>   46

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



prospective are added to the Amortizable Base. Geological and geophysical costs
associated with prospective acreage, as well as leasehold costs, are added to
the Amortizable Base when the prospects are drilled. Costs of prospective
acreage are reviewed annually for impairment on a property-by-property basis.

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

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

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

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

Revenue Recognition

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

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

Derivative Instruments

     Net realized gains or losses and related cash flows arising from the
Partnership's commodity price swaps (see Note 10) are recognized in the period
incurred as a component of natural gas and oil sales. If subsequent to being
hedged, underlying transactions are determined not to be likely to occur, the
related derivatives gains and losses are recognized in that period as "Other
income."

Federal and State Income Taxes

     The Subsidiaries other than Brigham, Inc. are not taxable entities and as a
result, no income tax provision has been recorded. However, the taxable income
or loss resulting from their operations will ultimately be included in the
federal and state income tax returns of the Company and may vary substantially
from the income or loss reported for financial reporting purposes.





                                     F2-12
<PAGE>   47

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



     Brigham, Inc., which is included in the Company's consolidated income tax
return, is subject to federal corporate income taxation and utilizes an asset
and liability approach for accounting for income taxes that requires the
recognition of deferred tax assets and liabilities for the expected future tax
consequences of temporary differences between the carrying amounts and tax bases
of assets and liabilities. Resulting tax liabilities, if any, are borne by the
Company.

Comprehensive Income

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

Recent Pronouncements

     In June 1998, the FASB issued SFAS No. 133, "Accounting for Derivative
Instruments and Hedging Activities." SFAS No. 133 requires that all derivative
instruments be recorded on the balance sheet at fair value. Changes in the fair
value of derivatives are recorded each period in current earnings or other
comprehensive income, depending on whether a derivative is designated as part of
a hedge transaction and, if it is, depending on the type of hedge transaction.
For fair value hedge transactions in which the 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 effective
January 1, 2000. The Partnership is in the process of analyzing the potential
impact of this standard on its financial statement presentation.

3.   ACQUISITION

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

Pro Forma Information

     The following unaudited pro forma statement of operations information has
been prepared to give effect to the Acquisition as if the transaction had
occurred at the beginning of 1997. The Partnership's historical results of


                                     F2-13
<PAGE>   48

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



operations have been adjusted to reflect (i) the difference between the acquired
properties' historical depletion and such expense calculated based on the value
allocated to the acquired assets, and (ii) the increase in interest expense
associated with the debt issued in the transaction. The pro forma amounts do not
purport to be indicative of the results of operations that would have been
reported had the Acquisition occurred as of the dates indicated, or that may be
reported in the future (in thousands).


<TABLE>
<CAPTION>
                                                          PRO FORMA
                                                         YEAR ENDED
                                                        DECEMBER 31,
                                                            1997
                                                        ------------
<S>                                                       <C>     
Revenues ..............................................   $ 11,194
Costs and expenses:
       Lease operating and production taxes ...........      1,864
       General and administrative .....................      3,570
       Depletion of natural gas and oil properties ....      3,307
       Depreciation and amortization ..................        593
       Interest expense, net ..........................      2,235
                                                          --------
       Total costs and expenses .......................     11,569
                                                          --------
Net loss ..............................................   $   (375)
                                                          ========
</TABLE>

     Upon consolidation with Brigham, Inc., pro-forma income tax expense would
be $5,040.

4.   PROPERTY AND EQUIPMENT

     Property and equipment (held by the Partnership), at cost, are summarized
as follows (in thousands):

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

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

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




                                     F2-14
<PAGE>   49

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



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

5.   NOTES PAYABLE AND SENIOR SUBORDINATED NOTES PAYABLE

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

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

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

     In March 1999, the Partnership and its lenders entered into an amendment to
the Credit Facility. Pursuant to this amendment, the borrowing availability
under the Credit Facility remains at $65 million and the initial borrowing
availability redetermination date was extended from January 31, 1999 to June 1,
1999, when the borrowing availability will be redetermined by the lenders based
on the Partnership's then proved reserve value and cash flows. To the extent
that the amounts outstanding under the Credit Facility exceed the borrowing
availability at the redetermination date, the Partnership may be required to
repay such excess under provision of the amendment. In addition, certain
financial covenants have been amended, additional covenants have been included
that place significant restrictions on the Partnership's ability to make certain
capital expenditures, and the annual interest rate for borrowings under the
Credit Facility is revised to the lender's base rate or LIBOR plus 3.0% 


                                     F2-15
<PAGE>   50

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



and the Partnership will pay the lender a $500,000 transaction fee over a ten
month period. The Partnership's obligations under the Credit Facility are
secured by substantially all of the natural gas and oil properties and other
tangible assets of the Partnership.

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

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

     The Notes are fully and unconditionally guaranteed, on a joint and several
basis, by each of the Subsidiaries all of which are directly or indirectly
wholly-owned by the Company. The obligations of the Subsidiaries under the
subsidiary guaranty agreements are subordinated to the senior indebtedness of
the Partnership. Furthermore, all Subsidiaries have pledged their respective
stock and Partnership interests as collateral for the Notes.

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

     The $40 million in proceeds from the Notes and Warrants were transferred
through a series of intercompany notes from the Company to Brigham, Inc.; from
Brigham, Inc. to Holdings II; and from Holdings II to the Partnership. Principal
on the intercompany notes is due at the maturity of the Notes and intercompany
interest accrues at rates corresponding to those applicable to the Notes.
Approximately $7.6 million of the proceeds from the common stock was transferred
through a series of intercompany capital contributions from the Company to
Holdings I ($5.2 million) and Brigham, Inc. ($2.4 million); from Holdings I to
the Partnership ($5.2 million); from Brigham, Inc. to Holdings II ($2.3 million)
and the Partnership ($75,000); and from Holdings II to the Partnership ($2.3
million).

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



                                     F2-16
<PAGE>   51


                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



6.   CAPITAL LEASE OBLIGATIONS

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


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

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

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

7.   INCOME TAXES

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


<TABLE>
<CAPTION>
                                                 YEAR ENDED
                                                 DECEMBER 31,
                                              ------------------
                                                1998       1997
                                              -------    -------
<S>                                           <C>        <C>    
Current income taxes:
    Federal................................   $    --    $    --
    State .................................        --         --
Deferred income taxes:
    Federal ...............................    (5,088)     5,088
    State .................................        --         --
                                              -------    -------
                                              $(5,088)   $ 5,088
                                              =======    =======
</TABLE>



                                     F2-17
<PAGE>   52

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



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

<TABLE>
<CAPTION>
                                                YEAR ENDED
                                               DECEMBER 31,
                                      ----------------------------
                                           1998            1997
                                      ------------    ------------
<S>                                   <C>             <C>         
Tax at statutory rate .............   $     (3,655)   $          7
Add (deduct) the effect of:
    Tax effect of Exchange ........         (1,433)          5,081
                                      ------------    ------------
                                      $     (5,088)   $      5,088
                                      ============    ============
</TABLE>

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


<TABLE>
<CAPTION>
                                                         DECEMBER 31,
                                                ----------------------------
                                                     1998            1997
                                                ------------    ------------
<S>                                             <C>             <C>         
Deferred tax assets:
    Net operating loss carryforwards ........   $      4,767    $      1,496
Deferred tax liability:
    Depreciable and depletable property .....         (4,767)         (6,584)
                                                ------------    ------------
                                                $         --    $     (5,088)
                                                ============    ============
</TABLE>

     At December 31, 1998, Brigham, Inc. had regular and alternative minimum tax
net operating loss carryforwards of approximately $14 million and $11 million,
respectively, each including separate return limitation year carryovers of
approximately $1.2 million, which expire by December 31, 2018.

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

Litigation

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

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

Lease Commitments

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


                                     F2-18
<PAGE>   53

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)




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

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

Factors Which May Affect Future Operations

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

     Due to an expectation for continuing difficult industry and capital markets
conditions, the Company and the Subsidiaries have substantially reduced their
planned capital budget for 1999 and have undertaken a number of strategic
initiatives in an effort to improve and preserve capital liquidity in the
current environment. The Company and the Subsidiaries have adapted their
business strategy in the near-term through the implementation of the following
principal strategic initiatives: (i) focusing all of the Partnership's planned
exploration efforts in 1999 towards the drilling of its highest grade 3-D
prospects, (ii) eliminating substantially all planned seismic and land
expenditures for new projects until its capital resources can support such
additional activity, (iii) seeking to divest certain producing natural gas and
oil properties in an effort to raise capital to reduce debt borrowings and to
redirect capital to drilling projects that have the potential to generate higher
investment returns, (iv) restructuring outstanding senior and subordinated debt
agreements to provide the Company and the Partnership with flexibility needed to
preserve cash flow to fund its expected near-term exploration activities, (v)
implementing an overhead reduction plan to reduce annual general and
administrative expenses, and (vi) evaluating opportunities to raise additional
equity capital either through the sales of interests in certain of its seismic
projects or the issuance of equity securities. The Company and the Subsidiaries
believe that the successful execution of these strategic initiatives will
provide sufficient capital resources to execute their planned 1999 exploration
program and position them to realize the significant value they believe the
Partnership has captured in its inventory of 3-D seismic projects and delineated
drilling locations. While the Company and the Subsidiaries have initiated each
of these strategic directives in late 1998 and early 1999, and have effected
certain of them to date, the successful completion of any or all of these
efforts to improve capital availability within the expected time frame is
uncertain and will likely have a material impact on the Company's and the
Subsidiaries' near-term capital expenditure levels and growth profiles.

 9.  SEGMENT INFORMATION

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




                                     F2-19
<PAGE>   54

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



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

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

10.  FINANCIAL INSTRUMENTS

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

     In 1997, the Partnership was a party to a crude oil swap arrangement
resulting in a fixed price over a period of time for a specified volume of crude
oil. Adjustment to the price received for oil under these swap arrangements
resulted in a decrease in oil revenues of $6,191 in 1997.

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

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

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




                                     F2-20
<PAGE>   55

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



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

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

11.  EMPLOYEE BENEFIT PLANS

Retirement Savings Plan

     During 1996 the Partnership adopted a defined contribution 401(k) plan for
substantially all of its employees. In 1997 Brigham, Inc. succeeded to the
401(k) plan when the employees of the Partnership became employees of Brigham,
Inc. Eligible employees may contribute up to 15% of their compensation to this
plan. The 401(k) plan provides that the employer may, at its discretion, match
employee contributions. The employer has not matched employee contributions in
any plan year.

Stock Compensation

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

     The Company adopted an incentive plan, effective upon completion of the
Exchange (see Note 1), which provides for the issuance of stock options, stock
appreciation rights, stock, restricted stock, cash or any combination of the
foregoing. The objective of this plan is to reward key employees whose
performance may have a significant effect on the success of the Company.
Non-cash compensation expense related to certain stock options granted under the
incentive plan by the Company on behalf of the Partnership has been allocated to
the Partnerships's results of operations. Compensation expense allocated to the
Partnership totaled $833,710 and $782,544 in 1997 and 1998, respectively.

12.  SUBSEQUENT EVENT

     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


                                     F2-21
<PAGE>   56



                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



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
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.

13.  NATURAL GAS AND OIL EXPLORATION AND PRODUCTION ACTIVITIES

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

     The Partnership's natural gas and oil properties are included in the
consolidated results of Brigham, Inc., subject to the minority interest of 68.5%
held by the Company in 1997 and by Holdings I in 1998.

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

<TABLE>
<CAPTION>
                                                                                            YEAR ENDED
                                                                                            DECEMBER 31,
                                                                                    ----------------------------
                                                                                       1998(a)         1997(a)
                                                                                    ------------    ------------
<S>                                                                                  <C>            <C>         
Natural gas and oil sales.........................................................   $    13,799    $      9,184
Costs and expenses:
    Lease operating...............................................................         2,172           1,151
    Production taxes..............................................................           850             549
    Depletion of natural gas and oil properties...................................         8,410           2,743
    Capitalized ceiling impairment................................................        24,847               -
                                                                                    ------------    ------------
Total costs and expenses..........................................................        36,279           4,443
                                                                                    ------------    ------------
                                                                                    $   (22,480)    $      4,741
                                                                                    ============    ============
Depletion per physical unit of production (equivalent Mcf of gas).................  $       1.27    $       0.88
                                                                                    ============    ============
</TABLE>

- ----------
     (a)   The income tax expense (benefit) related to Brigham, Inc. for 1997
           and 1998 is calculated at the statutory rate and determined without
           regard to deduction for general and administrative expenses, interest
           costs and other income tax deductions and credits. Upon consolidation
           of the Partnership interest into Brigham, Inc. for 1997 and 1998, the
           income tax expense (benefit) related to results of operations for
           natural gas and oil producing activities for Brigham, Inc. would be
           $(2,478) and $523, respectively.

     Natural gas and oil sales reflect the market prices of net production sold
or transferred, with appropriate adjustments for royalties, net profits interest
and other contractual provisions. Lease operating expenses include lifting costs
incurred to operate and maintain productive wells and related equipment,
including such costs as operating labor, repairs and maintenance, materials,
supplies and fuel consumed. Production taxes include



                                     F2-22
<PAGE>   57

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)



production and severance taxes. Depletion of natural gas and oil properties
relates to capitalized costs incurred in acquisition, exploration and
development activities. Results of operations do not include interest expense
and general corporate amounts.

Costs Incurred and Capitalized Costs

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

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

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

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

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

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


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



                                     F2-23
<PAGE>   58

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)





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

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

Natural Gas and Oil Reserve Data

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

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

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

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




                                     F2-24
<PAGE>   59

                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)




Standardized Measure of Discounted Future Net Cash Inflows and Changes Therein

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


<TABLE>
<CAPTION>
                                                                                             DECEMBER 31,
                                                                                     ----------------------------
                                                                                         1998            1997
                                                                                     ------------    ------------
<S>                                                                                  <C>             <C>         
Future cash inflows................................................................  $    198,082    $    165,156
Future development and production costs............................................      (61,064)        (40,923)
                                                                                     ------------    ------------
Future net cash inflows............................................................  $    137,018    $    124,233
                                                                                     ============    ============

Standardized measure of future net cash inflows discounted
    at 10% per annum...............................................................  $     81,741    $     69,249
                                                                                     ============    ============
</TABLE>

     Estimated future income tax expense as of December 31, 1997 and 1998
attributable to Brigham, Inc.'s interest in the Partnership was $7.2 million and
$2.2 million, respectively. The standardized measure of future net cash inflows
discounted at 10% per annum as of December 31, 1997 and 1998 after estimated
income taxes attributable to Brigham, Inc.'s interest in the Partnership was
$67.7 million and $81.7 million, respectively.

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




                                     F2-25
<PAGE>   60
                    BRIGHAM EXPLORATION COMPANY SUBSIDIARIES

                 NOTES TO THE FINANCIAL STATEMENTS - (CONTINUED)




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


<TABLE>
<CAPTION>
                                                                             DECEMBER 31,
                                                                         --------------------
                                                                           1998        1997
                                                                         --------    --------
<S>                                                                      <C>         <C>     
Beginning of period ..................................................   $ 69,249    $ 44,506
    Sales of natural gas and oil produced, net of production
         costs .......................................................    (10,776)     (7,484)
    Development costs incurred .......................................      5,423       1,955
    Extensions and discoveries .......................................     52,389      38,016
    Purchases of minerals-in-place ...................................        687      16,965
    Sales of minerals-in-place .......................................         --         (94)
    Net change of prices and production costs ........................    (11,921)    (20,466)
    Change in future development costs ...............................       (656)        319
    Changes in production rates and other ............................     (6,109)     (1,954)
    Revisions of quantity estimates ..................................    (23,470)     (6,964)
    Accretion of discount ............................................      6,925       4,450
                                                                         --------    --------
End of period ........................................................   $ 81,741    $ 69,249
                                                                         ========    ========
</TABLE>

         The estimated change in future net cash inflows discounted at 10% per
annum attributable to income taxes for the years ended December 31, 1997 and
1998 attributable to Brigham, Inc.'s interest in the Partnership was $(1.6)
million and $1.5 million, respectively.




                                     F2-26
<PAGE>   61
                               INDEX TO EXHIBITS

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

<PAGE>   62
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.1.3        -- Amendment No. 3 to Agreement of Limited Partnership of Brigham                  
                 Oil & Gas, L.P., dated August 24, 1995, by and among Brigham                    
                 Exploration Company, General Atlantic Partners III, L.P.,                       
                 GAP-Brigham Partners, L.P., Harold D. Carter, Craig M. Fleming,                 
                 David T. Brigham and Jon L. Glass (filed as Exhibit 10.1.3 to the               
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.1.4+       -- Amended and Restated Agreement of Limited Partnership of Brigham                
                 Oil & Gas, L.P., dated December 30, 1997 by and among Brigham, Inc.,            
                 Brigham Holdings I, L.L.C. and Brigham Holdings II, L.L.C.                      
                                                                                                 
10.2          -- Agreement of Limited Partnership of Venture Acquisitions, L.P.,                 
                 dated September 23, 1994, by and between Quest Resources, L.L.C. and            
                 RIMCO Energy, Inc. as general partners, and RIMCO Production                    
                 Company, Inc., RIMCO Exploration Partners, L.P. I and RIMCO                     
                 Exploration Partners, L.P. II, as limited partners (filed as Exhibit            
                 10.2 to the Company's Registration Statement on Form S-1                        
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.3          -- Regulations of Quest Resources, L.L.C. (filed as Exhibit 10.3 to                
                 the Company's Registration Statement on Form S-1 (Registration No.              
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.4          -- Management and Ownership Agreement, dated September 23, 1994, by                
                 and among Brigham Oil & Gas, L.P., Brigham Exploration Company,                 
                 General Atlantic Partners III, L.P., Harold D. Carter, Ben M.                   
                 Brigham and GAP-Brigham Partners, L.P. (filed as Exhibit 10.4 to the            
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.5*         -- Consulting Agreement, dated May 1, 1997, by and between Brigham                 
                 Oil & Gas, L.P. and Harold D. Carter (filed as Exhibit 10.4 to the              
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 33-53873), and incorporated herein by reference).                               
                                                                                                 
10.6*         -- Employment Agreement, by and between Brigham Exploration Company                
                 and Ben M. Brigham (filed as Exhibit 10.7 to the Company's                      
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.7*         -- Form of Confidentiality and Noncompete Agreement between the                    
                 Registrant and each of its executive officers (filed as Exhibit 10.8            
                 to the Company's Registration Statement on Form S-1 (Registration               
                 No. 333-22491), and incorporated herein by reference).                          
                                                                                                 
10.8*         -- 1997 Incentive Plan of Brigham Exploration Company (filed as                    
                 Exhibit 10.9 to the Company's Registration Statement on Form S-1                
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.8.1*       -- Form of Option Agreement for certain executive officers (filed as               
                 Exhibit 10.9.1 to the Company's Registration Statement on Form S-1              
                 (Registration No. 333- 22491), and incorporated herein by                       
                 reference).                                                                     
                                                                                                 
10.8.2*       -- Option Agreement dated as of March 4, 1997, by and between                      
                 Brigham Exploration Company and Jon L. Glass (filed as Exhibit                  
                 10.9.2 to the Company's Registration Statement on Form S-1                      
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.9*         -- Incentive Bonus Plan dated as of February 28, 1997 of Brigham,                  
                 Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit 10.10 to the                 
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.10         -- Two Bridgepoint Lease Agreement, dated September 30, 1996, by and               
                 between Investors Life Insurance Company of North America and                   
                 Brigham Oil & Gas, L.P.                                                         
</TABLE>



<PAGE>   63
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 (filed as Exhibit 10.14 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.10.1       -- First Amendment to Two Bridge Point Lease Agreement dated April                 
                 11, 1997 between Investors Life Insurance Company of North America              
                 and Brigham Oil & Gas, L.P. (filed as Exhibit 10.9.1 to the                     
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-53873), and incorporated herein by reference).                              
                                                                                                 
10.10.2       -- Second Amendment to Two Bridge Point Lease Agreement dated                      
                 October 13, 1997 between Investors Life Insurance Company of North              
                 America and Brigham Oil & Gas, L.P. (filed as Exhibit 10.9.2 to the             
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-53873), and incorporated herein by reference).                              
                                                                                                 
10.10.3       -- Letter dated April 17, 1998 exercising Right of First Refusal to                
                 Lease "3rd Option Space" (filed as Exhibit 10.9.3 to the Company's              
                 Registration Statement on Form S-1 (Registration No. 333-53873), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.11         -- Anadarko Basin Seismic Operations Agreement, dated February 15,                 
                 1996, by and between Brigham Oil & Gas, L.P. and Veritas                        
                 Geophysical, Ltd. (filed as Exhibit 10.15 to the Company's                      
                 Registration Statement on Form S-1 (Registration No. 333- 22491),               
                 and incorporated herein by reference).                                          
                                                                                                 
10.11.1       -- Letter Amendment to Anadarko Basin Seismic Operations Agreement,                
                 dated June 10, 1996, between Brigham Oil & Gas, L.P. and Veritas                
                 Geophysical, Ltd. (filed as Exhibit 10.15.1 to the Company's                    
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.12         -- Expense Allocation and Participation Agreement, dated April 1,                  
                 1996, between Brigham Oil & Gas, L.P. and Gasco Limited Partnership.            
                 (filed as Exhibit 10.16 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333- 22491), and incorporated herein by              
                 reference).                                                                     
                                                                                                 
10.12.1       -- Amendment to Expense Allocation and Participation Agreement,                    
                 dated October 21, 1996, between Brigham Oil & Gas, L.P. and Gasco               
                 Limited Partnership (filed as Exhibit 10.16.1 to the Company's                  
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.13         -- Expense Allocation and Participation Agreement, dated April 1,                  
                 1996, between Brigham Oil & Gas, L.P. and Middle Bay Oil Company,               
                 Inc. (filed as Exhibit 10.17 to the Company's Registration Statement            
                 on Form S-1 (Registration No. 333- 22491), and incorporated herein              
                 by reference).                                                                  
                                                                                                 
10.13.1       -- Amendment to Expense Allocation and Participation Agreement,                    
                 dated September 26, 1996, between Brigham Oil & Gas, L.P. and Middle            
                 Bay Oil Company, Inc. (filed as Exhibit 10.17.1 to the Company's                
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.13.2       -- Letter Amendment to Expense Allocation and Participation                        
                 Agreement, dated May 20, 1996, between Brigham Oil & Gas, L.P. and              
                 Middle Bay Oil Company, Inc. (filed as Exhibit 10.17.2 to the                   
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.14         -- Anadarko Basin Joint Participation Agreement, dated May 1, 1996,                
                 by and among Stephens Production Company and Brigham Oil & Gas, L.P.            
                 (filed as Exhibit 10.18 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333- 22491), and incorporated herein by              
                 reference).                                                                     
                                                                                                 
10.15         -- Anadarko Basin Joint Participation Agreement, dated May 1, 1996,                
                 by and between Vintage Petroleum, Inc. and Brigham Oil & Gas, L.P.              
                 (filed as Exhibit 10.19 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.16         -- Processing Alliance Agreement, dated July 20, 1993, between                     
                 Veritas Seismic Ltd. and Brigham Oil & Gas, L.P. (filed as Exhibit              
                 10.20 to the Company's Registration                                             
</TABLE>



<PAGE>   64
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 Statement on Form S-1 (Registration No. 333-22491), and incorporated            
                 herein by reference).                                                           
                                                                                                 
10.16.1       -- Letter Amendment to Processing Alliance Agreement, dated November               
                 3, 1994, between Veritas Seismic Ltd. and Brigham Oil & Gas, L.P.               
                 (filed as Exhibit 10.20.1 to the Company's Registration Statement on            
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.17         -- Agreement and Assignment of Interest, West Bradley Project, dated               
                 September 1, 1995, by and between Aspect Resources Limited Liability            
                 Company and Brigham Oil & Gas, L.P. (filed as Exhibit 10.21 to the              
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.18         -- Agreement and Assignment of Interests in lands located in Grady                 
                 County, Oklahoma, West Bradley Project, dated December 1, 1995, by             
                 and between Aspect Resources Limited Liability Company, Brigham Oil             
                 & Gas, L.P. and Venture Acquisitions, L.P. (filed as Exhibit 10.22              
                 to the Company's Registration Statement on Form S-1 (Registration               
                 No. 333-22491), and incorporated herein by reference).                          
                                                                                                 
10.19         -- Agreement and Assignment of Interests, West Bradley Project,                    
                 dated December 1, 1995, by and between Aspect Resources Limited                 
                 Liability Company and Brigham Oil & Gas, L.P. (filed as Exhibit                 
                 10.23 to the Company's Registration Statement on Form S-1                       
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.20         -- Geophysical Exploration Agreement, Hardeman Project, Hardeman and               
                 Wilbarger Counties, Texas and Jackson County, Oklahoma, dated March             
                 15, 1993 by and among General Atlantic Resources, Inc., Maynard Oil             
                 Company, Ruja Muta Corporation, Tucker Scully Interests Ltd., JHJ               
                 Exploration, Ltd., Cheyenne Petroleum Company, Antrim Resources,                
                 Inc., and Brigham Oil & Gas, L.P. (filed as Exhibit 10.24 to the                
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.21         -- Agreement and Partial Assignment of Interests in OK13-P Prospect                
                 Area, Jackson County, Oklahoma (Hardeman Project), dated August 1,              
                 1995, by and between Brigham Oil & Gas, L.P. and Aspect Resources               
                 Limited Liability Company (filed as Exhibit 10.25 to the Company's              
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.22         -- Agreement and Partial Assignment of Interests in Q140-E Prospect                
                 Area, Hardeman County, Texas (Hardeman Project), dated August 1,                
                 1995, by and between Brigham Oil & Gas, L.P. and Aspect Resources               
                 Limited Liability Company (filed as Exhibit 10.26 to the Company's              
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.23         -- Agreement and Partial Assignment of Interests in Hankins #1                     
                 Chappel Prospect Agreement, Jackson County, Oklahoma (Hardeman                  
                 Project), dated March 21, 1996, by and between Brigham Oil & Gas,               
                 L.P., NGR, Ltd. and Aspect Resources Limited Liability Company                  
                 (filed as Exhibit 10.27 to the Company's Registration Statement on              
                 Form S-1 (Registration No. 333-22491), and incorporated herein by               
                 reference).                                                                     
                                                                                                 
10.24         -- Form of Indemnity Agreement between the Registrant and each of                  
                 its executive officers (filed as Exhibit 10.28 to the Company's                 
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.25         -- Registration Rights Agreement dated February 26, 1997 by and                    
                 among Brigham Exploration Company, General Atlantic Partners III                
                 L.P., GAP-Brigham Partners, L.P., RIMCO Partners, L.P. II, RIMCO                
                 Partners L.P. III, and RIMCO Partners, L.P. IV, Ben M. Brigham, Anne            
                 L. Brigham, Harold D. Carter, Craig M. Fleming, David T. Brigham and            
                 Jon L. Glass (filed as Exhibit 10.29 to the Company's Registration              
                 Statement on Form S-1 (Registration No. 333-22491), and incorporated            
                 herein by reference).                                                           
</TABLE>




<PAGE>   65

<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
10.26         -- 1997 Director Stock Option Plan (filed as Exhibit 10.30 to the                  
                 Company's Registration Statement on Form S-1 (Registration No.                  
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.27         -- Form of Employee Stock Ownership Agreement (filed as Exhibit                    
                 10.31 to the Company's Registration Statement on Form S-1                       
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.28         -- Agreement and Assignment of Interest in Geophysical Exploration                 
                 Agreement, Esperson Dome Project, dated November 1, 1994, by and                
                 between Brigham Oil & Gas, L.P. and Vaquero Gas Company (filed as               
                 Exhibit 10.33 to the Company's Registration Statement on Form S-1               
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.29         -- Geophysical Exploration Agreement, Southwest Danbury Project,                   
                 Brazoria County, Texas, dated as of July 1, 1996, by and among                  
                 UNEXCO, Inc. and Brigham Oil & Gas, L.P. (filed as Exhibit 10.34 to             
                 the Company's Registration Statement on Form S-1 (Registration No.              
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.30         -- Geophysical Exploration Agreement, Welder Project, Duval County,                
                 Texas, dated as of October 1, 1996, by and among UNEXCO, Inc. and               
                 Brigham Oil & Gas, L.P. (filed as Exhibit 10.35 to the Company's                
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.31         -- Proposed Trade Structure, RIMCO/Tigre Project, Vermillion Parish,               
                 Louisiana, among Brigham Oil & Gas, L.P., Tigre Energy Corporation              
                 and Resource Investors Management Company (filed as Exhibit 10.36 to            
                 the Company's Registration Statement on Form S-1 (Registration No.              
                 333-22491), and incorporated herein by reference).                              
                                                                                                 
10.31.1       -- Letter relating to Proposed Trade Structure, RIMCO/Tigre Project,               
                 dated January 31, 1997, from Resource Investors Management Company              
                 to Brigham Oil & Gas, L.P. (filed as Exhibit 10.36 to the Company's             
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.32         -- Anadarko Basin Seismic Operations Agreement II, dated as of April               
                 1, 1997, by and between Brigham Oil & Gas, L.P. (filed as Exhibit               
                 10.37 to the Company's Registration Statement on Form S-1                       
                 (Registration No. 333-22491), and incorporated herein by reference).            
                                                                                                 
10.32.1       -- Letter Amendment to Anadarko Basin Seismic Operations Agreement                 
                 II, dated March 20, 1997, between Brigham Oil & Gas, L.P. and                   
                 Veritas DGC Land, Inc. (filed as Exhibit 10.37 to the Company's                 
                 Registration Statement on Form S-1 (Registration No. 333-22491), and            
                 incorporated herein by reference).                                              
                                                                                                 
10.33         -- Expense Allocation and Participation Agreement II, dated April 1,               
                 1997, between Brigham Oil & Gas, L.P., and Gasco Limited Partnership            
                 (filed as Exhibit 10.31 to the Company's Quarterly Report on Form               
                 10-Q for the quarter ended June 30, 1997, and incorporated herein by            
                 reference).                                                                     
                                                                                                 
10.36         -- Credit Agreement dated as of January 26, 1998 among Brigham Oil &               
                 Gas, L.P., Bank of Montreal, as Agent, and the lenders signatory                
                 thereto (filed as Exhibit 10.36 to the Company's Annual Report on               
                 Form 10-K for the year ended December 31, 1997, and incorporated                
                 herein by reference).                                                           
                                                                                                 
10.36.1+      -- First Amendment to Credit Agreement dated as of August 20, 1998                 
                 among Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and the              
                 lenders signatory thereto.                                                      
                                                                                                 
10.36.2++     -- Second Amendment to Credit Agreement dated as of March 26, 1999                 
                 among Brigham Oil & Gas, L.P., Bank of Montreal, as Agent, and the              
                 lenders signatory thereto.                                                      
                                                                                                 
10.37         -- Guaranty Agreement dated January 26, 1998 by Brigham Exploration                
                 Company in favor of Bank of Montreal, as Agent, and each of the                 
                 Lenders party to the Credit                                                     
</TABLE>



<PAGE>   66
<TABLE>
<CAPTION>
Number                          Description
- ------                          -----------
<S>           <C>                                        
                 Agreement (filed as Exhibit 10.33.1 to the Company's Registration               
                 Statement on Form S-1 (Registration No. 333-53873), and incorporated            
                 herein by reference).                                                           
                                                                                                 
10.37.1       -- First Amendment to Guaranty Agreement dated as of March 30, 1998                
                 between Brigham Exploration Company and Bank of Montreal, as Agent              
                 for the Lenders party to the Credit Agreement (filed as Exhibit                 
                 10.33.2 to the Company's Registration Statement on Form S-1                     
                 (Registration No. 333-53873), and incorporated herein by reference).            
                                                                                                 
10.37.2+      -- Second Amendment to Guaranty Agreement dated as of August 20,                   
                 1998 between Brigham Exploration Company and Bank of Montreal, as               
                 Agent for the Lenders party to the Credit Agreement.                            
                                                                                                 
10.37.3++     -- Third Amendment to Guaranty Agreement dated as of March 26, 1999                
                 between Brigham Exploration Company and Bank of Montreal, as Agent              
                 for the Lenders party to the Credit Agreement.                                  
                                                                                                 
10.38+        -- Securities Purchase Agreement dated as of August 20, 1998 among                 
                 Brigham Exploration Company, Enron Capital & Trade Resources Corp.              
                 and Joint Energy Development Investments II Limited Partnership.                
                                                                                                 
10.39+        -- Registration Rights Agreement dated as of August 20, 1998, by and               
                 among Brigham Exploration Company, Enron Capital & Trade Resources              
                 Corp. and Joint Energy Development Investments II Limited                       
                 Partnership.                                                                    
                                                                                                 
10.39.1++     -- Amendment to Registration Rights Agreement dated as of March 26,                
                 1999, by and among Brigham Exploration Company, Enron Capital &                 
                 Trade Resources Corp., ECT Merchant Investments Corp. and Joint                 
                 Energy Development Investments II Limited Partnership.                          
                                                                                                 
10.40+        -- Form of Guaranty for subsidiaries.                                              
                                                                                                 
10.41++       -- Exchange Agreement dated as of March 30, 1999 by and between                    
                 Brigham Exploration Company and Veritas DGC Land, Inc.                          
                                                                                                 
10.42++       -- Registration Rights Agreement dated as of March 30, 1999 by and                 
                 between Brigham Exploration Company and Veritas DGC Land, Inc.                  
                                                                                                 
21+           -- Subsidiaries of the Registrant.                                                 
                                                                                                 
23.1++        -- Consent of Pricewaterhouse Coopers LLP, independent public                      
                 accountants.                                                                    
                                                                                                 
23.2+         -- Consent of Cawley, Gillespie & Associates, Inc., independent                    
                 petroleum engineers.                                                            
                                                                                                 
27+           -- Financial Data Schedule.                                                        
</TABLE>      



- ----------
*      Management contract or compensatory plan.
+      Previously filed
++     Filed herewith.




<PAGE>   1
                                                                 Exhibit 4.2.1

                          FIRST AMENDMENT TO INDENTURE


         This FIRST AMENDMENT TO INDENTURE, dated as of March 26, 1999 ("this
Amendment"), is among BRIGHAM EXPLORATION COMPANY, a corporation duly organized
and existing under the laws of the State of Delaware (the "Borrower"), and
CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, a national banking association
existing under the laws of the United States, as trustee (the "Trustee").

                             PRELIMINARY STATEMENT

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

                                    RECITALS

         The Borrower and the Trustee are parties to that certain Indenture
dated as of August 20, 1998 (the "Indenture"). Capitalized terms used and not
otherwise defined herein are used with the meanings ascribed thereto in the
Indenture.

         The Borrower has advised the Noteholders and the Trustee that it
desires to amend certain provisions of the Indenture, and the Borrower has
requested that the Trustee and the Noteholders agree to various amendments to
certain provisions of the Indenture.

         The Trustee, upon the consent and authorization of the Noteholders,
has agreed to so amend certain provisions of the Indenture upon the terms and
subject to the conditions and limitations of this Amendment.

         NOW, THEREFORE, in consideration of the premises, covenants and
agreements contained herein, the parties hereto agrees as follows:

         Section 1. Definitions. The following capitalized terms shall have the
following respective meanings when used herein:

         A. "Duke Consent Letter" shall mean that certain Letter Agreement
dated as of February 18, 1999 executed by the Borrower and the Trustee.

         B. "Duke Transaction" shall mean the transactions contemplated by the
Duke Consent Letter.

         C. "Lending Relationship" shall refer to the Indenture and the other
Loan Documents, including, without limitation, this Amendment, together with any
and all negotiations, discussions, acts, omissions, renewals, extensions, and
other agreements or events related to the Indenture and such other Loan
Documents, the parties' obligations thereunder and the transactions contemplated



<PAGE>   2


thereby, including, without limitation, any such negotiations, discussions,
acts, omissions, renewals, extensions, other agreements or events that (a)
occurred prior to the date hereof, (b) may occur on the date hereof, or (c)
occurred prior to the execution of this Amendment and the instruments and
documents executed and delivered in connection herewith or relating hereto.

         D. "New Mortgage" shall mean that certain Mortgage, Deed of Trust,
Assignment of Production, Security Agreement and Financing Statement
(Non-Producing Properties) dated effective as of the date hereof from Brigham
Oil & Gas, L.P. to Gray H. Muzzy, as Trustee, for the benefit of Trustee.

         E. "RELEASED CLAIMS" SHALL MEAN ANY AND ALL CLAIMS (INCLUDING WITHOUT
LIMITATION ANY LIABILITIES, DAMAGES, DEMANDS AND CAUSES OF ACTION ARISING
THEREFROM), WHETHER (A) AT LAW OR IN EQUITY, (B) ON THE ALLEGED COMMISSION OF A
TORT, (C) ON THE ALLEGED BREACH (OR ANTICIPATORY BREACH OR REPUDIATION) OF ANY
CONTRACT, DUTY, OR WARRANTY (WHETHER ORAL OR WRITTEN, EXPRESS OR IMPLIED), (D)
ON THE ALLEGED VIOLATION OF ANY STATUTE, TARIFF, OR REGULATION (WHETHER
PROMULGATED BY THE UNITED STATES, ANY STATE THEREOF, ANY FOREIGN STATE OR
COUNTRY, OR ANY OTHER GOVERNMENTAL AGENCY OR ENTITY, WHEREVER LOCATED), OR (E)
ON ANY OTHER FACTUAL, LEGAL OR EQUITABLE THEORY, INCLUDING, WITHOUT LIMITATION,
ANY CLAIM FOR DAMAGES OF ANY TYPE OR NATURE, FOR INJUNCTIVE OR OTHER RELIEF,
FOR ATTORNEYS' FEES, INTEREST OR ANY OTHER LIABILITY WHATSOEVER ON ANY THEORY,
INCLUDING WITHOUT LIMITATION ANY LOSS, COST OR DAMAGE IN CONNECTION WITH OR
BASED UPON "LENDER LIABILITY", UNFAIR DEALING, DURESS, COERCION, CONTROL OR
UNDUE INFLUENCE, EXTORTION OR COMMERCIAL BRIBERY, BREACH OF AN IMPLIED COVENANT
OR DUTY OF GOOD FAITH AND FAIR DEALING, MATERIAL MISREPRESENTATION OR OMISSION,
OVERREACHING, UNCONSCIONABILITY, CONFLICT OF INTEREST, BAD FAITH, MALPRACTICE,
DISPARATE BARGAINING POSITION, DETRIMENTAL RELIANCE, PROMISSORY ESTOPPEL,
ESTOPPEL BY DEED, WAIVER, LACHES, OR ANY OTHER EQUITABLE THEORY, EQUITABLE
SUBORDINATION, BREACH OF FIDUCIARY DUTY OR ANY OTHER DUTY, OR TORTIOUS
INDUCEMENT TO COMMIT SUCH BREACH, TORTIOUS INTERFERENCE WITH CONTRACT OR
PROSPECTIVE BUSINESS RELATIONS, NEGLIGENT PERFORMANCE OF CONTRACTUAL
OBLIGATIONS, OR OTHER THEORIES OF NEGLIGENCE, NEGLIGENT OR INTENTIONAL
INFLICTION OF EMOTIONAL DISTRESS, SLANDER, LIBEL, OTHER DEFAMATION, FRAUDULENT
TRANSFER, CONVERSION, TRESPASS TO (OR CLOUDING THE TITLE OF) PROPERTY, USURY,
VIOLATIONS OF THE RACKETEER INFLUENCED AND CORRUPT ORGANIZATIONS ACT, DECEPTIVE
TRADE PRACTICES, CONSPIRACY, OR ANY THEORY OF LIABILITY AS PARTNERS OR JOINT
VENTURERS, THAT ANY RELEASING PARTY MAY HAVE AS OF THE DATE HEREOF AGAINST ANY
RELEASED PARTY WITH RESPECT TO THE LENDING RELATIONSHIP.

                                      -2-

<PAGE>   3



         F. "Released Party" shall mean each of the Trustee, the Noteholders
and their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").

         G. "Releasing Party" shall mean each of the Borrower and the
Guarantors and their respective predecessors, successors, assigns, directors,
officers, partners, employees, agents, attorneys, principals, Affiliates and
all other Persons who might have a claim against any Released Party
(collectively, the "Releasing Parties").

Section 2.  Amendments to Indenture.  The Indenture is amended hereby as 
follows:

         A. Section 1.01 is amended hereby as follows:

                  (i) by deleting the definition of the term "Basic Documents"
in its entirety and substituting the following therefor:

                  ""Basic Documents" means, collectively, this Indenture, the
         Securities Purchase Agreement and the other Loan Documents, as each
         may be amended, supplemented or restated from time to time.";

                  (ii) by inserting the following new definitions:

                  ""First Borrowing Base Determination Date" means June 1,
1999.";

                  ""Measurement Date" has the meaning set forth in the last
paragraph of Section 9.02(a)"

                  (iii) by inserting in the definition of the term "Guarantors"
after the reference to "Brigham Holdings II, LLC", the reference "Sooner
Production LLC"; and

                  (iv) by deleting the reference "Section 7.09" in the
definition of the term "Mortgage" and substituting the reference "Section
7.09(a)" therefor.

         B. Section 4.01(a) of the Indenture is amended hereby as follows:

                  (i) by inserting in clause (ii) following the reference "and
BOG", the phrase ", Sooner Production LLC and Quest Resources LLC"; and

                  (ii) by inserting at the end of Section 4.01(a) the
following:

                  "; and (v) a Security Agreement substantially in the form of
         Exhibit D duly executed by BOG in favor of the Trustee for the ratable
         benefit of the Noteholders granting a security interest in all of
         BOG's right, title and interest in and to the Capital Stock of DND Oil
         & Gas, L.P. and Quest Resources LLC, together with proper UCC-1
         Financing Statements duly filed

                                      -3-

<PAGE>   4




         in Texas; and (vi) a Security Agreement substantially in the form of
         Exhibit D duly executed by Sooner Production LLC in favor of the
         Trustee for the ratable benefit of the Noteholders granting a security
         interest in all of BOG's right, title and interest in and to the
         Capital Stock of Quest Resources LLC, together with proper UCC-1
         Financing Statements duly filed in Texas, in each case as such
         Security Agreements may be amended, modified or supplemented from time
         to time."

         C. Section 4.01(c) of the Indenture is amended hereby as follows:

                  (i) by deleting the word "A" from the beginning of such
section and inserting the phrase "One or more".

         D. Section 4.01 (d) of the Indenture is amended hereby as follows:

                  (i) by deleting the words "BOG, Brigham, Inc., Brigham
Holdings I, LLC and Brigham Holding II, LLC" and replacing them with the words
"the Guarantors".

         E. Section 7.01 of the Indenture is amended hereby as follows:

                  (i) by inserting the following new subsection (c):

                  "(c) Monthly Financial Statements. As soon as available and
         in any event within thirty (30) days after the end of each calendar
         month that is not also the end of one of the Borrower's first three
         fiscal quarterly periods or of the Borrower's fiscal year,
         consolidated statements of income and changes in financial position of
         the Borrower and its Consolidated Subsidiaries for such period and for
         the period from the beginning of the respective fiscal year to the end
         of such period, and the related consolidated balance sheets as at the
         end of such period and, beginning March 31, 2000, statements setting
         forth in each case in comparative form the corresponding figures for
         the corresponding period in the preceding fiscal year, accompanied by
         the certificate of a Responsible Officer, which certificate shall
         state that such financial statements fairly present the consolidated
         financial condition and results of operations of the Borrower and its
         Consolidated Subsidiaries in accordance with GAAP, as at the end of,
         and for, such period (subject to normal year-end audit adjustments).";

                  (ii) by relettering the existing subsections (c) through (i)
as subsections (d) through (j);

                  (iii) by deleting in subsection (i), as relettered by (ii)
above, the reference "Concurrent with the First Reserve Report and each January
1 Reserve Report thereafter" and substituting therefor the reference "On or
before January 31 of each year"; and

                  (iv) by inserting after the reference "paragraph (a) or (b)"
in the final paragraph of Section 7.01 the reference "or (c)" and by inserting
the phrase "(and for each June 30 quarter end

                                      -4-

<PAGE>   5




and December 31 year end, commencing June 30, 2000, calculating the ratio
described in the last paragraph of Section 9.02(a) for such Measurement Date).

         F. Section 7.07 of the Indenture is amended hereby by deleting each
reference to "January 1" in subsection (b) and substituting therefor the
reference "January 31".


         G. Section 7.09(a) of the Indenture is amended to add the following
proviso at the end thereof:

         "; provided that, with respect to any non-proved properties, the
         phrase "second-priority" as found in the fifth line of this subsection
         7.09(a) shall be replaced with the word "perfected" and the phrase
         "previous Collateral Documents" as found in the twelfth line of
         subsection 7.09(a) shall be replaced with the phrase "New Mortgage and
         any associated financing statements"."

         H. Section 8.01 of the Indenture is amended hereby as follows:

                  (i) by deleting the reference "1.5 to 1.0" in the first
sentence of subsection (a) and substituting therefore the reference "(A) for
any Debt incurred on or after July 1, 1999 and on or before December 31, 1999,
1.3 to 1.0 and (B) for any Debt incurred on on or after January 1, 2000, 1.5 to
1.0."; and

                  (ii) by deleting the sum "$75,000,000," from the last
sentence of subsection (a) and replacing it with the phrase "the lesser of (i)
$75,000,000 and (ii) the loan commitments available from time to time under
such refinanced Senior Loan,".

         I. Section 8.16 of the Indenture is amended hereby deleting the
section in its entirety and substituting the following therefor:

         "Section 8.16 Consolidated Interest Coverage Ratio. As of the last day
         of each fiscal quarter, beginning December 31, 1999, the Borrower will
         not permit the Consolidated Interest Coverage Ratio to be less than
         (i) 1.5 to 1.0 as of December 31, 1999, (ii) 1.75 to 1.0 as of March
         31, 2000, and (iii) 2.0 to 1.0 as of the end of each fiscal quarter
         thereafter."

         J. Section 8.17 of the Indenture is amended hereby by deleting the
reference "The" from the beginning of the first sentence and substituting
therefore the reference "On and after December 31, 1999, the".

         K. Section 9.02 of the Indenture is amended hereby as follows:

                  (i) by adding to the end of subsection (a) the following:

         "Notwithstanding the foregoing (i) if, as of any June 30 or December
         31, commencing with June 30, 2000 (each such date being a "Measurement
         Date"), the ratio of (A) the Borrower's


                                      -5-

<PAGE>   6




         Adjusted Consolidated Net Tangible Assets as of such Measurement Date
         to (B) the sum of (1) Borrower's Consolidated Indebtedness as of such
         Measurement Date plus (2) past due interest on Debt as of such
         Measurement Date, is less than 2.0 to 1.0, the applicable rate of
         interest specified in this Section 9.01(a) as then in effect
         (including after giving effect to increases that may have occurred
         prior to the applicable Measurement Date, if any) shall increase by
         0.5% effective as of such Measurement Date. Any such increase shall be
         effective from the applicable Measurement Date and remain effective
         (subject to subsequent additional increases pursuant to this
         paragraph, if any) until the Obligations are paid in full, subject to
         the provisions of Section 9.02(c) and 9.02(f)."; and

                  (ii) by deleting the first five (5) sentences of subsection
(b) and substituting the following therefore:

         "The Borrower shall have the option to pay accrued interest on the
         Notes in kind on each of the six (6) consecutive Interest Payment
         Dates commencing with and following February 20, 1999, as provided in
         this Section 9.02(b). In such event the accrued interest due on such
         Interest Payment Dates shall be calculated at the rates set forth in
         this Section 9.02(b) and the interest due (calculated at the rates set
         forth in this Section 9.02(b)) shall be deemed an advance of principal
         on the Notes and, as of the applicable Interest Payment Date, shall be
         added to the outstanding principal balance of the Notes
         (notwithstanding the outstanding principal balance may exceed, in the
         aggregate, the face amount of the Notes). In order to not exercise its
         option under this Section 9.02(b), the Borrower must, on or before the
         applicable Interest Payment Date, deliver written notice to the Agent
         executed by a Responsible Officer notifying Agent of its election to
         not pay interest in kind. Should Borrower fail to deliver such written
         notice in a timely fashion, Borrower shall be deemed to have
         irrevocably elected to make payment of accrued interest in kind on the
         next applicable Interest Payment Date. Should Borrower deliver such
         notice in a timely fashion, Borrower shall be deemed to have
         irrevocably elected to make payment of accrued interest in cash and
         any subsequent failure to do so in a timely fashion (subject to the
         thirty (30) day grace period provided in Section 10.01(a)) shall
         constitute an Event of Default hereunder."

         L. Exhibit D to the Indenture is amended in its entirety to read as
set forth in Exhibit D attached hereto.

         Section 3. Covenants. The Borrower covenants and agrees that during
the period from February 1, 1999 through and including June 1, 1999:

         A. The Borrower shall deliver weekly cash budgets reasonably
satisfactory to the Agent in the form attached hereto as Exhibit B, and weekly
cash flow statements reasonably satisfactory to the Agent based on such form,
with variance analysis to budget (including accounts receivables and accounts
payables reporting) not later than the Friday following the week to which such
budgets and statements relate.

         B. The Borrower shall provide to the Agent from time to time upon
request by the Agent the certificate of a Responsible Officer of the Borrower
stating that, except as disclosed in a schedule


                                      -6-

<PAGE>   7




thereto, the Borrower has not received written notice that any mechanics' liens
have been filed or will be filed on the Mortgaged Properties; provided that
mere receipt of an invoice for services rendered shall not constitute written
notice that a mechanics' lien will be filed.

         C. The Borrower shall cause its Subsidiary, DND Oil & Gas, LLP, to
transfer all assets held by it to BOG and, thereafter, to dissolve on or before
June 1, 1999.

         D. The Borrower will not, and will not allow any of its Subsidiaries
to, (i) transfer any assets to Quest Resources LLC or (ii) make any investments
in or loans or advances to Quest Resources LLC.

         E. The Borrower shall deliver within 30 days after the date of this
Agreement a First Amendment to Security Agreement executed by Brigham Holdings
I, LLC and a First Amendment to Security Agreement executed by Brigham Holdings
II, LLC, in each case in favor of the Agent, together with (a) evidence that
all other actions necessary or, in the opinion of the Agent, desirable to
perfect and protect the security interests and Liens granted thereby have been
taken, and (b) an opinion of the Borrower's counsel in form reasonably
satisfactory to the Agent.

Breach by the Borrower and its Subsidiaries of any of the foregoing covenants
(regardless of the reason therefor) shall constitute an Event of Default under
the Indenture.

         Section 4. Conditions Precedent. This Amendment shall become binding
upon receipt by the Agent of the following documents and satisfaction of the
other conditions provided in this Section 4, each of which must be satisfactory
to the Agent in form and substance:

         A. counterparts of this Amendment executed by the Borrower and the
Trustee;

         B. The Borrower shall have satisfied all of its obligations under
Section 7.09(a) of the Indenture, including the delivery to the Agent of all
Mortgages required thereby;

         C. evidence that all new Mortgages (including the New Mortgage) and
the related UCC-1 financing statements delivered pursuant to Section 7.09(a) of
the Indenture have been filed in all jurisdictions necessary to perfect and
protect the security interests, assignments and Liens created thereby;

         D. certificates of the Secretary or an Assistant Secretary of the
Borrower and each of the Guarantors setting forth for each of them (i) the
resolutions of its board of directors or managers (or if such Guarantor is a
partnership, resolutions of the general partner of such partnership), as
applicable, with respect to the authorization to execute and deliver this
Amendment and consummate the transactions contemplated hereby; (ii) the
Responsible Officer of such entity authorized to sign this Amendment, and (iii)
the signature of such authorized Responsible Officer of such entity;

         E. a monthly cash budget for 1999 of the Borrower and its
Subsidiaries, which shall include projected revenues, expenses and capital
expenditures;



                                      -7-

<PAGE>   8




         F. a First Amendment to Security Agreement executed by the Borrower in
favor of the Trustee and evidence that all other actions necessary or, in the
opinion of the Agent desirable to perfect and protect the security interests
and Liens granted thereby have been taken;

         G. a First Amendment to Security Agreement executed by Brigham, Inc.
in favor of the Trustee granting, among other things, a second priority
security interest in all of Brigham, Inc.'s right, title and interest in its
ownership interests in Quest Resources LLC, and evidence that all other actions
necessary or, in the opinion of the Agent, desirable to perfect and protect the
security interests and Liens granted thereby have been taken;

         H. a First Amendment to Security Agreements executed by BOG in favor
of the Trustee granting, among other things, a second priority security
interest in all of BOG's right, title and interest in its ownership interests
in Quest Resources LLC, and evidence that all other actions necessary or, in
the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken;

         I. a First Amendment to Security Agreement executed by Brigham
Holdings I, LLC in favor of the Trustee and evidence that all other actions
necessary or, in the opinion of the Agent, desirable to perfect and protect the
security interests and Liens granted thereby have been taken;

         J. a First Amendment to Security Agreement executed by Brigham
Holdings II, LLC in favor of the Trustee and evidence that all other actions
necessary or, in the opinion of the Agent, desirable to perfect and protect the
security interests and Liens granted thereby have been taken;

         K. a First Amendment to Security Agreement executed by Sooner
Production LLC in favor of the Trustee and evidence that all other actions
necessary or, in the opinion of the Agent, desirable to perfect and protect the
security interests and Liens granted thereby have been taken;

         L. a Consent and Acknowledgment executed by each of the Guarantors;

         M. an opinion of counsel to Borrower substantially in the form
attached hereto as Exhibit C;

         N. duly executed warrants issued by the Borrower to ECT and JEDI-II in
their respective Participations in substitution for the original Warrants
issued pursuant to Section 2.03 of the Securities Purchase Agreement, for the
purchase of an aggregate of 1,000,000 shares of Common Stock, and which
warrants shall constitute the "Warrants" under the Indenture and the Securities
Purchase Agreement for all purposes;

         O. payment of the expenses of the Agent and the Noteholders in
accordance with Section 7 hereof; and

         P. such other documents as Agent or its counsel may reasonably
request.



                                      -8-

<PAGE>   9




         Section 5. Representations and Warranties.

         A. Except as provided in subsection (iii) of this Section 5.A., the
Borrower hereby reaffirms that, as of the date of this Amendment, the
representations and warranties made by the Borrower in the Securities Purchase
Agreement are true and correct as though made on and as of the date hereof, and
further, the Borrower represents that,

                  (i) as of the date hereof, no Default or Material Adverse
Effect has occurred and is continuing except as previously disclosed to the
Agent in writing;

                  (ii) the execution, delivery and performance by the Borrower
or the Guarantors of this Amendment and the other Loan Documents and all
instruments and documents to be delivered by the Borrower or the Guarantors, to
the extent a party thereto, hereunder and thereunder and the creation of all
Liens provided for herein and therein: (a) are within the Borrower's or such
Guarantor's corporate power; (b) have been duly authorized by all necessary or
proper corporate action, including the consent of stockholders, members and/or
partners therein or thereof; (c) are not in contravention of any provision of
the Borrower's or such Guarantor's certificate of incorporation, bylaws or
similar organizational and/or governing documents; (d) will not violate (1) any
law or regulation or (2) any order or decree of any court or governmental
instrumentality; (e) will not conflict with or result in the breach or
termination of, constitute a default under or accelerate any performance
required by, any indenture, mortgage, deed of trust, lease, agreement or other
instrument to which the Borrower or any of the Guarantors is a party or by
which the Borrower or any of the Guarantors or any of their respective property
is bound; (f) will not result in the creation or imposition of any Lien upon
any of the property of the Borrower or the Guarantors other than those in favor
of the Agent pursuant to the terms of this Amendment and the other Loan
Documents to be delivered in connection herewith; and (g) do not require the
consent or approval of any governmental body, agency, authority or any other
Person that has not been duly obtained, made or complied with prior to the date
hereof. At or prior to the date hereof, each of this Amendment and the other
Loan Documents to be delivered in connection herewith shall have been duly
executed and delivered for the benefit of or on behalf of the Borrower or the
Guarantors, in each case to the extent a party thereto, and each shall then
constitute a legal, valid and binding obligation of the Borrower or such
Guarantor, enforceable against it in accordance with its terms; and

                  (iii) notwithstanding the foregoing, the representations and
warranties contained in the last sentence of Section 4.10(a) of the Securities
Purchase Agreement (and not those contained in the first two sentences) are
reaffirmed with respect to the Mortgaged Property covered by or described in
the New Mortgage.

         B. Each of the Borrower and the Guarantors further represents and
warrants, for itself only that it (i) is executing this Amendment, and the
documents executed in connection herewith to which it is a party, after
consultation with counsel of its own choosing, (ii) has read and understands
the release granted by Section 6 hereof, (iii) desires to execute this
Amendment and such documents to which it is a party and (iv) has the requisite
authority to enter into and be bound by this Amendment and such documents to
which it is a party, including the release granted by Section 6 hereof.


                                      -9-

<PAGE>   10




         Section 6. Release.

         A. EACH OF THE RELEASING PARTIES DESIRES AND INTENDS FULLY TO
COMPROMISE, RELEASE AND SETTLE ANY AND ALL OF THE RELEASED CLAIMS; AND EACH OF
THE RELEASING PARTIES HEREBY COVENANTS, WARRANTS AND REPRESENTS UNTO EACH OF
THE RELEASED PARTIES THAT SUCH RELEASING PARTY DOES HEREBY FOREVER RELEASE,
ACQUIT, WAIVE AND DISCHARGE EACH OF THE RELEASED PARTIES OF AND FROM THE
RELEASED CLAIMS AND EACH OF THE RELEASING PARTIES HEREBY DECLARES THE SAME
FOREVER RELEASED, ACQUITTED, WAIVED, SETTLED AND DISCHARGED. THIS RELEASE IS
EFFECTIVE WITHOUT REGARD TO WHETHER (I) SUCH RELEASED CLAIMS ARE KNOWN OR
UNKNOWN, (II) DAMAGES ARISING OUT OF SUCH RELEASED CLAIMS HAVE YET ACCRUED,
(III) SUCH RELEASED CLAIMS AROSE COLLATERALLY, DIRECTLY, DERIVATIVELY, OR
OTHERWISE BETWEEN THE PARTIES HERETO OR (IV) AN ORDINARY PERSON IN THE SAME OR
SIMILAR CIRCUMSTANCES WOULD OR WOULD NOT, THROUGH THE EXERCISE OF DUE CARE,
HAVE DISCOVERED SUCH CLAIMS BY THE DATE OF THIS AMENDMENT. IN CONNECTION WITH
THE FOREGOING RELEASE:

         B. Borrower and each of the Guarantors represents and warrants that it
has the full power and authority to perform the release granted in this Section
6 and that it has not in any manner made any assignment of any Released Claim
to any third party.

         C. The release granted in this Section 6 will be effective upon
execution of this Amendment by all of the parties hereto.

         D. Each party executing this Amendment understands and agrees that the
release granted in this Section 6 is a full, final and complete release of the
Released Claims and that such release may be pleaded as an absolute and final
bar to any or all suits which may hereafter be filed or prosecuted by any one
or more of the Releasing Parties or anyone claiming by, through or under any
one or more of the Releasing Parties in respect of any of the matters released
hereby, and that no recovery on account of the Released Claims may hereafter be
had from any of the Released Parties; and that the consideration given for such
release is not an admission of liability or fault on the part of any of the
Released Parties (it being the express intent of the parties hereto to obtain
peace of mind and avoid the expense and uncertainty of potential litigation),
and that none of the Releasing Parties or those claiming by, through or under
any of them will ever claim that it is.

         E. The parties hereto acknowledge that the release granted by this
Section 6 does not have any effect with respect to relationships between the
Borrower and each of the Guarantors and the Noteholders and the Agent other
than in connection with the Lending Relationship.

         Section 7. Payment of Fees and Expenses; Form of Payment.

         A. The Borrower agrees, whether or not the transactions contemplated
hereby are consummated, to pay all reasonable expenses of the Agent and the
Noteholders (including, without


                                      -10-

<PAGE>   11




limitation, all reasonable fees and disbursements of counsel and other outside
consultants for the Agent and/or the Noteholders) in connection with the
negotiation, investigation, preparation, execution and delivery of, recording
and filing of, preservation of rights under and enforcement of this Amendment
and the other Loan Documents to be delivered in connection herewith.

         B. All payments to be made by the Borrower under this Amendment shall
be made in Dollars, in immediately available funds, to the Agent at such
account as the Agent shall specify.

          Section 8. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or condition of the Securities Purchase
Agreement or the Indenture or any of the other Loan Documents, or (b) prejudice
any right or rights which the Noteholders or the Agent may now have or may have
in the future under or in connection with the Securities Purchase Agreement or
the Indenture or any of the other Loan Documents. Except as expressly
supplemented, amended or modified hereby, the terms and provisions of the
Securities Purchase Agreement or the Indenture or any other Loan Documents are
and shall remain in full force and effect. In the event of a conflict between
this Amendment and any of the foregoing documents, the terms of this Amendment
shall be controlling.

         Section 9. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Indenture shall be construed
in accordance with and be governed by the laws of the State of Texas and the
United States of America.

         Section 10. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 11. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.




                                      -11-

<PAGE>   12




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

            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES BEFORE
OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS
OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL
AGREEMENT BETWEEN THE PARTIES.


BORROWER:                           BRIGHAM EXPLORATION COMPANY


                                    By: /s/ Karen E. Lynch                     
                                       ---------------------------------------
                                            Karen E. Lynch
                                            Vice President



TRUSTEE:                            CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
                                    as Trustee


                                    By: /s/ Mauri J. Cowen                     
                                       ----------------------------------------
                                            Mauri J. Cowen
                                            Vice President and Trust Officer




                                      -12-

<PAGE>   13




GUARANTORS:                         BRIGHAM INC., a Nevada corporation


                                    By: /s/ Karen E. Lynch                    
                                       ---------------------------------------
                                            Karen E. Lynch
                                            Vice President


                                    BRIGHAM OIL & GAS, L.P.

                                    By: Brigham, Inc. a Nevada corporation, its
                                        General Partner


                                    By: /s/ Karen E. Lynch                    
                                       ----------------------------------------
                                            Karen E. Lynch
                                            Vice President


                                    BRIGHAM HOLDINGS I, LLC


                                    By: /s/ Ben M. Brigham 
                                       ----------------------------------------
                                    Name:  Ben M. Brigham 
                                         --------------------------------------
                                    Title: President 
                                           ------------------------------------


                                    BRIGHAM HOLDINGS II, LLC


                                    By: /s/ Ben M. Brigham 
                                       ----------------------------------------
                                    Name:  Ben M. Brigham  
                                         --------------------------------------
                                    Title: President 
                                          -------------------------------------


                                    DND OIL & GAS, L.P., a Texas limited 
                                    partnership

                                    By: Sooner Production Company, LLC, a Texas
                                        limited liability company, its General 
                                        Partner


                                                By: /s/ Karen E. Lynch        
                                                   ----------------------------
                                                        Karen E. Lynch
                                                        Vice President



                                      -13-

<PAGE>   14




                                    SOONER PRODUCTION COMPANY, LLC, a Texas
                                    limited liability company


                                    By: /s/ Karen E. Lynch                   
                                       ----------------------------------------
                                            Karen E. Lynch
                                            Vice President




                                      -14-

<PAGE>   15



The Noteholders have joined herein solely for the purpose of evidencing their
(i) consent to the foregoing, and (ii) authorization to the Trustee to execute
this Amendment:

                                    JOINT ENERGY DEVELOPMENT INVESTMENTS
                                    II LIMITED PARTNERSHIP, a Delaware limited
                                    partnership, as Purchaser

                                    By: Enron Capital Management II Limited
                                        Partnership, its General Partner

                                        By: Enron Capital II Corp., its
                                            General Partner


                                            By: /s/ Mark J. Warner            
                                                -------------------------------
                                                    Mark J. Warner
                                                    Agent and Attorney-in-Fact


                                    ENRON CAPITAL & TRADE RESOURCES
                                    CORP., a Delaware corporation


                                        By: /s/ Mark J. Warner                 
                                           ------------------------------------
                                                Mark J. Warner
                                                Agent and Attorney-in-Fact





<PAGE>   1
                                                                    Exhibit 4.3



                                      FORM
                              WARRANT CERTIFICATE


Number of Warrants: See Schedule I                 Warrant No.  See Schedule I 

                This warrant certificate ("Warrant Certificate")
                      certifies that, for value received,


                                 See Schedule I

is the registered holder of the number of warrants (the "Warrants") set forth
above. Each Warrant entitles the holder thereof, at any time or from time to
time during the Exercise Period, to purchase from the Company one fully paid
and nonassessable share of Common Stock at the Exercise Price, subject to
adjustment as provided herein. The Warrants constitute, as of the initial
Issuance Date, 4.9206% of the outstanding Common Stock on a fully diluted basis
including, for purposes of such calculation, the Acquired Shares and the
Warrant Shares. Initially capitalized terms used but not defined herein shall
have the meanings ascribed to them in the Securities Purchase Agreement. This 
Warrant Certificate amends and restates Warrant No. [see Schedule I] issued to 
[See Schedule I] on August 20, 1998.

         "Common Stock" means the common stock, $.01 par value per share, of
the Company and such other class of securities as shall then represent the
common equity of the Company.

         "Company" means Brigham Exploration Company, a Delaware corporation.

         "Exercise Period" means the period of time between the Funding Date,
as defined in the Securities Purchase Agreement and 5:00 p.m. (New York City
time) on the Expiration Date.

         "Exercise Price," subject in all circumstances to adjustment in
accordance with Section 2, means $3.50.

         "Expiration Date" means August 22, 2008.

         "Funding Date" is defined in the Securities Purchase Agreement.

         "IPO" shall mean the initial public offering of securities of the
Company consummated on May 24, 1997, pursuant to a registration statement filed
under the Securities Act of 1933, as amended, and the rules and regulations
promulgated thereunder.

         "Issuance Date" means August 20, 1998.



<PAGE>   2




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

         "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 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, or, in all other
cases, the Estimated Private Market Equity Value divided by the number of
outstanding shares (on a fully diluted basis using the treasury stock method).
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.

         "Securities Purchase Agreement" means the Securities Purchase
Agreement, dated as of August 20, 1998, among the Company, Enron Capital &
Trade Resources Corp. and Joint Energy Development Investments II Limited
Partnership, individually and as agent.

         1. EXERCISE OF WARRANTS. (a) The Warrants may be exercised in whole or
in part, at any time or from time to time, during the Exercise Period, by
presentation and surrender to the Company at its address set forth in Section 9
of (i) this Warrant Certificate with the Election To Exercise, attached hereto
as Exhibit A, duly completed and executed, and (ii) payment of the Exercise
Price, by bank draft or cashier's check, for the number of Warrants being
exercised. If the holder of this Warrant Certificate at any time exercises less
than all the Warrants, the Company shall issue to such holder a warrant
certificate identical in form to this Warrant Certificate, but evidencing a
number of Warrants equal to the number of Warrants originally represented by
this Warrant Certificate less the number of Warrants previously exercised.
Likewise, upon the presentation and surrender of this Warrant Certificate to
the Company at its address set forth in Section 9 and at the request of the
holder, the Company will, without expense, at the option of the holder, issue
to the holder in substitution for this Warrant Certificate one or more warrant
certificates in identical form and for an aggregate number of Warrants equal to
the number of Warrants evidenced by this Warrant Certificate.

                  (b) To the extent that the Warrants have not been exercised
at or prior to the Expiration Date, such Warrants shall expire and the rights
of the holder shall become void and of no effect.


                                      -2-

<PAGE>   3




         2. ANTIDILUTION ADJUSTMENTS. The shares of Common Stock purchasable on
exercise of the Warrants are shares of Common Stock as constituted as of the
Issuance Date. The number and kind of securities purchasable upon the exercise
of the Warrants, and the Exercise Price, shall be subject to adjustment from
time to time upon the happening of certain events, as follows:

                  (a) Mergers, Consolidations and Reclassifications. In case of
any reclassification or change of outstanding securities issuable upon exercise
of the Warrants at any time after the Issuance Date (other than a change in par
value, or from par value to no par value, or from no par value to par value or
as a result of a subdivision or combination to which subsection 2(b) applies),
or in case of any consolidation or merger of the Company with or into another
entity or other person (other than a merger with another entity or other person
in which the Company is the surviving corporation and which does not result in
any reclassification or change in the securities issuable upon exercise of this
Warrant Certificate), the holder of the Warrants shall have, and the Company,
or such successor corporation or other entity, shall covenant in the
constituent documents effecting any of the foregoing transactions that such
holder does have, the right to obtain upon the exercise of the Warrants, in
lieu of each share of Common Stock, other securities, money or other property
theretofore issuable upon exercise of a Warrant, the kind and amount of shares
of stock, other securities, money or other property receivable upon such
reclassification, change, consolidation or merger by a holder of the shares of
Common Stock, other securities, money or other property issuable upon exercise
of a Warrant if the Warrants had been exercised immediately prior to such
reclassification, change, consolidation or merger. The constituent documents
effecting any such reclassification, change, consolidation or merger shall
provide for adjustments which shall be as nearly equivalent as may be
practicable to the adjustments provided in this subsection 2(a). The provisions
of this subsection 2(a) shall similarly apply to successive reclassifications,
changes, consolidations or mergers.

                  (b) Subdivisions and Combinations. If the Company, at any
time after the Issuance Date, shall subdivide its shares of Common Stock into a
greater number of shares, the Exercise Price in effect immediately prior to
such subdivision shall be proportionately reduced, and the number of shares of
Common Stock purchasable upon exercise of the Warrants shall be proportionately
increased, as at the effective date of such subdivision, or if the Company
shall take a record of holders of its Common Stock for such purpose, as at such
record date, whichever is earlier. If the Company, at any time after the
Issuance Date, shall combine its shares of Common Stock into a smaller number
of shares, the Exercise Price in effect immediately prior to such combination
shall be proportionately increased, and the number of shares of Common Stock
purchasable upon exercise of the Warrants shall be proportionately reduced, as
at the effective date of such combination, or if the Company shall take a
record of holders of its Common Stock for purposes of such combination, as at
such record date, whichever is earlier.

                  (c) Dividends and Distributions. If the Company at any time
after the Issuance Date shall declare a dividend on its Common Stock payable in
stock or other securities of the Company to the holders of its Common Stock,
the holder of this Warrant Certificate shall, without

                                      -3-

<PAGE>   4




additional cost, be entitled to receive upon any exercise of a Warrant, in
addition to the Common Stock to which such holder would otherwise be entitled
upon such exercise, the number of shares of stock or other securities which
such holder would have been entitled to receive if he had been a holder
immediately prior to the record date for such dividend (or, if no record date
shall have been established, the payment date for such dividend) of the number
of shares of Common Stock purchasable on exercise of such Warrant immediately
prior to such record date or payment date, as the case may be.

                  (d) Certain Issuances of Securities. If the Company at any
time after the Issuance Date shall issue any additional shares of Common Stock
(otherwise than as provided in paragraphs (a) through (c) of this Section 2) at
a price per share less than the average Price per share of Common Stock for the
20 trading days immediately preceding the date of the authorization of such
issuance (the "Market Price") by the Board of Directors, then the Exercise
Price upon each such issuance shall be adjusted to that price determined by
multiplying the Exercise Price by a fraction:

                           i. the numerator of which shall be the sum of (1)
         the number of shares of Common Stock outstanding immediately prior to
         the issuance of such additional shares of Common Stock multiplied by
         the Market Price, and (2) the consideration, if any, received by the
         Company upon the issuance of such additional shares of Common Stock,
         and

                           ii. the denominator of which shall be the Market
         Price multiplied by the total number of shares of Common Stock
         outstanding immediately after the issuance of such additional shares
         of Common Stock.

         No adjustments of the Exercise Price shall be made under this
paragraph (d) upon the issuance of any additional shares of Common Stock that
(y) are issued pursuant to thrift plans, stock purchase plans, stock bonus
plans, stock option plans, employee stock ownership plans and other incentive
or profit sharing arrangements for the benefit of employees ("Employee Benefit
Plans") that otherwise would cause an adjustment under this paragraph (d);
provided that the aggregate number of shares of Common Stock so issued
(including the shares issued pursuant to any options, rights or warrants or
convertible or exchangeable securities issued under such Employee Benefit Plans
containing the right to purchase shares of Common Stock) pursuant to Employee
Benefit Plans after the closing date of the IPO, as adjusted for any stock
splits, stock dividends or subdivisions or combinations of Common Stock prior
to the Expiration Date, shall not in the aggregate exceed 5% of the Company's
outstanding Common Stock at the time of such issuance; or (z) are issued
pursuant to any Common Stock Equivalent (as hereinafter defined) (i) if upon
the issuance of any such Common Stock Equivalent, any such adjustments shall
previously have been made pursuant to paragraph (e) of this Section 2 or (ii)
if no adjustment was required pursuant to paragraph (e) of this Section 2.

                  (e) Common Stock Equivalents. If the Company shall, after the
Issuance Date, issue any security or evidence of indebtedness which is
convertible into or exchangeable for

                                      -4-

<PAGE>   5




Common Stock ("Convertible Security"), or any warrant, option or other right to
subscribe for or purchase Common Stock or any Convertible Security, other than
pursuant to Employee Benefit Plans (together with Convertible Securities,
"Common Stock Equivalent"), or if, after any such issuance, the price per share
for which additional shares of Common Stock may be issuable thereunder is
amended, then the Exercise Price upon each such issuance or amendment shall be
adjusted as provided in subsection (d) on the basis that (i) the maximum number
of additional shares of Common Stock issuable pursuant to all such Common Stock
Equivalents shall be deemed to have been issued as of the earlier of (a) the
date on which the Company shall enter into a firm contract for the issuance of
such Common Stock Equivalent, or (b) the date of actual issuance of such Common
Stock Equivalent; and (ii) the aggregate consideration for such maximum number
of additional shares of Common Stock shall be deemed to be the minimum
consideration received and receivable by the Company for the issuance of such
additional shares of Common Stock pursuant to such Common Stock Equivalent;
provided, however, that no adjustment shall be made pursuant to this subsection
(e) unless the consideration received and receivable by the Company per share
of Common Stock for the issuance of such additional shares of Common Stock
pursuant to such Common Stock Equivalent is less than the Market Price. No
adjustment of the Exercise Price shall be made under this subsection (e) upon
the issuance of any Convertible Security which is issued pursuant to the
exercise of any warrants or other subscription or purchase rights therefor, if
any adjustment shall previously have been made in the Exercise Price then in
effect upon the issuance of such warrants or other rights pursuant to this
subsection (e).

                  (f) Miscellaneous. The following provisions shall be
applicable to the making of adjustments in the Exercise Price hereinbefore
provided in this Section 2:

                           i. The consideration received by the Company shall
         be deemed to be the following: (I) to the extent that any additional
         shares of Common Stock or any Common Stock Equivalent shall be issued
         for cash consideration, the consideration received by the Company
         therefor, or, if such additional shares of Common Stock or Common
         Stock Equivalent are offered by the Company for subscription, the
         subscription price, or, if such additional shares of Common Stock or
         Common Stock Equivalent are sold to underwriters or dealers for public
         offering without a subscription offering, the initial public offering
         price, in any such case excluding any amounts paid or receivable for
         accrued interest or accrued dividends and without deduction of any
         compensation, discounts, commissions or expenses paid or incurred by
         the Company for and in the underwriting of, or otherwise in connection
         with, the issue thereof; (II) to the extent that such issuance shall
         be for a consideration other than cash, then, except as herein
         otherwise expressly provided, the fair value of such consideration at
         the time of such issuance as determined in good faith by the Board of
         Directors, as evidenced by a certified resolution of the Board of
         Directors delivered to the holder of this Warrant Certificate setting
         forth such determination. The consideration for any additional shares
         of Common Stock issuable pursuant to any Common Stock Equivalent shall
         be the consideration received by the Company for issuing such Common
         Stock Equivalent, plus the additional consideration payable to the
         Company upon the exercise,

                                      -5-

<PAGE>   6




         conversion or exchange of such Common Stock Equivalent. In case of the
         issuance at any time of any additional shares of Common Stock or
         Common Stock Equivalent in payment or satisfaction of any dividend
         upon any class of stock other than Common Stock, the Company shall be
         deemed to have received for such additional shares of Common Stock or
         Common Stock Equivalent (which shall not be deemed to be a dividend
         payable in, or other distribution of, Common Stock under subsection
         (c) above) consideration equal to the amount of such dividend so paid
         or satisfied.

                           ii. Upon the expiration of the right to convert,
         exchange or exercise any Common Stock Equivalent the issuance of which
         effected an adjustment in the Exercise Price, if any such Common Stock
         Equivalent shall not have been converted, exercised or exchanged, the
         number of shares of Common Stock deemed to be issued and outstanding
         because they were issuable upon conversion, exchange or exercise of
         any such Common Stock Equivalent shall no longer be computed as set
         forth above, and the Exercise Price shall forthwith be readjusted and
         thereafter be the price which it would have been (but reflecting any
         other adjustments in the Exercise Price made pursuant to the
         provisions of subsection (d) after the issuance of such Common Stock
         Equivalent) had the adjustment of the Exercise Price made upon the
         issuance or sale of such Common Stock Equivalent been made on the
         basis of the issuance only of the number of additional shares of
         Common Stock actually issued upon exercise, conversion or exchange of
         such Common Stock Equivalent and thereupon only the number of
         additional shares of Common Stock actually so issued shall be deemed
         to have been issued and only the consideration actually received by
         the Company (computed as in subparagraph (i) of this paragraph (f))
         shall be deemed to have been received by the Company.

                           iii. The number of shares of Common Stock at any
         time outstanding shall not include any shares thereof then directly or
         indirectly owned or held by or for the account of the Company or its
         wholly owned subsidiaries.

                           iv. For the purposes of this Section 2, the term
         "shares of Common Stock" shall mean shares of (i) the class of stock
         designated as the Common Stock at the date hereof or (ii) any other
         class of stock resulting from successive changes or reclassifications
         of such shares consisting solely of changes in par value, or from par
         value to no par value, or from no par value to par value. If at any
         time, because of an adjustment pursuant to subsection (a), the
         Warrants shall entitle the holders to purchase any securities other
         than shares of Common Stock, thereafter the number of such other
         securities so purchasable upon exercise of each Warrant and the
         Exercise Price of such securities shall be subject to adjustment from
         time to time in a manner and on terms as nearly equivalent as
         practicable to the provisions with respect to the Common Stock
         contained in this Section 2.

                  (g) Calculation of Exercise Price. The Exercise Price in
effect from time to time shall be calculated to four decimal places and rounded
to the nearest thousandth.

                                      -6-

<PAGE>   7




         3. NOTICE OF ADJUSTMENTS. Whenever the Exercise Price or the number of
shares of Common Stock is required to be adjusted as provided in Section 2, the
Company shall forthwith compute the adjusted Exercise Price or the number of
shares of Common Stock issuable and shall prepare and mail to the holder hereof
a certificate setting forth such adjusted Exercise Price or such number of
shares of Common Stock, showing in reasonable detail the facts upon which the
adjustment is based.

         4. VOLUNTARY REDUCTION. (a) The Company may at its option, but shall
not be obligated to, at any time during the term of the Warrants, reduce the
then current Exercise Price by any amount selected by the Board of Directors;
provided that if the Company elects so to reduce the then current Exercise
Price, such reduction shall be irrevocable during its effective period and
remain in effect for a minimum of 30 days following the date of such election,
after which time the Company may, at its option, reinstate the Exercise Price
in effect prior to such reduction. Whenever the Exercise Price is reduced, the
Company shall mail to the holder a notice of the reduction at least 30 days
before the date the reduced Exercise Price takes effect, stating the reduced
Exercise Price and the period for which such reduced Exercise Price will be in
effect.

                  (b) The Company may make such decreases in the Exercise
Price, in addition to those required or allowed by this Section 4, as shall be
determined by it, as evidenced by a certified resolution of the Board of
Directors delivered to the holders, to be advisable to avoid or diminish any
income tax to the holder resulting from any dividend or distribution of stock
or issuance of rights or warrants to purchase or subscribe for stock or from
any event treated as such for income tax purposes.

         5. NOTICES TO WARRANT HOLDERS. In the event:

                  (a) the Company shall authorize any consolidation or merger
to which the Company is a party and for which approval of any stockholders of
the Company is required, or of the conveyance or sale of all or substantially
all of the assets of the Company, or of any reclassification or change of the
Common Stock or other securities issuable upon exercise of the Warrants (other
than a change in par value, or from par value to no par value, or from no par
value to par value or as a result of a subdivision or combination), or a tender
offer or exchange offer for shares of Common Stock (or other securities
issuable upon the exercise of the Warrants); or

                  (b) the Company shall declare any dividend (or any other
distribution) on the Common Stock or any other class of its capital stock; or

                  (c) the Company shall authorize the granting to the holders
of Common Stock or any other class of its capital stock of rights or warrants
to subscribe for or purchase any shares of any class or series of capital stock
or any other securities convertible into or exchangeable for shares of stock;
or


                                      -7-

<PAGE>   8




                  (d) of the voluntary or involuntary dissolution, liquidation
or winding up of the Company;

         then the Company shall cause to be sent to the holder hereof, at least
30 days prior to the applicable record date hereinafter specified, or promptly
in the case of events for which there is no record date, a written notice
stating (x) the date for the determination of the holders of record of shares
of Common Stock (or other securities issuable upon the exercise of the
Warrants) entitled to receive any such dividends or other distribution, (y) the
initial expiration date set forth in any tender offer or exchange offer for
shares of Common Stock (or other securities issuable upon the exercise of the
Warrants), or (z) the date on which any of the events specified in subsections
(a)-(d) is expected to become effective or consummated, and the date as of
which it is expected that holders of record of shares of Common Stock (or other
securities issuable upon the exercise of the Warrants) shall be entitled to
exchange such shares for securities or other property, if any, deliverable upon
any such event. Failure to give such notice or any defect therein shall not
affect the legality or validity of any such event, or the vote upon any such
action.

         6. REPORTS TO WARRANT HOLDERS. The Company will cause to be delivered,
by first-class mail, postage prepaid, to the holder at such holder's address
appearing hereon, or such other address as the holder shall specify, a copy of
any reports delivered by the Company to the holders of Common Stock.

         7. COVENANTS OF THE COMPANY. The Company covenants and agrees that:

                  (a) Until the Expiration Date, the Company shall at all times
reserve and keep available, free from preemptive rights, out of the aggregate
of its authorized but unissued Common Stock (and other securities), for the
purpose of enabling it to satisfy any obligation to issue shares of Common
Stock (and other securities) upon the exercise of the Warrants, the number of
shares of Common Stock (and other securities) issuable upon the exercise of
such Warrants.

                  (b) The Company shall pay all expenses, taxes and other
charges payable in connection with the preparation, issuance and delivery of
new warrant certificates on transfer of the Warrants.

                  (c) All Common Stock (and other securities) which may be
issued upon exercise of the Warrants shall upon issuance be validly issued,
fully paid, non-assessable and free from all preemptive rights and all taxes,
liens and charges with respect to the issuance thereof, and will not be subject
to any restrictions on voting or transfer thereof except as set forth in any
stockholders agreement.

                  (d) All original issue taxes payable in respect of the
issuance of shares of Common Stock to the registered holder hereof upon the
exercise of the Warrants shall be borne by the Company; provided, that the
Company shall not be required to pay any tax or charge imposed

                                      -8-

<PAGE>   9




in connection with any transfer involved in the issuance of any certificate
representing shares of Common Stock (and other securities) in any name other
than that of the registered holder hereof, and in such case the Company shall
not be required to issue or deliver any certificate representing shares of
Common Stock (and other securities) until such tax or other charge has been
paid or it has been established to the Company's satisfaction that no such tax
or charge is due.

                  (e) As soon as practicable after the receipt from the holder
of this Warrant Certificate of notice of the exercise of a number of warrants
sufficient to require a filing under the Hart-Scott-Rodino Antitrust
Improvements Act of 1976 and the rules, regulations and formal interpretations
thereunder, as amended from time to time (the "HSR Act"), but in any event no
later than the 10th business day after receipt of such notice, the Company will
(i) prepare and file with the Antitrust Division of the Department of Justice
(the "DOJ") and the Federal Trade Commission (the "FTC") the Notification and
Report Form (accompanied by all documentary attachments contemplated thereby)
required by the HSR Act, (ii) upon the request of the holder, request early
termination of the waiting period imposed by the HSR Act, (iii) coordinate and
cooperate with the holder in responding to formal and informal requests for
additional information and documentary material from the DOJ and the FTC in
connection with such filing, (iv) use its best efforts to take, or cause to be
taken, all reasonable action and to do, or cause to be done, all things
necessary and appropriate to permit the issuance to the holder of the shares of
Common Stock issuable upon the exercise of the warrants with respect to which
any filing is required under the HSR Act, and (v) reimburse the holder for the
entire amount of any filing fee or any other costs and expenses incurred by the
holder in connection therewith (including legal fees), or as required to be
paid under the HSR Act.

                  (f) QUOTATION ON NASDAQ. The Company shall maintain the
designation and quotations, or listing, of its Common Stock on the NASDAQ
national market (or on the New York Stock Exchange or the American Stock
Exchange) until the date on which none of the Warrants or Warrant Shares remain
outstanding.

         8. NO RIGHTS AS STOCKHOLDER. The holder of the Warrants shall not, by
virtue of holding such Warrants, be entitled to any rights of a stockholder of
the Company either at law or in equity, and the rights of the holder of the
Warrants are limited to those expressed herein.

         9. NOTICES. All notices provided for hereunder shall be in writing and
may be given by registered or certified mail, return receipt requested, telex,
telegram, telecopier, air courier guaranteeing overnight delivery of personal
delivery, if to the holder at the following address:


                                      -9-

<PAGE>   10


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

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

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

                  -----------------------
                  Attention:                         
                            -------------
                  Telecopier:                        
                             ------------

         and, if to the Company:

                  Brigham Exploration Company
                  6300 Bride Point Parkway
                  Building 2, Suite 500
                  Austin, Texas 78730
                  Attention: Craig M. Fleming
                  Telecopier: (512) 472-3400

         10. GOVERNING LAW. This Warrant Certificate shall be governed by and
construed in accordance with the laws of the State of Texas without regard to
principles of conflict of laws.

         11. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT CERTIFICATES. Upon
receipt by the Company of evidence reasonably satisfactory to it of the
ownership of and the loss, theft, destruction or mutilation of any Warrant
Certificate, then, in the absence of notice to the Company that such Warrant
Certificate has been acquired by a bona fide purchaser, the Company shall
execute and deliver, in exchange for or in lieu of the lost, stolen, destroyed
or mutilated Warrant Certificate, a substitute Warrant Certificate of the same
tenor and evidencing a like number of Warrants.

         12. ASSIGNMENT. The holder of this Warrant Certificate shall be
entitled, without obtaining the consent of the Company, to transfer or assign
its rights, title and interest in (and rights, title and interest under) this
Warrant Certificate in whole or in part to any Person or Persons. Upon
surrender of this Warrant Certificate to the Company, with the Transfer Form
annexed hereto as Exhibit B duly executed, the Company shall, without charge,
execute and deliver a new warrant certificate or warrant certificates,
identical in form to this Warrant Certificate, evidencing the number of
Warrants being transferred pursuant to the Transfer Form in the name of the
assignee or assignees named in such Transfer Form. If the holder's entire
interest is not being assigned, the Company shall, without charge, execute and
deliver one or more new warrant certificates identical in form to this Warrant
Certificate, but evidencing a number of Warrants equal to the number of
Warrants originally represented by this Warrant Certificate less the number
being transferred pursuant to the Transfer Form, and this Warrant Certificate
shall promptly be canceled. The terms and provisions of this Warrant
Certificate shall inure to the benefit of the holder and its successors and
assigns and shall be binding upon the Company and its successors and assigns,
including, without limitation, any Person succeeding the Company by merger,
consolidation or acquisition of all or substantially all of the Company's
assets.

                                      -10-

<PAGE>   11



         IN WITNESS WHEREOF, the Company has caused this Warrant Certificate to
be executed as of March 26, 1999, by the undersigned, thereunto duly
authorized.


                                    BRIGHAM EXPLORATION COMPANY


                                    By: /s/ Karen E. Lynch                   
                                       ----------------------------------------
                                            Karen E. Lynch
                                            Vice President


                                      -11-

<PAGE>   12




                                   EXHIBIT A

                              ELECTION TO EXERCISE
             [To be executed on exercise of the Warrants evidenced
                         by this Warrant Certificate]

TO:      Brigham Exploration Company

         The undersigned, the holder of the Warrants evidenced by the attached
Warrant Certificate, hereby irrevocably elects to exercise Warrants, and
herewith makes payment of ($______) representing the aggregate Exercise Price
thereof, and requests that the certificate representing the securities issuable
hereunder be issued in the name of _____________________ and delivered to ,
whose address is ___________________________________________.

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

                                    Name of Registered Holder:               
                                                            -------------------
                                    Signature:                                 
                                              ---------------------------------
                                    Title:                                     
                                          -------------------------------------
                                    Address:                                   
                                            -----------------------------------


NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.


                                      -12-

<PAGE>   13




                                   EXHIBIT B

                                 TRANSFER FORM
               [To be executed only upon transfer of the Warrants
                    evidenced by this Warrant Certificate]


         FOR VALUE RECEIVED, the undersigned hereby sells, assigns and
transfers unto ______________________________________________________ the
Warrants represented by the within Warrant Certificate, together with all
right, title and interest therein, and does hereby irrevocably constitute and
appoint _____________________________________ Attorney-in-Fact, to transfer
same on the books of the Company with full power of substitution in the
premises.

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

                                    Name of Registered Holder:              
                                                               ----------------
                                    Signature:                               
                                              ---------------------------------
                                    Title:                                    
                                          -------------------------------------
                                    Address:                                  
                                            -----------------------------------


WITNESS:


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





NOTICE: The above signature(s) must correspond with the name as written on the
face of the Warrant Certificate in every detail, without alteration or
enlargement or any change whatsoever.


                                      -13-

<PAGE>   14



                                   SCHEDULE I
                                   ----------

<TABLE>
<CAPTION>

Warrant Number          Issued To                                       Number of Warrants
- --------------          ---------                                       ------------------
<S>                     <C>                                             <C>
A-3                     ECT MERCHANT INVESTMENTS CORP.                  250,000

A-4                     JOINT ENERGY DEVELOPMENT                        750,000
                        INVESTMENTS II LIMITED PARTNERSHIP

</TABLE>

Warrant No. A-3 amends and restates Warrant No. 1 issued to Enron Capital & 
Trade Resources Corp; and Warrant No. A-4 amends and restates Warrant No. A-2 
issued to Joint Energy Development Investments II Limited Partnership.










                                     -14-

<PAGE>   1

                                                                EXHIBIT 10.36.2

                      SECOND AMENDMENT TO CREDIT AGREEMENT

         SECOND AMENDMENT TO CREDIT AGREEMENT, dated as of March 26, 1999
("this Amendment"), among 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 Bank of Montreal, a Canadian bank, as agent
for Lenders under the Credit Agreement (in such capacity, the "Agent").

                                    RECITALS


         WHEREAS, the Borrower, the Lenders and 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 (as so
amended, the "Credit Agreement"); and

         WHEREAS, the Borrower has advised the Lenders and the Agent that it
desires to amend certain provisions of the Credit Agreement, and the Borrower
has 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 this Amendment;

         NOW, THEREFORE, in consideration of the premises, covenants and
agreements contained herein, the parties hereto hereby agrees as follows:


         Section 1. Definitions. Capitalized terms used and not otherwise
defined herein are used with the meanings ascribed thereto in the Credit
Agreement. The following capitalized terms shall have the following respective
meanings when used herein:

         A. "Duke Consent Letter" shall mean that certain Letter Agreement
dated as of February 18, 1999 executed by the Borrower and the Lenders, a copy
of which is attached hereto as Exhibit A.

         B. "Duke Transaction" shall mean the transactions contemplated by the
Duke Consent Letter.

         C. "Lending Relationship" shall refer to the Credit Agreement and the
other Loan Documents, including, without limitation, this Amendment, together
with any and all negotiations, discussions, acts, omissions, renewals,
extensions, and other agreements or events related to the Credit Agreement and
such other Loan Documents, the parties' obligations thereunder and the
transactions contemplated thereby, including, without limitation, any such
negotiations, discussions, acts, omissions, renewals, extensions, other
agreements or events that (a) occurred prior to the date hereof, (b) may



                                       1
<PAGE>   2

occur on the date hereof, or (c) occurred prior to the execution of this
Amendment and the instruments and documents executed and delivered in
connection herewith or relating hereto.

         D. "New Mortgage" shall mean that certain Mortgage, Deed of Trust,
Assignment of Production, Security Agreement and Financing Statement dated as
of the date hereof from Brigham Oil & Gas, L.P. to Thomas McGraw, as Trustee,
for the benefit of Bank of Montreal, as Agent.

         E. "Released Claims" shall mean any and all claims (including without
limitation any liabilities, damages, demands and causes of action arising
therefrom), whether (a) at law or in equity, (b) on the alleged commission of a
tort, (c) on the alleged breach (or anticipatory breach or repudiation) of any
contract, duty, or warranty (whether oral or written, express or implied), (d)
on the alleged violation of any statute, tariff, or regulation (whether
promulgated by the United States, any state thereof, any foreign state or
country, or any other governmental agency or entity, wherever located), or (e)
on any other factual, legal or equitable theory, including, without limitation,
any claim for damages of any type or nature, for injunctive or other relief,
for attorneys' fees, interest or any other liability whatsoever on any theory,
including without limitation any loss, cost or damage in connection with or
based upon "lender liability", unfair dealing, duress, coercion, control or
undue influence, extortion or commercial bribery, breach of an implied covenant
or duty of good faith and fair dealing, material misrepresentation or omission,
overreaching, unconscionability, conflict of interest, bad faith, malpractice,
disparate bargaining position, detrimental reliance, promissory estoppel,
estoppel by deed, waiver, laches, or any other equitable theory, equitable
subordination, breach of fiduciary duty or any other duty, or tortious
inducement to commit such breach, tortious interference with contract or
prospective business relations, negligent performance of contractual
obligations, or other theories of negligence, negligent or intentional
infliction of emotional distress, slander, libel, other defamation, fraudulent
transfer, conversion, trespass to (or clouding the title of) property, usury,
violations of the Racketeer Influenced and Corrupt Organizations Act, deceptive
trade practices, conspiracy, or any theory of liability as partners or joint
venturers, that any Releasing Party may have as of the date hereof against any
Released Party with respect to the Lending Relationship.

         F. "Released Party" shall mean each of the Agent, the Lenders and
their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").

         G. "Releasing Party" shall mean each of the Borrower and the
Guarantors and their respective predecessors, successors, assigns, directors,
officers, partners, employees, agents, attorneys, principals, Affiliates and
all other Persons who might have a claim against any Released Party
(collectively, the "Releasing Parties").



                                       2
<PAGE>   3


         Section 2. Amendments to Credit Agreement. The Credit Agreement is
amended hereby as follows:

         A. Section 1.02 is amended hereby:

                  (i) by deleting the definition of the term "Aggregate Maximum
Credit Amounts" in its entirety and substituting the following therefor:

                  "'Aggregate Maximum Credit Amounts' at any time shall equal
         the sum of the Maximum Credit Amounts of the Lenders ($65,000,000), as
         the same may be reduced pursuant to Section 2.03(b) and Section
         2.07(d).";

                  (ii) by deleting the definition of the term "Applicable
Margin" in its entirety and substituting the following therefor:

                  "'Applicable Margin' shall mean (i) 2% with respect to Base
         Rate Loans and (ii) 3% with respect to Eurodollar Loans.";

                  (iii) by deleting the reference "and to participate in the
Letters of Credit as provided in Section 2.01(b)" in the definition of the term
"Commitment";

                  (iv) by deleting the reference "January 31, 1999" in the
definition of the term "First Borrowing Base Determination Date" and
substituting therefor the reference "June 1, 1999";

                  (v) by inserting in the definition of the term "Guaranty
Agreements" after the reference to "Brigham Holdings II, LLC", the reference
"Sooner Production LLC";

                  (vi) by deleting all text after the word "Loans" in the
definition of the term "Initial Funding" and inserting a period after the word
"Loans";

                  (vii) by deleting the first paragraph of the definition of
the term "Interest Period" in its entirety and substituting therefor the
following new definition:

                  "'Interest Period' shall mean, with respect to (i) any
         Eurodollar Loan made prior to the First Borrowing Base Determination
         Date, the period commencing on the date such Eurodollar Loan is made
         and ending on the numerically corresponding day in the first month
         thereafter, and (ii) any Eurodollar Loan made after the First
         Borrowing Base Determination Date, the period commencing on the date
         such Eurodollar Loan is made and ending on the numerically
         corresponding day in the first or third calendar month thereafter, as
         Borrower may select as provided in Section 2.02, except that each
         Interest Period which commences on the last Business Day of a calendar
         month (or on any day for which there is no numerically corresponding
         day in the appropriate subsequent calendar month) shall end on the
         last Business Day of the appropriate subsequent calendar month.";



                                       3
<PAGE>   4

                  (viii) by deleting the definition of the term "Issuing Bank"
in its entirety;

                  (ix) by deleting the definition of the term "LC Commitment"
in its entirety;

                  (x) by deleting the definition of the term "LC Exposure" in
its entirety;

                  (xi) by deleting the definition of the term "Letter of Credit
Agreements" in its entirety;

                  (xii) by deleting the definition of the term "Letters of
Credit" in its entirety;

                  (xiii) by deleting the reference "the Letters of Credit, the
Letter of Credit Agreements," and the reference ", or reimbursement obligations
under the Letters of Credit," in the definition of the term "Loan Documents";
and

                  (xiv) by deleting the reference "Section 8.09(a)" in the
definition of the term "Mortgage" and substituting the reference "Section
8.09(b)" therefor.

         B. Section 2.01 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference "and Letters of Credit" in the
section title;

                  (ii) by deleting the reference "together with the LC
Exposure" in subsection (a); and

                  (iii) by deleting the text of subsection (b) in its entirety
and substituting therefor the reference "Intentionally left blank."

         C. Section 2.02 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference "and Letters of Credit" in the
section title;

                  (ii) by deleting the reference "All" in the third sentence of
subsection (d) and substituting the following therefor:

                  "So long as the Borrowing Base is equal to or greater than
         the outstanding principal amount of the Loans, all"; and

                  (iii) by deleting the reference "All" in the third sentence
of subsection (e) and substituting the following therefor:

                  "So long as the Borrowing Base is equal to or greater than
         the outstanding principal amount of the Loans, all"; and


                                       4
<PAGE>   5


                  (iv) by deleting subsection (g) in its entirety.

         D. Section 2.03 of the Credit Agreement is amended hereby by deleting
the text of subsection (a) in its entirety, and substituting the following
therefor:

                  "The Aggregate Commitments shall at all times be equal to
         $65,000,000 until the First Borrowing Base Determination Date after
         which date the Aggregate Commitments shall be equal to the lesser of
         (i) the Aggregate Maximum Credit Amounts or (ii) the Borrowing Base as
         determined from time to time.".

         E. Section 2.04 of the Credit Agreement is amended hereby by deleting
the title and text of subsection (b) in their entirety and substituting
therefor the reference "Intentionally left blank."

         F. Section 2.05 of the Credit Agreement is amended hereby by deleting
the reference "or to provide funds for disbursements or reimbursements under
Letters of Credit".

         G. Section 2.07 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference to "plus the LC Exposure" in
subsection (b);

                  (ii) by deleting the text of subsection (c) in its entirety
and substituting the following therefor:

                  "Upon any redetermination of the amount of the Borrowing Base
in accordance with Section 2.08, if the redetermined Borrowing Base is less
than the aggregate outstanding principal amount of the Loans then, within
ninety (90) days (or such shorter period as hereinafter provided) of receipt of
written notice of the redetermined Borrowing Base, the Borrower shall prepay
the Loans in an aggregate principal amount equal to such excess, together with
interest on the principal amount paid accrued to the date of such prepayment;
provided however, that following the first Borrowing Base determination such
required prepayment shall be made on or before thirty (30) days after such
first Borrowing Base determination if the amount of the required payment equals
or exceeds an amount equal to 10% of the redetermined Borrowing Base."; and

                  (iii) by inserting the following reference before the last
sentence of subsection (d):

                  "Prior to the initial Borrowing Base determination, all
prepayments on the Loans shall reduce the Maximum Credit Amounts pro tanto;
provided that immediately following any such prepayment the Maximum Credit
Amounts shall be automatically reinstated pro tanto in an aggregate amount
equal to the lesser of (i) $5,000,000 and (ii) the amount of such prepayment."



                                       5
<PAGE>   6

         H. Section 2.08 of the Credit Agreement is amended hereby by as
follows:


                  (i) by deleting the reference "or any LC Exposure" in
subsection (a);

                  (ii) by deleting the text of subsection (c) in its entirety
and substituting the following therefor:

         "The Agent may exclude any Oil and Gas Property or portion of
         production therefrom or any income from any other Property from the
         Borrowing Base, at any time, because title information is not
         reasonably satisfactory, such Property is not Mortgaged Property or
         such Property is not assignable. No Property of the Borrower subject
         to the New Mortgage nor any production or income therefrom shall be
         included in the Borrowing Base until such time as an amendment or
         supplement to the New Mortgage in form satisfactory to the Agent is
         filed of record, which shall contain with respect to such Property
         such representations, warranties and covenants as to title, defense of
         title, revenue and cost bearing interest, rentals paid and leases in
         effect, and such other provisions, as the Agent may request."

         I. Section 2.09 of the Credit Agreement is amended hereby by deleting
the title and text of such section in its entirety and substituting therefor
the reference "Intentionally left blank."

         J. Section 2.10 of the Credit Agreement is amended hereby by deleting
the title and text of such section in its entirety and substituting therefor
the reference "Intentionally left blank."

         K. Section 3.02 of the Credit Agreement is amended hereby by deleting
the paragraph beginning "Accrued interest on Base Rate Loans" in its entirety
and substituting the following therefor:

                  "Accrued interest on Base Rate Loans shall be payable on the
         last day of each calendar month, and accrued interest on each
         Eurodollar Loan shall be payable on the last day of the Interest
         Period therefor and, if such Interest Period is longer than one month
         at one-month intervals following the first day of each Interest
         Period, except that interest payable at the Post-Default Rate shall be
         payable from time to time on demand and interest on any Eurodollar
         Loan that is converted into a Base Rate Loan (pursuant to Section
         5.04) shall be payable on the date of conversion (but only to the
         extent so converted)."

         L. Section 4.02 of the Credit Agreement is amended hereby as follows:

                  (i) by inserting the word "and" before the reference "(iii)";
and


                                       6
<PAGE>   7

                  (ii) by deleting the reference "and (iv) each reimbursement
by the Borrower of disbursements under Letters of Credit shall be made for the
account of the Issuing Bank or, if funded by the Lenders, pro rata for the
account of the Lenders, in accordance with the amounts of reimbursement
obligations due and payable to each respective Lender".

         M. Section 4.04 of the Credit Agreement is amended hereby by deleting
the reference "or a payment under a Letter of Credit to be made by it
hereunder".

         N. Section 4.05 of the Credit Agreement is amended hereby by deleting
the following references in subsection (b):

                  (i) "(or reimbursement as to any Letter of Credit)";

                  (ii) "(or reimbursement)";

                  (iii) "(or participants in Letters of Credit)";

                  (iv) "(or reimbursements of Letters of Credit)"; and

                  (v) "(or Letters of Credit)".

         O. Section 5.01 of the Credit Agreement is amended hereby by deleting
all references to "Letters of Credit" in subsections (a), (c) and (d).

         P. Section 5.06 of the Credit Agreement is amended hereby by deleting
the reference "and participation interests in Letters of Credit (if any)" in
subsection (d).

         Q. Section 6.02 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the reference "and Letters of Credit" in the
section title;

                  (ii) by deleting the reference "and to issue, renew, extend
or reissue Letters of Credit for the account of the Borrower" in the
introductory paragraph of such section; and

                  (iii) by deleting all references "or issuance, renewal,
extension or reissuance of a Letter of Credit" in subsection (c).

         R. The introductory language to Article VII of the Credit Agreement is
amended hereby by deleting the reference "and issuance, renewal, extension or
reissuance of a Letter of Credit".

         S. Section 8.01 of the Credit Agreement is amended hereby as follows:

                  (i) by inserting the following new subsection (c):



                                       7
<PAGE>   8

                  "(c) Monthly Financial Statements. As soon as available and
         in any event within thirty (30) days after the end of each calendar
         month that is not also the end of one of Brigham Exploration's first
         three fiscal quarterly periods or of Brigham Exploration's fiscal
         year, consolidated statements of income and changes in financial
         position of Brigham Exploration and its Consolidated Subsidiaries for
         such period and for the period from the beginning of the respective
         fiscal year to the end of such period, and the related consolidated
         balance sheets as at the end of such period and, beginning March 31,
         2000, statements setting forth in each case in comparative form the
         corresponding figures for the corresponding period in the preceding
         fiscal year, accompanied by the certificate of a Responsible Officer,
         which certificate shall state that such financial statements fairly
         present the consolidated financial condition and results of operations
         of Brigham Exploration and its Consolidated Subsidiaries in accordance
         with GAAP, as at the end of, and for, such period (subject to normal
         year-end audit adjustments).";

                  (ii) by relettering the existing subsections (c) through (i)
as subsections (d) through (j);

                  (iii) by deleting in subsection (i), as relettered by (ii)
above, the reference "Concurrent with the First Reserve Report and each January
1 Reserve Report thereafter" and substituting therefor the reference "On or
before January 31 of each year"; and

                  (iv) by inserting after the reference "paragraph (a) or (b)"
in the final paragraph of Section 8.01 of the reference "or (c)".

         T. Section 8.07 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the text of subsection (a) in its entirety
     and substituting therefor the reference "Intentionally left blank"; and

                  (ii) by deleting the reference "January 31, 1999 " in the
     first sentence of subsection (b) and substituting therefor the reference 
     "June 1, 1999"; and;

                  (ii) by deleting each reference to "January 1" in subsection
     (b) and substituting therefor the reference "January 31".

         U. Section 8.09 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting the text of subsection (a) in its entirety
and substituting the following therefor:

                  "The Borrower will grant and will cause each of its
         Subsidiaries to grant to the Agent as security for the Indebtedness a
         perfected Lien on the Borrower's or such Subsidiary's interest in any
         Oil and Gas Properties 


                                       8
<PAGE>   9

         acquired after the date hereof at the cash acquisition cost to the
         Borrower or such Subsidiary equal to or exceeding $1,000,000, which
         Lien will be created and perfected by and in accordance with the
         provisions of deeds of trust, security agreements and financing
         statements, or other Loan Documents, all in form substantially the
         same as the New Mortgage (subject to such changes as are necessary as
         a result of, to reflect and/or to account for changes in applicable
         law) and in sufficient executed (and acknowledged where necessary or
         appropriate) counterparts for recording purposes.";

                  (ii) by inserting the following new subsection (b):

                  "(b) The Borrower will grant and will cause each of its
         Subsidiaries to grant to the Agent as security for the Indebtedness a
         first-priority Lien interest (subject only to Excepted Liens and the
         matters set forth on Schedule 7.10 hereto) on the Borrower's or such
         Subsidiary's interest in any Oil and Gas Properties identified after
         the Closing Date as containing proved Hydrocarbon reserves, which Lien
         will be created and perfected by and in accordance with the provisions
         of deeds of trust, security agreements and financing statements, or
         other Loan Documents, all in form substantially the same as the
         previous Mortgages (subject to such changes as are necessary as a
         result of, to reflect and/or to account for changes in applicable law)
         and in sufficient executed (and acknowledged where necessary or
         appropriate) counterparts for recording purposes.";

                  (iii) by relettering subsections (b) and (c) as subsections
(c) and (d);

                  (iv) by deleting in subsection (c), as relettered by (iii)
above, the reference "Section 8.09(a)" and substituting therefor the reference
"Section 8.09(b)";

                  (v) by deleting the reference "80%" in subsection (c) (as
relettered by (iii) above) and substituting therefor the reference "90%"; and

                  (vi) by inserting after the reference "Loan Document in any
state" in subsection (d), as relettered by (iii) above, the following
reference:

                  "other than the New Mortgage and any other mortgage filed
         pursuant to subsection (a) of this Section 8.09 or any other mortgage
         substantially in the form of the New Mortgage."

         V. Section 9.01 of the Credit Agreement is amended hereby by deleting
the text of subsection (h) in its entirety and substituting the following
therefor:

                  "Debt of the Borrower described on Schedule 9.01(h) and such
         other Debt of the Borrower related to the acquisition of software and
         licensing rights related thereto that does not exceed $100,000 at any
         one time outstanding."



                                       9
<PAGE>   10

         W. Section 9.13 of the Credit Agreement is amended hereby by deleting
the reference "and (iv) during any consecutive four fiscal quarters, sales of
Hydrocarbon Interests containing identified proved Hydrocarbon reserves which
shall not exceed $2,500,000 in the aggregate".

         X. Section 9.16 of the Credit Agreement is amended hereby as follows:

                  (i) by inserting a period after the reference "investment in
a Subsidiary"; and

                  (ii) by deleting the reference ", unless such Subsidiary is
or becomes a Guarantor and provided further, that all" and substituting
therefor the reference "All".

         Y. Section 10.01 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting in subsection (a) the reference ", or any
reimbursement obligation for a disbursement made under any Letter of Credit";
and

                  (ii) by deleting subsection (k) it its entirety and
relettering subsections (l) through (o) as subsections (k) through (n).

         Z. Section 10.02 of the Credit Agreement is amended hereby as follows:

                  (i) by deleting in subsections (a) and (b) the reference
"(including without limitation the payment of cash collateral to secure the LC
Exposure as provided in Section 2.10(b) hereof)"; and

                  (ii) by deleting in subsection (c) the reference "fifth to
serve as cash collateral to be held by the Agent to secure the LC Exposure;".

         AA. Section 11.03 of the Credit Agreement is amended hereby by
deleting the reference "or failure to reimburse for Letter of Credit drawings".

         BB. Section 11.04 of the Credit Agreement is amended hereby by
deleting the reference "and its participation in the issuance of Letters of
Credit".

         CC. Section 12.03 of the Credit Agreement is amended hereby as
follows:

                  (i) by deleting the reference "OR LETTERS OF CREDIT" in
subsection (b); and

                  (ii) by deleting the reference "THE ISSUANCE, EXECUTION AND
DELIVERY OR TRANSFER OF OR PAYMENT OR FAILURE TO PAY UNDER ANY LETTER OF
CREDIT," in subsection (b).

         DD. Section 12.06 of the Credit Agreement is amended hereby as
follows:


                                      10
<PAGE>   11

                  (i) by deleting the reference "or any Letters of Credit" in
subsection (a);

                  (ii) by deleting the first three sentences of subsection (b)
in their entirety and substituting the following therefor:

                  "Any Lender may sell, assign, transfer or negotiate to one or
         more other lenders, commercial banks, insurance companies, other
         financial institutions or any other Person all or any portion of its
         rights and obligations hereunder, and acceptance of such assignment by
         any assignee shall constitute the agreement of such assignee to be
         bound by the terms of this Agreement applicable to the assigning
         Lender. Promptly after receiving evidence of an assignment under this
         Section 12.06(b), the Agent shall send a notice of such assignment to
         the Borrower. Upon receipt of such notice and of the Notes that are
         the subject thereof, the Borrower will, at its own expense, execute
         and deliver new Notes to the assignor and/or assignee, as appropriate,
         in accordance with their respective interests.";

                  (iii) by deleting the reference "no such participant to which
the Borrower has not consented (such consent not to be unreasonably withheld)
shall be given any non-public information provided by the Borrower or the
Guarantors under the Loan Documents, and (iii)" in subsection (c);

                  (iv) by deleting all references "or Letters of Credit" in
subsection (c);

                  (v) by deleting the reference "to which the Borrower has
consented (such consent not to be unreasonably withheld)" in subsection (d);
and

                  (vi) by deleting the last sentence of subsection (d) in its
entirety.

         EE. the Credit Agreement is amended hereby by deleting all references
to "the Issuing Bank" in:

                  (i) the definition of the term "Indebtedness";

                  (ii) subsections (a) and (c) of Section 4.06; and

                  (iii) Section 11.05.

         FF. the Credit Agreement is amended hereby by adding Schedule 9.01(h)
- - Certain Agreements thereto.

         Section 3. Covenants. The Borrower or Brigham Exploration, as the case
may be, covenants and agrees that during the period from February 1, 1999
through and including June 1, 1999:



                                      11
<PAGE>   12

         A. Brigham Exploration shall deliver weekly cash budgets reasonably
satisfactory to the Agent in the form attached hereto as Exhibit B, and weekly
cash flow statements reasonably satisfactory to the Agent based on such form,
with variance analysis to budget (including accounts receivables and accounts
payables reporting) not later than the Friday following the week to which such
budgets and statements relate.

         B. The Borrower shall not spud any wells or conduct any other drilling
operations (other than routine workovers normally expensed in accordance with
past practice) without the prior written consent of the Agent and the Lenders,
and shall not use any amounts advanced by the Lenders under the Credit
Agreement to acquire acreage, leases or seismic data or to pay any drilling
costs or expenses other than for wells for which drilling had commenced on or
before January 1, 1999; provided that the Borrower may use the Escrow Cash (as
defined in the Duke Consent Letter) to spud, drill, complete, operate and
maintain wells contemplated thereby; provided further that, notwithstanding the
foregoing, the Borrower may incur up to $300,000, in the aggregate, in
discretionary new commitments during the period from the date hereof through
and including June 1, 1999 to acquire leases and seismic data (or licenses
thereto) if, and only if, the Borrower shall grant the Agent, for the benefit
of the Lenders, a perfected Lien on its interest in any new leases acquired
pursuant to this proviso within thirty (30) days or, upon request by the Agent,
within fifteen (15) days, of any such acquisition under a form of mortgage
substantially identical to that of the New Mortgage.

         C. The Borrower shall prepay the Loans in an amount equal to the cash
proceeds of sale of any equity or equity derivative securities and the proceeds
of any asset sales requiring the consent of the Agent under the Credit
Agreement as amended hereby; provided however nothing herein shall be deemed to
constitute a consent by the Agent or any Lender to any such asset sale.

         D. The Borrower shall use all amounts, other than the Escrow Cash,
received by it in connection with the Duke Transaction as working capital.

         E. The Borrower shall provide to the Agent from time to time upon
request by the Agent the certificate of a Responsible Officer of the Borrower
stating that, except as disclosed in a schedule thereto, the Borrower has not
received written notice that any mechanics' liens have been filed or will be
filed on the Mortgaged Properties; provided that mere receipt of an invoice for
services rendered shall not constitute written notice that a mechanics' lien
will be filed.

         F. The Borrower shall cause its Subsidiary, DND Oil & Gas, LLP to
transfer all assets held by it to the Borrower and, thereafter, to dissolve on
or before June 1, 1999.

         G. The Borrower will not, and will not allow any of its Subsidiaries
to, (i) transfer any assets to Quest Resources LLC or (ii) make any investments
in or loans or advances to Quest Resources LLC.

         Section 4. Conditions Precedent. This Amendment shall become binding
upon receipt by the Agent of the following documents and satisfaction of the



                                      12
<PAGE>   13

other conditions provided in this Section 4, each of which must be satisfactory
to the Agent in form and substance:

         A. counterparts of this Amendment executed by the Borrower, the Agent
and the Lenders;

         B. counterparts of the New Mortgage executed by the Borrower;

         C. evidence that the New Mortgage and the related UCC-1 financing
statements have been filed in all jurisdictions necessary to perfect and
protect the security interests, assignments and Liens created thereby;

         D. certificates of the Secretary or an Assistant Secretary of the
Borrower and each of the Guarantors setting forth for each of them (i) the
resolutions of its board of directors or managers (or if such Guarantor is a
partnership, resolutions of the general partner of such partnership), as
applicable, with respect to the authorization to execute and deliver this
Amendment and consummate the transactions contemplated hereby; (ii) the
Responsible Officer of such entity authorized to sign this Amendment, and (iii)
the signature of such authorized Responsible Officer of such entity;

         E. a monthly cash budget for 1999 of Brigham Exploration and its
Subsidiaries, which shall include projected revenues, expenses and capital
expenditures;

         F. a Third Amendment to Guaranty Agreement executed by Brigham
Exploration Company;

         G. a First Amendment to Security Agreement executed by the Borrower in
favor of the Agent granting, among other things, a first priority security
interest in all of the Borrower's right, title and interest in its ownership
interests in Quest Resources LLC, and evidence that all other actions necessary
or, in the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken;

         H. a First Amendment to Security Agreement executed by Brigham, Inc.
in favor of the Agent granting, among other things, a first priority security
interest in all of Brigham, Inc.'s right, title and interest in its ownership
interests in Sooner Production LLC and Quest Resources LLC, and evidence that
all other actions necessary or, in the opinion of the Agent, desirable to
perfect and protect the security interests and Liens granted thereby have been
taken;

         I. a First Amendment to Intercreditor and Subordination Agreement
executed by Brigham Exploration Company, Enron Capital & Trade Resources Corp.
and Joint Energy Development Investments II Limited Partnership, individually
and as agent for the subordinated Lender as defined therein;

         J. a Consent and Acknowledgement executed by each of the Guarantors;

         K. an opinion of counsel to Borrower substantially in the form
attached hereto as Exhibit C;



                                      13
<PAGE>   14

         L. evidence that Brigham Exploration has obtained the consent and
agreement of the holders of the Notes (as defined in the Indenture) to convert
all interest payments due under such Notes in 1999 to in kind payments as
provided in Section 1X. 2(2) of the Indenture;

         M. payment to the Agent for the ratable benefit of the Lenders of all
accrued and unpaid Interest outstanding under the Credit Agreement and the
Notes;

         N. payment of a $50,000 installment of the Amendment Fee in accordance
with Section 8.A(i) hereof;

         O. payment of the expenses of the Agent and the Lenders in accordance
with Section 8.B hereof; and

         P. such other documents as Agent or its counsel may reasonably
request.

         Section 5. Representations and Warranties.

         A. Except as provided in subsection (iii) of this Section 5.A., the
Borrower hereby reaffirms that, as of the date of this Amendment, the
representations and warranties made by the Borrower and Brigham Exploration in
the Credit Agreement are true and correct as though made on and as of the date
hereof, and further, the Borrower represents that,

                  (i) as of the date hereof, no Default or Material Adverse
Effect has occurred and is continuing except as previously disclosed to the
Agent in writing;

                  (ii) the execution, delivery and performance by the Borrower
or the Guarantors of this Amendment and the other Loan Documents and all
instruments and documents to be delivered by the Borrower or the Guarantors, to
the extent a party thereto, hereunder and thereunder and the creation of all
Liens provided for herein and therein: (a) are within the Borrower's or such
Guarantor's corporate power; (b) have been duly authorized by all necessary or
proper corporate action, including the consent of stockholders, members and/or
partners therein or thereof; (c) are not in contravention of any provision of
the Borrower's or such Guarantor's certificate of incorporation, bylaws or
similar organizational and/or governing documents; (d) will not violate (1) any
law or regulation or (2) any order or decree of any court or governmental
instrumentality; (e) will not conflict with or result in the breach or
termination of, constitute a default under or accelerate any performance
required by, any indenture, mortgage, deed of trust, lease, agreement or other
instrument to which the Borrower or any of the Guarantors is a party or by
which the Borrower or any of the Guarantors or any of their respective property
is bound; (f) will not result in the creation or imposition of any Lien upon
any of the property of the Borrower or the Guarantors other than those in favor
of the Agent pursuant to the terms of this Amendment and the other Loan
Documents to be delivered in connection herewith; and (g) do not require the
consent or approval of any governmental body, agency, authority or any other
Person that has not been duly obtained, made or complied with prior to the date
hereof. At or prior to the date hereof, each of this Amendment and the other
Loan Documents to be delivered in connection



                                      14
<PAGE>   15

herewith shall have been duly executed and delivered for the benefit of or on
behalf of the Borrower or the Guarantors, in each case to the extent a party
thereto, and each shall then constitute a legal, valid and binding obligation
of the Borrower or such Guarantor, enforceable against it in accordance with
its terms; and

                  (iii) notwithstanding the foregoing, the representations and
warranties contained in the last sentence of Section 7.10(a) of the Credit
Agreement (and not those contained in the first two sentences) are reaffirmed
with respect to the Mortgaged Property covered by or described in the New
Mortgage.

         B. Each of the Borrower and the Guarantors further represents and
warrants, for itself only that he or it (i) is executing this Amendment after
consultation with counsel of his or its own choosing, (ii) has read and
understands the release granted by Section 6 hereof, (iii) desires to execute
this Amendment and (iv) has the requisite authority to enter into and be bound
by this Amendment, including the release granted by Section 6 hereof.

         Section 6. Release.

         A. Each of the Releasing Parties desires and intends fully to
compromise, release and settle any and all of the Released Claims; and each of
the Releasing Parties hereby covenants, warrants and represents unto each of
the Released Parties that such Releasing Party does hereby FOREVER RELEASE,
ACQUIT, WAIVE AND DISCHARGE each of the Released Parties of and from the
Released Claims and each of the Releasing Parties hereby declares the same
FOREVER RELEASED, ACQUITTED, WAIVED, SETTLED AND DISCHARGED. This release is
effective without regard to whether (i) such Released Claims are known or
unknown, (ii) damages arising out of such Released Claims have yet accrued,
(iii) such Released Claims arose collaterally, directly, derivatively, or
otherwise between the parties hereto or (iv) an ordinary person in the same or
similar circumstances would or would not, through the exercise of due care,
have discovered such claims by the date of this Amendment. In connection with
the foregoing release:

         B. Borrower and each of the Guarantors represents and warrants that it
has the full power and authority to perform the release granted in this Section
6 and that it has not in any manner made any assignment of any Released Claim
to any third party.

         C. The release granted in this Section 6 will be effective upon
execution of this Amendment by all of the parties hereto.

         D. Each party executing this Amendment understands and agrees that the
release granted in this Section 6 is a full, final and complete release of the
Released Claims and that such release may be pleaded as an absolute and final
bar to any or all suits which may hereafter be filed or prosecuted by any one
or more of the Releasing Parties or anyone claiming by, through or under any
one or more of the Releasing Parties in respect of any of the matters released
hereby, and that no recovery on account of the Released Claims may hereafter be
had from any of the Released Parties; and that the consideration given for such
release is not an admission of liability or fault on the part of 



                                      15
<PAGE>   16

any of the Released Parties (it being the express intent of the parties hereto
to obtain peace of mind and avoid the expense and uncertainty of potential
litigation), and that none of the Releasing Parties or those claiming by,
through or under any of them will ever claim that it is.

         E. The parties hereto acknowledge that the release granted by this
Section 6 does not have any effect with respect to relationships between the
Borrower and each of the Guarantors and the Lenders and the Agent other than in
connection with the Lending Relationship.

         Section 7. Events of Default and Remedies.

         A. The occurrence of any one or more of the following events
(regardless of the reason therefor) shall constitute an "Event of Default"
hereunder:

                  (i) The Borrower shall fail to deliver within 30 days after
closing a First Amendment to Security Agreement executed by Brigham Holdings I,
LLC in favor of the Agent, and evidence that all other actions necessary or, in
the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken;

                  (ii) The Borrower shall fail to deliver within 30 days after
closing a First Amendment to Security Agreement executed by Brigham Holdings
II, LLC in favor of the Agent, and evidence that all other actions necessary
or, in the opinion of the Agent, desirable to perfect and protect the security
interests and Liens granted thereby have been taken; and

                  (iii) The Borrower shall fail to deliver within 30 days after
closing a legal opinion of Borrower's counsel in form reasonably satisfactory
to the Agent.

         B. The occurrence and continuation of an Event of Default hereunder
shall constitute an Event of Default under the Credit Agreement as amended
hereby.

         Section 8. Payment of Fees and Expenses; Form of Payment.

         A. The Borrower agrees to pay to the Agent for the ratable benefit of
the Lenders a fee (the "Amendment Fee") in the amount of $500,000 payable by
the Borrower as follows:

                  (i) a $50,000 installment shall be due and payable on the
date hereof; and

                  (ii) a $50,000 installment shall be due with each monthly
interest payment required to be made under Section 3.02 of the Credit Agreement
as amended hereby; provided that the unpaid balance of the Amendment Fee shall
be payable on the earlier of (a) the date on which the Bank of Montreal ceases
to be the Agent or (b) the cancellation of the Commitments and repayment in
full by the Borrower of the Indebtedness.



                                      16
<PAGE>   17

         B. The Borrower agrees, whether or not the transactions contemplated
hereby are consummated, to pay all reasonable expenses of the Agent and the
Lenders (including, without limitation, all reasonable fees and disbursements
of counsel and other outside consultants for the Agent and/or the Lenders) in
connection with the negotiation, investigation, preparation, execution and
delivery of, recording and filing of, preservation of rights under and
enforcement of this Amendment and the other Loan Documents to be delivered in
connection herewith.

         C. All payments to be made by the Borrower under this Amendment shall
be made in Dollars, in immediately available funds, to the Agent at such
account as the Agent shall specify by notice in accordance with Section 4.01 of
the Credit Agreement.

         Section 9. Limitations. The amendments set forth herein are limited
precisely as written and shall not be deemed to (a) be a consent to, or waiver
or modification of, any other term or condition of the Credit Agreement or any
of the other Loan Documents, or (b) prejudice any right or rights which the
Lenders or the Agent may now have or may have in the future under or in
connection with the Credit Agreement or any of the other Loan Documents. Except
as expressly supplemented, amended or modified hereby, the terms and provisions
of the Credit Agreement or any other Loan Documents are and shall remain in
full force and effect. In the event of a conflict between this Amendment and
any of the foregoing documents, the terms of this Amendment shall be
controlling.

         Section 10. Non-Reliance on Agent and Other Lenders. Each Lender
acknowledges and agrees that it has, independently and without reliance on the
Agent or any other Lender, and based on such documents and information as it
has deemed appropriate, made its own decision to enter into this Amendment, and
that it will, independently and without reliance upon the Agent or any other
Lender, and based on such documents and information as it shall deem
appropriate at the time, continue to make its own analysis and decisions in
taking or not taking action under this Amendment or the Credit Agreement. The
Agent shall not be required to keep itself informed as to the performance or
observance by the Borrower of this Amendment or any other Loan Document or any
other document referred to or provided for herein or therein or to inspect the
properties or books of the Borrower. Except for notices, reports and other
documents and information expressly required to be furnished to the Lenders by
the Agent hereunder and under the Credit Agreement, the Agent shall not have
any duty or responsibility to provide any Lender with any credit or other
information concerning the affairs, financial condition or business of the
Borrower (or any of its Affiliates) which may come into the possession of the
Agent or any of its Affiliates. In this regard, each Lender acknowledges that
Weil, Gotshal & Manges LLP is acting in this transaction as special counsel to
the Agent only. Each Lender will consult with its own legal counsel to the
extent that it deems necessary in connection with this Amendment and the
matters contemplated herein.

         Section 11. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Credit Agreement shall be
construed in accordance with and be governed by the laws of the State of Texas
and the United States of America.



                                      17
<PAGE>   18

         Section 12. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 13. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.



                                      18
<PAGE>   19

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

            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

         THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES
BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS
OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL
AGREEMENT BETWEEN THE PARTIES.

BORROWER:                           BRIGHAM OIL & GAS, L.P.

                                    By: Brigham, Inc., its General Partner



                                    By: /s/ Karen E. Lynch
                                        ------------------------
                                    Name: Karen E. Lynch
                                         -----------------------
                                    Title: Vice President
                                          ----------------------

AGENT:                              BANK OF MONTREAL



                                    By: /s/ Thomas E. McGraw
                                        ------------------------
                                          Thomas E. McGraw
                                          Director


LENDER:                             BANK OF MONTREAL



                                    By: /s/ Thomas E. McGraw
                                        ------------------------
                                          Thomas E. McGraw
                                          Director



                                      19
<PAGE>   20


LENDER:                             SOCIETE GENERALE, Southwest Agency



                                    By: /s/ Paul E. Cornell
                                        ------------------------
                                    Name: Paul E. Cornell  
                                         -----------------------
                                    Title: Managing Director                    
                                          ----------------------



                                      20


<PAGE>   1
                                                                 EXHIBIT 10.37.3


                     THIRD AMENDMENT TO GUARANTY AGREEMENT



         THIS THIRD AMENDMENT TO GUARANTY AGREEMENT (this "Amendment") dated as
of March 26, 1999 is between BRIGHAM EXPLORATION COMPANY, a Delaware
corporation (the "Guarantor") and BANK OF MONTREAL, as agent ("Agent") for the
lenders (the "Lenders") that are or become parties to the Credit Agreement
defined below.

                                    RECITALS

              A. Brigham Oil & Gas, L.P., a Delaware limited partnership (the
     "Borrower"), the Agent and the Lenders previously entered into that
     certain Credit Agreement dated as of January 26, 1998 as amended by First
     Amendment to Credit Agreement dated August 20, 1998 and Second Amendment
     to Credit Agreement of even date herewith (as amended, the "Credit
     Agreement"), pursuant to which the Lenders agreed to make certain loans
     and extensions of credit to the Borrower.

              B. Pursuant to the terms and conditions stated in the Credit
     Agreement, Guarantor executed that certain Guaranty Agreement dated
     January 26, 1998 by Guarantor, as amended by First Amendment to Guaranty
     Agreement dated March 30, 1998 and Second Amendment to Guaranty Agreement
     dated August 20, 1998 (as amended, the "Guaranty Agreement").

              C. Guarantor and the Agent now desire to amend certain provisions
     of the Guaranty Agreement.

         NOW THEREFORE, in consideration of the mutual covenants and agreements
herein contained, the Guarantor, the Agent and the Lenders hereby agree that
the Guaranty Agreement shall be amended as follows:

         Section 1. Certain Definitions. As used in this Amendment, the terms
"Agent", "Amendment", "Borrower", "Credit Agreement", "Guarantor" and "Lenders"
shall have the meanings indicated above; and unless otherwise defined herein,
all terms beginning with a capital letter which are defined in the Guaranty
Agreement shall have the same meanings herein as therein unless the context
hereof otherwise requires.

         Section 2. Amendments to Guaranty Agreement.

                  Section 5.2.  Section 5.2 is hereby amended as follows:

                  (a) Section 5.2(q) is hereby deleted in its entirety, and the 
         following substituted therefor:

                           "(q) Current Ratio. The Guarantor will not permit
                  its ratio of (i) consolidated current assets of the Guarantor
                  and its Consolidated Subsidiaries to (ii) their consolidated
                  current liabilities (excluding the Indebtedness) to be less
                  than 1.0 to 1.0 for the quarter ended December 31, 1999 or at
                  any time thereafter."

                  (b) Section 5.2(r) is hereby deleted in its entirety.



                                       1

<PAGE>   2


                  (c) Section 5.2(s) is hereby deleted in its entirety, and the
         following is substituted therefor:

                           "(r) Interest Coverage Ratio. The Guarantor will not
                  permit its Interest Coverage Ratio as of the end of any
                  fiscal quarter of the Guarantor (calculated quarterly at the
                  end of each fiscal quarter) to be less than the following
                  ratios during the following periods. Interest Coverage Ratio
                  shall mean the ratio of (i) EBITDA to (ii) interest payments
                  accruing (excluding amortizations of fee expense incurred in
                  connection with this Agreement and the closing of the
                  Indenture and Securities Purchase Agreement and any
                  capitalized lease expense included in interest) during the
                  following periods (for purposes hereof interest on the
                  Subordinated Debt shall be deemed cash payments, calculated
                  at the cash interest rate applicable to the Subordinated
                  Debt, whether paid in cash or in kind, except that if a
                  payment of interest is made in kind on any interest payment
                  date applicable to the Subordinated Debt, an amount equal to
                  the cash payment of interest that would have been due on such
                  interest payment date if payment in kind had not been made
                  shall be deemed subtracted from interest expense for the
                  applicable test period ending on the last day of the fiscal
                  quarter preceding such interest payment date (but not for any
                  other test period):

                           (i)    not less than 2.0 to 1.0 for the six (6) month
                                  period ending December 31, 1999;

                           (ii)   not less than 2.0 to 1.0 for the nine (9)
                                  month period ending March 31, 2000;

                           (iii)  not less than 2.25 to 1.0 for the twelve (12)
                                  month period ending June 30, 2000;

                           (iv)   not less than 2.5 to 1.0 for the twelve (12)
                                  month period ending September 30, 2000;

                           (v)    not less than 2.5 to 1.0 for the twelve (12)
                                  month period ending December 31, 2000; and

                           (vi)   thereafter, not less than 3.0 to 1.0 for the
                                  twelve (12) month periods ending at the end of
                                  each fiscal quarter of the Guarantor."

                  (d) Section 5.2(u) is hereby deleted in its entirety, and the
         following is substituted therefor:

                  "(u) Payments on Subordinated Debt. No prepayments of
         principal will be made on the Subordinated Debt without prior written
         consent of the Lenders. No payment of interest will be made in cash on
         the Subordinated Debt prior to September 30, 2000 and from and after
         September 30, 2000 no payments of interest will be made in cash on the
         Subordinated



                                       2

<PAGE>   3







         Debt if (i) an Event of Default under Section 10.01(a) of the Credit
         Agreement has occurred or (ii) a Borrowing Base deficiency is in
         existence under the Credit Agreement."

         Section 3. Representations and Warranties. Guarantor hereby reaffirms
that as of the effective date of this Amendment, the representations and
warranties made by the Guarantor in Article III of the Guaranty Agreement will
be true and correct as though made on and as of the effective date of this
Amendment.

         Section 4. Ratification. Guarantor hereby expressly ratifies and
affirms its obligations under the Guaranty Agreement as amended by this
Amendment and agrees that the Guaranty Agreement as amended by this Amendment
remains in full force and effect.

         Section 5. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Credit Agreement shall be
construed in accordance with and be governed by the laws of the State of Texas
and the United States of America.

         Section 6. Descriptive Headings, etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 7. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.



                                       3

<PAGE>   4



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

            NOTICE PURSUANT TO TEX. BUS. & COMM. CODE SECTION 26.02

         THIS AMENDMENT AND OTHER LOAN DOCUMENTS EXECUTED BY ANY OF THE PARTIES
BEFORE OR SUBSTANTIALLY CONTEMPORANEOUSLY WITH THE EXECUTION HEREOF TOGETHER
CONSTITUTE A WRITTEN LOAN AGREEMENT AND REPRESENT THE FINAL AGREEMENT BETWEEN
THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS
OR SUBSEQUENT ORAL AGREEMENTS OF THE PARTIES. THERE ARE NOT UNWRITTEN ORAL
AGREEMENT BETWEEN THE PARTIES.

GUARANTOR:                              BRIGHAM EXPLORATION COMPANY


                                        By: /s/ Karen E. Lynch
                                           -------------------------------------
                                        Name: Karen E. Lynch
                                             -----------------------------------
                                        Title: Vice President
                                              ----------------------------------


AGENT AND LENDER:                       BANK OF MONTREAL


                                        By: /s/ Thomas E. McGraw            
                                            ------------------------------------
                                            Thomas E. McGraw
                                            Director









                                       4

<PAGE>   1
                                                                 EXHIBIT 10.39.1


                   AMENDMENT TO REGISTRATION RIGHTS AGREEMENT


         This AMENDMENT TO REGISTRATION RIGHTS AGREEMENT (the "Amendment")
dated as of March 26, 1999, among Brigham Exploration Company, a Delaware
corporation (the "Company"), Joint Energy Development Investments II Limited
Partnership, a Delaware limited partnership ("JEDI-II"), and ECT Merchant
Investments Corp. ("ECT Merchant"), amends the Registration Rights Agreement
dated as of August 20, 1998 among the Company, JEDI-II and Enron Capital &
Trade Resources Corp., a Delaware corporation ("ECT").

         NOW, THEREFORE, in consideration of the mutual covenants and
agreements set forth herein and for good and valuable consideration, the
receipt of which is hereby acknowledged, the parties agree as follows:

                                    ARTICLE I
            MODIFICATION OF DEFINITION OF WARRANTS AND WARRANT SHARES

         Section 1.01. Definition of Warrant. "Warrants" means the Warrants
issued by the Company to JEDI-II and ECT Merchant as of the date hereof for the
purchase of an aggregate of 1,000,000 shares of Common Stock, evidenced as of
the date hereof by Warrant Certificates Nos. A-3 and A-4, and any Warrants
issued upon the transfer thereof or in substitution therefor, as the same may
be amended from time to time.

         Section 1.02. Definition of Warrant Shares. "Warrant Shares" shall mean
the shares of Common Stock and other securities receivable upon exercise of the
Warrants.

                                   ARTICLE II
                                  MISCELLANEOUS

         Section 2.01 Execution in Counterparts. This Amendment may be executed
in any number of counterparts and by different parties on separate counterparts
and all of such counterparts shall together constitute one and the same
instrument.

         Section 2.02 Governing Law. This Amendment and the rights and
obligations of the parties hereunder shall be construed in accordance with and
be governed by the laws of the State of Texas and the United States of America.

         Section 2.01 Descriptive Headings, etc. The descriptive headings of
the sections of this Amendment are inserted for convenience only and shall not
be deemed to affect the meaning or construction of any of the provisions
hereof.



<PAGE>   2



         IN WITNESS WHEREOF, the parties have executed this Amendment to
Registration Rights Agreement as of the date first written above.

                                 BRIGHAM EXPLORATION COMPANY



                                 By:/s/ Karen E. Lynch
                                    --------------------------------------------
                                          Karen E. Lynch
                                          Vice President

                                 JOINT ENERGY DEVELOPMENT
                                 INVESTMENTS II LIMITED PARTNERSHIP

                                 By: Enron Capital Management II Limited
                                     Partnership, its General Partner

                                     By:  Enron Capital II Corp., its General 
                                          Partner


                                     By:  /s/ Mark J. Warner
                                          --------------------------------------
                                          Mark J. Warner
                                          Agent and Attorney-in-fact

                                 ECT MERCHANT INVESTMENTS CORP.


                                 By:      /s/ Mark Warner
                                          --------------------------------------
                                 Name:    Mark Warner 
                                          --------------------------------------
                                 Title:   Agent and Attorney in Fact
                                          --------------------------------------



                                      -2-

<PAGE>   1
                                                                   EXHIBIT 10.41







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


                               EXCHANGE AGREEMENT





                                  BY AND AMONG

                             VERITAS DGC LAND, INC.

                                       AND

                           BRIGHAM EXPLORATION COMPANY





                           DATED AS OF MARCH 30, 1999



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




<PAGE>   2




                               EXCHANGE AGREEMENT


         This Exchange Agreement (the "Agreement") is made this 30th day of
March, 1999, by and between Brigham Exploration Company ("BEXP" or the
"Company") and Veritas DGC Land, Inc. ("Veritas" or the "Investor"). Certain
capitalized terms not defined in the text of this Agreement are defined in
Appendix A to this Agreement.

         WHEREAS, BEXP or its affiliates currently owe Veritas certain amounts
for certain seismic services rendered by Veritas;

         WHEREAS, the parties hereto desire to exchange BEXP Common Stock (as
defined below) for (i) all of the current payables owed to Veritas and its
affiliates by Brigham Oil & Gas, L.P. ("BOG"), (ii) certain future payables and
other liabilities which will be due to Veritas on or before December 31, 1999
pursuant that certain Anadarko Basin Seismic Operations Agreement II, dated
April 1, 1997, by and between BOG and Veritas, as amended (the "Alliance
Agreement II"), and (iii) certain future seismic processing services provided by
Veritas Geoservices, Ltd. ("Veritas Geoservices"); and

         WHEREAS, each of the parties hereto is making certain representations,
warranties, covenants and indemnities herein to induce the other to enter into
this Agreement;

         NOW, THEREFORE, in consideration of the respective representations,
warranties, covenants and indemnities contained herein, BEXP and Veritas hereby
agree as follows:

                                   ARTICLE I.
                             ISSUANCE OF SECURITIES

         1.1 AUTHORIZATION AND ISSUANCE OF COMMON STOCK.

         Exchange for Existing Payables. Upon execution of this Agreement, the
Company will authorize the issuance and sale to the Investor, and, within
fifteen (15) days of the date hereof, shall deliver to Investor certificates
evidencing 918,989 shares of BEXP's common stock, par value $.01 per share (the
"Common Stock"), in exchange for and in full extinguishment of $3,216,459.88 of
existing payables and other liabilities, identified on Schedule 1.1 hereto, that
BOG owes to Veritas and its Affiliates (including without limitation Veritas
Geoservices) as of March 26, 1999, pursuant to the Alliance Agreement II, that
certain Anadarko Basin Seismic Operations Agreement dated February 15, 1996 by
and between BOG and Veritas' predecessor, as amended (the "Alliance Agreement
I"), and any processing agreements between BOG and any Affiliates of Veritas
(the "Processing Agreements"); provided that the extinguishment of such
liability is conditioned upon the delivery to Investor of such shares. In the
event that it is subsequently determined by mutual agreement of the parties that
as of March 26, 1999, there existed payables and other liabilities that were
owed to Veritas and its Affiliates under any of such agreements in excess of
$3,216,459.88, the first $100,000 of such additional payables or liabilities in
existence as of March 26, 1999, shall





<PAGE>   3




be paid for by the Company using shares of the Common Stock (using a value of
$3.50 per share), such shares to be delivered within thirty (30) days of the
date that the parties mutually agree on the existence and amount of such
additional payable or liability. Any remaining payables or liabilities shall be
paid for by the Company in cash according to Veritas standard payment terms, net
thirty (30) days. Interest shall accrue at ten percent (10%) per annum on all
balances (other than those exchanged for common stock as provided herein) due
for more than fifteen (15) days after the original thirty (30) days.

         1.2 ADDITIONAL CONSIDERATION.

                  (A) Stock Exchange for Additional Alliance Agreement II
Payables. In addition to the exchange described in Section 1.1 above, on the
date hereof, the Company shall issue to Investor, and Investor shall purchase,
83,876 shares of the Common Stock as payment for an additional $293,566 in
payables and liabilities for services already performed by Investor under and
pursuant to the Alliance Agreement II. The delivery of these shares will
extinguish BEXP's and BOG's obligation to pay such additional $293,566 of
payables under the Alliance Agreement II. Any additional payables and
liabilities, other than those extinguished through the issuance of the Common
Stock pursuant to this Section 1.2(A), that become due and payable under the
Alliance Agreement II on or after March 26, 1999, are to be paid to the Investor
in cash in accordance with the terms of the Alliance Agreement II; provided that
any such amounts that remain due and payable for fifteen (15) days after such
amounts are due under the Alliance Agreement II shall bear interest at ten
percent (10%) per annum.

                  (B) Payment for Future Seismic Processing Services. In
addition to the exchanges described in Sections 1.1 and 1.2(A), to the extent
Veritas Geoservices performs or has performed additional seismic processing
services which have not been invoiced to BOG prior to March 26, 1999, the
Investor will invoice the Company for such services according to its standard
billing practices, and the Company will be obligated to pay those invoices that
it receives during each calendar quarter or prior to the tenth day after the end
of such quarter, in cash within thirty (30) days from the end of each calendar
quarter, and any amounts that remain due and payable for forty-five (45) days
after the end of each quarter shall bear interest at ten percent (10%) per
annum; provided, however, that if the Company has not paid such amounts within
fifteen (15) days after the end of each quarter, the Company must pay such
amounts with shares of the Common Stock (deemed to be valued at $3.50 per share)
which shares shall be issued within thirty (30) days of the end of the Calendar
Quarter. The Company's obligation to pay such liabilities using the Common Stock
shall only apply to the first $1 million of such liabilities, and shall only
apply to seismic processing services provided by Veritas Geoservices during
calendar year 1999.

         1.3 CLOSING. The closing (the "Closing") of the transactions provided
for in this Agreement shall take place at the offices of Locke Liddell & Sapp
LLP, 3400 Chase Tower, Houston, Texas. The Closing shall take place on March 30,
1998 (the "Closing Date"), or at such other time and place as the parties hereto
shall mutually agree. Except as specifically provided herein, failure to
consummate the purchases and sales provided for in this Agreement on the date
and


                                       2

<PAGE>   4




time and at the place determined pursuant to this Section 1.3 shall not result
in the termination of this Agreement, and shall not relieve any parties to this
Agreement of any obligation hereunder.

         1.4 CROSS RECEIPT. Upon delivery of Common Stock hereunder, the Company
and the Investor shall each execute and deliver a cross receipt acknowledging
the extinguishment of BEXP's debt (to the extent provided herein) and the
receipt of the Common Stock, respectively.

         1.5 OTHER DOCUMENTS TO BE DELIVERED ON THE CLOSING DATE. The Company
shall deliver to the Investor the following at the Closing (or as otherwise
indicated below):

                           (A) Certificates representing the shares of Common
         Stock purchased by the Investor pursuant hereto, including as described
         in Sections 1.1 and 1.2(A) and (B) (to be delivered as promptly as
         practicable, but no later than fifteen (15) days after the Closing
         Date;

                           (B) The Certificate of Incorporation of the Company,
         as amended and in effect as of the Closing Date, certified by the
         Secretary of State of the State of Delaware;

                           (C) Certificates, as of a date that is within five
         (5) days of the Closing, as to the corporate good standing of the
         Company, issued by the Secretary of State of the State of Delaware;

                           (D) A certificate of the Secretary of the Company
         attesting to the incumbency of the Company's officers, the authenticity
         of the resolutions authorizing the transactions contemplated by this
         Agreement, and the authenticity and continuing validity of the
         Organizational Documents of the Company;

                           (E) Executed copy of this Agreement.

                                   ARTICLE II.
                         REPRESENTATIONS OF THE COMPANY

         The Company represents and warrants to the Investor as follows:

         2.1 ORGANIZATION, EXISTENCE AND GOOD STANDING. The Company is a Company
duly organized, validly existing and in good standing under the laws of the
State of Delaware and has all requisite corporate power and authority to carry
on its business as now being conducted and as proposed to be conducted, and is
duly qualified as a foreign Company to do business and is in good standing in
each other jurisdiction in which the nature of the business conducted by it
makes such qualification necessary, except where the failure to so qualify would
not have a Material Adverse Effect.




                                       3

<PAGE>   5




         2.2 CAPITALIZATION.

                           (A) The authorized capital stock of the Company
         consists of 40,000,000 shares of Common Stock, par value $0.01 per
         share, 13,306,206 shares of which are issued and outstanding, and
         10,000,000 shares of Preferred Stock, none of which are issued and
         outstanding. All such issued shares have been duly issued in accordance
         with applicable laws, including federal and state securities laws. All
         of the outstanding shares of capital stock of the Company and each
         Subsidiary have been duly authorized and are validly issued, fully paid
         and nonassessable. All dividends and other distributions declared with
         respect to the issued and outstanding shares of the capital stock of
         the Company have been paid or distributed.

                           (B) The certificates representing the Common Stock to
         be delivered to the Investor pursuant hereto, both at the Closing and
         otherwise, and the signatures on the endorsements thereof or stock
         powers delivered therewith, will be valid and genuine. The stock
         certificates, endorsements, stock powers and other documents to be
         delivered to the Investor on the Closing Date or subsequent thereto
         will transfer to and vest in the Investor good, valid and indefeasible
         title to the Common Stock to be issued hereunder, free and clear of any
         adverse claims of any other person, including without limitation any
         Encumbrance.

                           (C) No stock transfer taxes or other similar taxes
         are or will be required to be paid by the Investor with respect to the
         transfer of any of the Common Stock as provided herein.

                           (D) Except as provided in clause (A) above, the SEC
         Filings (as defined herein) or on Schedule 2.2, as of the Closing Date
         and except for (i) warrants to purchase an aggregate of 1,000,000
         shares of Common Stock issued to Joint Energy Development II Limited
         Partnership and Enron Capital & Trade Resources Corp. and (ii) options
         to purchase an aggregate of 1,194,654 shares of Common Stock under the
         Company's 1997 Incentive Plan, there will be no outstanding

                           (1)      shares of Common Stock or Preferred Stock
                                    ("Capital Stock") or voting securities of
                                    the Company;

                           (2)      securities of the Company convertible into
                                    or exchangeable for shares of Capital Stock
                                    or voting securities of the Company; or

                           (3)      options or other rights to acquire from the
                                    Company, or other obligations of the Company
                                    to issue, any Capital Stock, voting
                                    securities, or securities convertible into
                                    or exchangeable for Capital Stock or voting
                                    securities of the Company.

                           (E) There are no outstanding obligations of the
         Company to repurchase, redeem, or otherwise acquire any existing
         securities of the Company.



                                       4

<PAGE>   6





         2.3 AUTHORITY. The Company has full corporate power and authority to
execute and deliver this Agreement and to consummate the transactions
contemplated hereby. The execution and delivery of this Agreement and the
consummation of the transactions contemplated hereby have been duly and validly
authorized and approved by the board of directors of the Company, and no other
corporate proceedings on the part of the Company are necessary to authorize this
Agreement or the consummation of the transactions contemplated hereby. This
Agreement has been duly and validly executed and delivered by the Company, and
this Agreement constitutes the legal, valid and binding agreement of the Company
enforceable against the Company in accordance with its terms, subject to (i)
bankruptcy, insolvency and other similar laws now or hereafter affecting the
enforcement of the rights of creditors generally and (ii) general principles of
equity.

         2.4 SECURITIES FILINGS.

                           (A) The Company and each Subsidiary has filed all
         forms, reports, and documents required to be filed with the Securities
         and Exchange Commission (the "SEC"; such forms, reports, and documents,
         the "SEC Filings") since it was first required to make such filings.
         The SEC Filings:

                           (1)      were prepared in all material respects in
                                    accordance with the requirements of the
                                    Securities Act or the Exchange Act, as
                                    applicable; and

                           (2)      did not at the time they were filed (or if
                                    amended or superseded by a filing prior to
                                    the date of this Agreement, then on the date
                                    of such filing) contain any untrue statement
                                    of a material fact or omit to state a
                                    material fact required to be stated therein
                                    or necessary to make the statements therein,
                                    in light of the circumstances under which
                                    they were made, not misleading.

                           (B) Each of the consolidated financial statements
         (including, in each case, any related notes thereto) contained in the
         SEC Filings has been prepared in accordance with GAAP applied on a
         consistent basis throughout the periods involved (except as may be
         indicated in the notes thereto) and each fairly represents the
         financial position of the Company and its Subsidiaries as at the
         respective dates thereof and the results of its operations and cash
         flows for the periods indicated, except that the unaudited financials
         were or are subject to normal and recurring year-end adjustments which
         were not or are not expected to be material in amount.

                           (C) For purposes hereof, "SEC Filings" shall include
         the draft Annual Report Form 10-K for the fiscal year ended December
         31, 1998, together with all Exhibits being filed therewith, excluding
         exhibits regarding Enron or its affiliates previously filed in draft
         form with the Company's Registration Statement declared effective in
         August, 1998, attached hereto as Schedule 2.4 (the "Draft 1998 10-K").



                                       5

<PAGE>   7





         2.5 NO VIOLATION. The execution and delivery of this Agreement, the
consummation of the transactions contemplated hereby, or the compliance by the
Company or any Subsidiary with any of the provisions hereof will not (i)
conflict with or result in any breach of any provision of the Articles of
Incorporation, Bylaws or other Organizational Document of the Company or any
Subsidiary, (ii) result in a violation or breach of or constitute (with or
without due notice or lapse of time or both) a default (or give rise to any
right of termination, cancellation or acceleration) under, or require any
consent or other action by any Person as a result of, any of the terms,
conditions or provisions of any note, contract, agreement, commitment, bond,
mortgage, indenture, license, pledge agreement or other instrument or obligation
to which the Company or any Subsidiary is a party or by which the Company or any
Subsidiary may be bound, or (iii) violate any law, regulation, judgment, order,
writ, injunction or decree applicable to the Company or any Subsidiary.

         2.6 GOVERNMENTAL CONSENTS. None of the circumstances in connection with
the offer, issue, sale or delivery of the Common Stock or the execution and
delivery of this Agreement is such as to require a consent, approval or
authorization of, or filing, registration or qualification with any Governmental
Authority on the part of the Company or any Subsidiary in connection with the
execution and delivery of this Agreement or the offer, issue, sale or delivery
of the Common Stock.

         2.7 NON-CONTRAVENTION. Except for exceptions that do not have a
Material Adverse Effect on the Company or any Subsidiary, neither the Company
nor any Subsidiary is in breach of, default under, or in violation of any
applicable law, decree, order, rule or regulation, or any indenture, contract,
agreement, deed, lease, loan agreement, commitment, bond, note, deed of trust,
restrictive covenant, license or other instrument or obligation to which it is a
party or by which it is bound or to which any of its assets are subject, the
execution, delivery and performance of this Agreement and the issuance, sale and
delivery of the Common Stock and other documents will not constitute any such
breach, default or violation or require consent or approval of any court or
Governmental Authority except as contemplated herein.

         2.8 FINANCIAL STATEMENTS. The audited and unaudited consolidated
financial statements, together with the notes thereto, the Company included (or
incorporated by reference) in the SEC Filings fairly present the financial
condition of the Company and its consolidated subsidiaries as of the dates
thereof and the results of their operations and changes in financial positions
for the periods then ended in accordance with GAAP (except as stated in such
financial statements, including the related notes, and except that the quarterly
financial statements do not contain all the footnote disclosures required by
GAAP), subject, in the case of the unaudited financial statements, to normal
year-end audit adjustments and any other adjustments described therein. The
information in the Draft 1998 10-K, when read together with the information
included in this Agreement and the schedules and exhibits hereto, does not
contain any untrue statement of a material fact or omit to state a material fact
required to be stated therein or necessary in order to make the statements made
therein, in the light of the circumstances under which they were made, not
misleading. The Company has provided the Investor with a copy of each document
which is of the character of document which would otherwise be required to be
filed by the Company with the SEC as an exhibit (other than financial
statements, financial exhibits or financial schedules) to any Annual Report on



                                       6

<PAGE>   8




Form 10-K, Quarterly Report on Form 10-Q or Current Report on Form 8-K required
to be filed by the Company under the Exchange Act, if filed with respect to a
period ending on the date hereof, which has not been previously filed or
incorporated by reference in the SEC Filings or which is not referred to in the
Schedules hereto.

         2.9 ABSENCE OF CERTAIN CHANGES. Except as disclosed in the SEC Filings
or Schedule 2.9, since December 31, 1998, there has not been (a) any material
adverse change in the business, properties, assets, condition (financial or
otherwise), results of operations or prospects of the Company and its
Subsidiaries, taken as a whole, (b) in the case of the Company, any declaration
setting aside or payment of any dividend or other distribution with respect to
its Capital Stock, or (c) any material change by the Company in accounting
principles or methods.

         2.10 NO BROKER'S OR FINDER'S FEES. No agent, broker, investment banker,
person or firm has acted directly or indirectly on behalf of the Company or any
Subsidiary in connection with this Agreement or the transactions contemplated
hereby, and no such person or entity is or will be entitled to any broker's or
finder's fee or any other commission or similar fee or expense, directly or
indirectly, in connection with this Agreement or the transactions contemplated
hereby.

         2.11 EXEMPTION FROM REGISTRATION. Based in part on the representations
of the Investor herein, the offer, sale and delivery of the Common Stock
pursuant to this Agreement is exempt from the registration requirements of the
Securities Act and all applicable state securities laws.

         2.12 NO UNDISCLOSED MATERIAL LIABILITIES. There are no liabilities of
the Company or any Subsidiary of any kind whatsoever, whether accrued,
contingent, absolute, determined, determinable or otherwise, and there is no
existing condition, situation or set of circumstances which could reasonably be
expected to result in such a liability, other than:

                           (A) liabilities provided for in the consolidated
         financial statements of the Company included in the Draft 1998 10-K, or
         disclosed in the notes thereto;

                           (B) liabilities disclosed on any of the Schedules 
         attached hereto; and

                           (C) other undisclosed liabilities which, individually
         or in the aggregate, are not material to the Company or any
         Subsidiaries considered as a whole.

         2.13 DISCLOSURE. Neither this Agreement nor any other document,
certificate or statement furnished to the Investor by or on behalf of the
Company in connection herewith, contains any untrue statement of a material fact
or omits to state a material fact necessary in order to make the statements
contained herein and therein not misleading. There is no fact regarding the
Company or any Subsidiary known to the Company or any Subsidiary which the
Company or any Subsidiary reasonably believes will materially and adversely
affect the business or financial condition of the Company or any Subsidiary,
which heretofore has not been set forth in this Agreement or in the other
documents, certificates and written statements furnished or otherwise provided
in writing to the Investor by or on behalf of the Company or any Subsidiary
prior to the date hereof in connection



                                       7

<PAGE>   9




with the transactions contemplated hereby. All information previously provided,
or to be provided to Investor, and all Schedules contemplated hereby are, or
shall be, respectively, true, accurate and complete in all material respects.


                                  ARTICLE III.
                         REPRESENTATIONS OF THE INVESTOR

         The Investor represents and warrants to the Company as follows:

         3.1 ORGANIZATION AND EXISTENCE. The Investor is a Company duly
organized, validly existing and in good standing under the laws of Delaware, and
has all requisite power and authority to carry on its business as now being
conducted.

         3.2 AUTHORITY. The Investor has full power and authority to execute and
deliver this Agreement and to consummate the transactions contemplated hereby.
The execution and delivery of this Agreement and the consummation of the
transactions contemplated hereby have been duly and validly authorized and
approved by the board of directors of the Investor, and no other proceedings on
the part of the Investor are necessary to authorize this Agreement or the
consummation of the transactions contemplated hereby. This Agreement has been
duly and validly executed and delivered by the Investor and constitutes the
legal, valid and binding agreement of the Investor, enforceable against the
Investor in accordance with its terms, subject to (i) bankruptcy, insolvency and
other similar laws now or hereafter affecting the enforcement of the rights of
creditors generally and (ii) general principles of equity.

         3.3 NO VIOLATION. Neither the execution and delivery of this Agreement,
the consummation of the transactions contemplated hereby, nor the compliance by
the Investor with any of the provisions hereof will (i) conflict with or result
in any breach of any provision of the Certificate of Incorporation or Bylaws of
the Investor, (ii) result in a violation or breach of or constitute (with or
without due notice or lapse of time or both) a default (or give rise to any
right of termination, cancellation or acceleration) under, any of the terms,
conditions or provisions of any note, contract, agreement, commitment, bond,
mortgage, indenture, license, pledge agreement or other instrument or obligation
to which the Investor is a party or by which such Investor may be bound, or
(iii) violate any law, regulation, judgment, order, writ, injunction or decree
applicable to the Investor.

         3.4 NO BROKER'S OR FINDER'S FEES. No agent, broker, investment banker,
person or firm has acted directly or indirectly on behalf of such Investor in
connection with this Agreement or the transaction contemplated hereby, and no
such person or entity is or will be entitled to any broker's or finder's fee or
any other commission or similar fee or expense, directly or indirectly, in
connection with this Agreement or the transaction contemplated hereby.




                                       8

<PAGE>   10




         3.5 INVESTMENT INTENT. The Investor represents that it has had an
opportunity to ask questions of and receive answers from the Company regarding
the Company and its business, assets, results of operation and financial
condition and the terms and conditions of the issuance of the Common Stock
hereunder for the purpose of evaluating the proposed acquisition of the Common
Stock.

                  (A) The Investor is acquiring the Common Stock hereunder
         solely by and for its own account, for investment purposes only and not
         for the purpose of resale or distribution; and Investor has no
         contract, undertaking, agreement or arrangement with any person or
         entity to sell, transfer or pledge to such person or anyone else any of
         the Common Stock; and Investor has no present plans or intentions to
         enter into any such contract, undertaking or arrangement.

                  (B) The Investor acknowledges and understands that (i) no
         registration statement relating to the Common Stock has been or is to
         be filed with the SEC under the Securities Act or pursuant to the
         securities laws of any state; (ii) the Common Stock cannot be sold or
         transferred without compliance with the registration provisions of the
         Securities Act or compliance with exemptions, if any, available
         thereunder; (iii) the certificates representing the Shares will include
         a legend thereon that refers to the foregoing; and (iv) the Company has
         no obligation or intention to register the Common Stock under any
         federal or state securities act or law; except to the extent in each
         case that the terms of the Registration Rights Agreement shall
         otherwise provide.

                  (C) The Investor (i) is an "accredited investor" as defined in
         Rule 501 of the rules promulgated pursuant to the Securities Act; (ii)
         has such knowledge and experience in financial and business matters in
         general that it has the capacity to evaluate the merits and risks of an
         investment in the Common Stock and to protect its own interest in
         connection with an investment in the Common Stock; (iii) has such a
         financial condition that it has no need for liquidity with respect to
         its investment in the Common Stock to satisfy any existing or
         contemplated undertaking, obligation or indebtedness; and (iv) is able
         to bear the economic risk of its investment in the Common Stock for an
         indefinite period of time.

                  (D) The acquisition of the Common Stock by the Investor at the
         Closing, as applicable, shall constitute Investor's confirmation of the
         foregoing representations.

         3.6 NO ADDITIONAL REPRESENTATIONS OR WARRANTIES. The Investor is making
no representations or warranties, express or implied, of any nature whatsoever
except as specifically set forth in Article III of this Agreement.





                                       9

<PAGE>   11




                                   ARTICLE IV.
                      POST-CLOSING COVENANTS OF THE COMPANY

         4.1 POST-CLOSING COVENANTS. From the date hereof and for as long as the
Investor continues to hold Common Stock, the Company covenants that it will make
all SEC Filings required to be made pursuant to the Securities Act or the
Exchange Act, or the rules promulgated thereunder. No investigation by the
Investor or other information received by the Investor shall operate as a waiver
or otherwise affect any representation, warranty, or agreement given or made by
the Company hereunder.

         4.2 INFORMATION REQUIREMENTS. As long as the Investor or an Affiliate
of the Investor owns any of the Common Stock it acquires hereby, the Company
covenants to the Investor that it will deliver to the Investor,
contemporaneously with the filing, publication or distribution of such, copies
of all SEC Filings, communications from the Company to its shareholders after
the date of this Agreement. Nothing contained in this Article IV is intended to
influence the general management or overall operations of the Company or any
Subsidiary in a manner not permitted by applicable law and the provisions hereof
shall automatically be reduced in compliance therewith.


                                   ARTICLE V.
                      POST-CLOSING COVENANTS OF THE PARTIES

         5.1 RESTRICTIONS ON TRANSFER. For a period of six months from the date
hereof, the Investor will not sell, exchange or assign any of the Common Stock
received pursuant to this Agreement. Thereafter, the Investor will have no
further restrictions on its right to sell, exchange or otherwise transfer the
Common Stock, except as provided by applicable law.

         5.2 AMENDMENT OF ALLIANCE AGREEMENTS. For purposes of Alliance
Agreement I, the "Exclusivity Period" (as defined in the Alliance Agreement I)
shall be deemed to have expired on September 9, 1999, and for purposes of the
Alliance Agreement II, the "Exclusivity Period" (as defined in the Alliance
Agreement II) shall be deemed to have expired on November 25, 2000. Effective as
of November 25, 1998, all seismic operating activities pursuant to Alliance
Agreement II ceased and neither Veritas nor the Company shall have any
obligation to conduct any additional seismic operating activities under Alliance
Agreement II. Any seismic processing agreements between BOG and Veritas or any
Affiliates and all other agreements related to any of the payables described in
Article I shall be deemed to have been properly and timely paid in accordance
with the terms of such agreements, provided that the Common Stock is properly
issued to Veritas in accordance with the terms set forth herein. Veritas and its
Affiliates and BOG shall enter into all amendments to the Alliance Agreement I
and the Alliance Agreement II and any processing agreements which are necessary
to cause BOG to receive credit for the payment of the payables described in
Article I in accordance with the terms hereof. In addition, the Company agrees
that in the event that "Final Payout" (as defined in the Alliance Agreement I)
does not occur under Alliance Agreement I, then to the extent allowed under the
terms of BOG's currently existing agreements with Stephens Production Company
and Vintage Petroleum, Inc., BOG shall provide Veritas with



                                       10

<PAGE>   12




copies of all available permits, OB logs, survey notes, SEG P1 files, field
tapes, any intermediate processing files (i.e., CDP Gathers), bin and survey
maps, processing sequences, final stacked tapes and final migration tapes
related to the seismic data acquired pursuant to Alliance Agreement I; provided,
however, that Veritas shall pay for all reproduction costs incurred to provide
such copies. In the event that "Final Payout" (as defined in the Alliance
Agreement II) does not occur under Alliance Agreement II, BOG shall provide
Veritas with copies of all available permits, OB logs, survey notes, SEG P1
files, field tapes, intermediate processing files (i.e., CDP Gathers), bin and
survey maps, processing sequences, final stacked tapes and final migration tapes
related to the seismic data acquired pursuant to Alliance Agreement II;
provided, however, that Veritas shall pay for all reproduction costs incurred to
provide such copies.

         5.3 FIRST RIGHT OF REFUSAL FOR SEISMIC ACQUISITION. From the date
hereof until March 26, 2004, if BOG or any successor to substantially all of the
assets of BOG receives a good-faith bid by a reputable unaffiliated service
provider to provide it with seismic processing, operations or acquisition
services, BOG or such successor will provide Veritas with the opportunity (which
must be accepted, if at all, within ten (10) days after receipt by Veritas or
any of its Affiliates of notice of the terms and conditions of the third-party
offer) to offer to BOG or such successor, the same terms and conditions as are
offered by such third party bid. In the event that the bid received by BOG or
such successor includes a risk-sharing structure or any kind of investment in
the 3-D seismic project by the service provided, Veritas also must match those
terms in order to receive the contract.

         5.4 CERTAIN FILINGS. The parties hereto shall cooperate with one
another

                           (A) in determining whether any action by or in
         respect of, or filing with, any Governmental Authority is required, or
         any actions, consents, approvals, or waivers are required to be
         obtained from parties to any material contracts, in connection with the
         consummation of the transactions contemplated by this Agreement; and

                           (B) in taking such actions or making such filings,
         furnishing information required in connection therewith and seeking
         timely to obtain any such actions, consents, approvals, or waivers.

         5.5 PUBLICITY. Except as otherwise required by law, the parties shall
determine in advance, by mutual agreement and consent, the timing and content of
any announcement, including press releases or other public statements concerning
the transactions contemplated by this Agreement.





                                       11

<PAGE>   13




                                   ARTICLE VI.
                                 INDEMNIFICATION

         6.1 INDEMNIFICATION BY THE COMPANY. The Company shall indemnify the
Investor, its Affiliates, and their directors, officers, employees, agents and
counsel (collectively, the "Investor Indemnified Parties") from, and hold each
of them harmless against, any and all actions, suits, losses, liabilities,
claims and damages, and expenses in connection therewith, including reasonable
counsel's fees and disbursements, whether foreseeable or unforeseeable
("Indemnified Liabilities") to which any of them may become subject arising
from:

                           (A) exercise by the Investor or any Affiliate of
         their respective rights under this Agreement;

                           (B) proceedings brought against the Investor or any
         Affiliate in their capacity as shareholders in the Company; and

                           (C) breach by the Company of this Agreement,
         including without limitation any inaccuracy in any representation or
         warranty of the Company under this Agreement, the Schedules hereto, or
         any agreement, certificate or other document delivered or to be
         delivered by the Company pursuant hereto in any respect.

Notwithstanding the foregoing, the Company shall not be required to indemnify
the Investor Indemnified Parties for Indemnified Liabilities arising from the
Investor Indemnified Parties' intentional misconduct, gross negligence or breach
of this Agreement.

         6.2 INDEMNIFICATION BY THE INVESTOR. The Investor shall indemnify the
Company, its Affiliates, and its directors, officers, employees, agents and
counsel (collectively, the ACompany Indemnified Parties@) from, and hold each of
them harmless against Indemnified Liabilities to which any of them may become
subject arising in connection with this Agreement, the transactions contemplated
hereby, and any action, omission to act, occurrence or condition in connection
herewith, including Indemnified Liabilities that arise out of or relate to any:

                           (A) breach by the Investor of this Agreement,
         including without limitation any inaccuracy in any representation or
         warranty of the Investor under this Agreement, the Schedules hereto, or
         any agreement, certificate or other document delivered or to be
         delivered by the Investor pursuant hereto in any respect, whether or
         not the Company Indemnified Party relied thereon or had Knowledge
         thereof and without regard to any qualifications contained in such
         representations and warranties limiting such representations and
         warranties (a) to matters within the Knowledge of the Investor, or (b)
         as to materiality; and

                           (B) breach or nonfulfillment of any covenant,
         agreement or other obligation of the Investor under this Agreement or
         any agreement or document delivered pursuant hereto.



                                       12

<PAGE>   14




         6.3 LIMITATION OF LIABILITY. No indemnification shall be required to be
made by the Company or the Investor pursuant to this Article VI with respect to
any Indemnified Liabilities unless and until the aggregate amount of Indemnified
Liabilities incurred by the Investor Indemnified Parties or the Company
Indemnified Parties, respectively (whether asserted, resulting, imposed, or
incurred before, on, or after the Closing Date), exceeds $5,000; provided,
however that once such amount exceeds $5,000, the Investor Indemnified Parties
or the Company Indemnified Parties, as applicable, shall be entitled to recover
all amounts to which they are entitled, including such initial $5,000.

         6.4 NOTICE AND DEFENSE OF THIRD-PARTY CLAIMS. If any Proceeding shall
be brought or asserted under this Article VI against a party claiming
indemnification under this Agreement (for purposes of this Section 6.4, an
"Indemnified Party") in respect of which indemnity may be sought under this
Article from the party from whom indemnification is sought (for purposes of this
Section 6.4, an "Indemnifying Party"), the Indemnified Party shall give prompt
written notice of such Proceeding to the Indemnifying Party who shall assume the
defense thereof, including the employment of counsel reasonably satisfactory to
the Indemnified Party and the payment of all expenses; provided, that any delay
or failure so to notify the Indemnifying Party shall relieve the Indemnifying
Party of its obligations hereunder only to the extent, if at all, that it is
prejudiced by reason of such delay or failure. In no event shall any Indemnified
Party be required to make any expenditure or bring any cause of action to
enforce the Indemnifying Party's obligations and liability under and pursuant to
the indemnifications set forth in this Article. In addition, actual or
threatened action by a Governmental Authority or other Person is not a condition
or prerequisite to the Indemnifying Party's obligations under this Article. The
Indemnified Party shall have the right to employ separate counsel in any of the
foregoing Proceedings and to participate in the defense thereof, but the fees
and expenses of such counsel shall be at the expense of the Indemnified Party
unless the Indemnified Party shall in good faith determine that there exist
actual or potential conflicts of interest which make representation by the same
counsel inappropriate. The Indemnified Party's right to participate in the
defense or response to any Proceeding should not be deemed to limit or otherwise
modify the Indemnifying Party's obligations under this Article. In the event
that the Indemnifying Party, within five days after notice of any such
Proceeding, fails to assume the defense thereof, the Indemnified Party shall
have the right to undertake the defense, compromise or settlement of such
Proceeding for the account of the Indemnifying Party, subject to the right of
the Indemnifying Party to assume the defense of such Proceeding with counsel
reasonably satisfactory to the Indemnified Party at any time prior to the
settlement, compromise or final determination thereof. Anything in this Article
VI to the contrary notwithstanding, the Indemnifying Party shall not, without
the Indemnified Party's prior written consent, settle or compromise any
Proceeding or consent to the entry of any judgment with respect to any
Proceeding for anything other than money damages paid by the Indemnifying Party.
The Indemnifying Party may, without the Indemnified Party's prior written
consent, settle or compromise any such Proceeding or consent to entry of any
judgment with respect to any such Proceeding that requires solely the payment of
money damages by the Indemnifying Party and that includes as an unconditional
term thereof the release by the claimant or the plaintiff of the Indemnified
Party from all liability in respect of such Proceeding.




                                       13

<PAGE>   15




         6.5 PARTICIPATION IN PUBLIC OFFERING. No Person may participate in any
Public Offering hereunder unless such Person (a) agrees to sell such Person's
securities on the basis provided in any underwriting agreement approved by the
Persons entitled hereunder to approve such arrangements and (b) completes and
executes all questionnaires, powers of attorney, indemnities, underwriting
agreements and other documents reasonably required under the terms of such
underwriting arrangements and the provisions of this Agreement in respect of
registration rights.

         6.6 STOCK LEGENDS. All stock certificates representing Registerable
Shares issued pursuant to the provisions of this Agreement shall bear a legend
stating that such shares are subject to the provisions of this Agreement.

                                  ARTICLE VII.
                                  MISCELLANEOUS

         7.1 EXPENSES. Whether or not the purchase of the Common Stock herein
contemplated is consummated, all costs and expenses incurred by Investor in
connection with this Agreement and the transactions contemplated hereby
(including but not limited to attorneys and brokerage fees and expenses) shall
be paid by Investor and all such costs and expenses incurred by the Company
shall be paid by the Company.

         7.2 AMENDMENT AND MODIFICATION. This Agreement may be amended, modified
or supplemented only by the written agreement of the parties hereto.

         7.3 WAIVER OF COMPLIANCE; CONSENTS. Any failure of the Investor, on the
one hand, or the Company, on the other hand, to comply with any obligation,
covenant, agreement or condition herein may be waived by the Company or the
Investor, respectively, only by a written instrument signed by the party
granting such waiver, but such waiver or failure to insist upon strict
compliance with such obligation, covenant, agreement or condition shall not
operate as a waiver of, or estoppel with respect to, any subsequent or other
failure. Whenever this Agreement requires or permits consent by or on behalf of
any party hereto, such consent shall be given in writing in a manner consistent
with the requirements for a waiver of compliance as set forth in this Section
7.3.

         7.4 NOTICES. All notices and other communications hereunder shall be in
writing and shall be deemed given if (i) delivered personally, (ii) mailed by
registered or certified mail (return receipt requested), whereupon notice shall
be deemed given three days after mailing, or (iii) sent by telecopy with
confirmation, to the other party at the following addresses (or at such other
address for a party as shall be specified by like notice; provided that notices
of a change of address shall be effective only upon receipt thereof):

         If to the Company:    Brigham Exploration Company
                               6300 Bridge Point Parkway,
                               Bldg. 2, Suite 500
                               Austin, Texas 78730
                               Attn: President
                               Telecopy Number:  (512) 427-3400


                                       14

<PAGE>   16






         with a copy to:   Joe Dannenmaier
                               Thompson & Knight
                               1700 Pacific Avenue, Suite 3300
                               Dallas, Texas 75201
                               Telecopy Number: (214) 969-1751

                               and

                               Brigham Exploration Company
                               6300 Bridge Point Parkway,
                               Bldg. 2, Suite 500
                               Austin, Texas 78730
                               Attn: General Counsel
                               Telecopy Number: (512) 427-3400

         If to the Investor:   Veritas DGC Land, Inc.
                               3701 Kirby Drive, Suite 932
                               Houston, Texas 77098-3982
                               Attn: Deanna L. M. Goodwin
                               Telecopy Number: (713) 512-8729

         with a copy to:   Locke Liddell & Sapp LLP
                               2600 Texas Commerce Tower
                               600 Travis
                               Houston, Texas 77002
                               Attn: Mr. H. William Swanstrom
                               Telecopy number: (713) 223-3717

                               and

                               Veritas DGC, Inc.
                               3701 Kirby Drive, Suite 1112
                               Houston, Texas 77098
                               Attn: Larry L. Worden
                               Telecopy number: (713) 512-8701

         7.5 ASSIGNMENT. This Agreement and all of the provisions hereof shall
be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns. Neither this Agreement nor any of
the rights, interests or obligations hereunder shall be assigned by the Company
without the prior written consent of the Investor. No permitted assignment shall
relieve the assigning party of any of its obligations hereunder.




                                       15

<PAGE>   17




         7.6 GOVERNING LAW. This Agreement shall be governed by the laws of the
State of Texas (regardless of the laws that might otherwise govern under
applicable Texas principles of conflicts of law) as to all matters, including
but not limited to matters of validity, construction, effect, performance and
remedies.

         7.7 DISPUTE RESOLUTION.

                           (A) If a dispute arises between the parties hereto
         regarding any issue that relates to this Agreement, the parties agree
         that their respective representatives shall meet and consult in good
         faith in an attempt to settle the dispute, within thirty (30) days of
         written notice thereof, as a condition precedent to the initiative of
         arbitration proceedings under the Commercial Arbitration Rules of the
         American Arbitration Association.

                           (B) In the event the parties are unable to resolve
         their differences, such dispute shall be submitted to arbitration.
         Arbitration shall be conducted in Houston, Texas, under the Commercial
         Arbitration Rules then in force of the American Arbitration
         Association. The arbitration proceedings shall be conducted before a
         panel of three (3) members of the State Bar of Texas in which the
         arbitration is conducted, actively engaged in commercial transactions.
         The parties agree that discovery shall be limited and shall be handled
         expeditiously. Discovery proceedings available in litigation before the
         courts shall not apply in an arbitration conducted pursuant to this
         Agreement. However, each party shall produce relevant and
         non-privileged documents or copies thereof requested by the other party
         within the time limits set and to the extent required by order of the
         arbitrators. All disputes regarding discovery shall be promptly
         resolved by the arbitrators. Strict rules of evidence shall not apply
         in such arbitration. The parties may offer such evidence as they desire
         and the arbitrators shall accept such evidence as the arbitrators deems
         relevant to the issues and accord it such weight as the arbitrators
         deem appropriate. In rendering the award, the arbitrators shall
         determine the respective rights and obligations of the parties
         according to the laws of the State of Texas. The arbitrators shall
         award to the prevailing party, if any, as determined by the arbitrator
         all of the prevailing party's costs and fees. "Costs and fees" shall
         include the reasonable pre-award expenses of the arbitration, including
         arbitrator's fees, administrative fees, witness fees and attorney's
         fees. The parties and arbitrators shall treat all aspects of the
         arbitration proceedings, including without limitation, discovery,
         testimony and other evidence, briefs and the award, as strictly
         confidential. The arbitrators' decision may include any remedy
         contemplated by this Agreement.

                           (C) It is the intent of the parties that, excepting
         extraordinary circumstances, any arbitration shall be concluded within
         four (4) months of the date arbitration is commenced. The parties may,
         upon agreement, extend the time limits or the arbitrators may determine
         that such an extension is necessary in the interest of justice.

                           (D) The arbitrators will use their best efforts to
         issue a final award within forty-five (45) days after closure of the
         proceedings. The arbitration award shall be in writing and specify the
         factual and legal basis for the award.



                                       16
<PAGE>   18





                           (E) Either party may appeal the arbitrators' award to
         an appellate arbitrator by filing with the AAA within twenty (20) days
         after transmittal of the award, a written brief, not to exceed twenty
         (20) pages stating the reason(s) why the arbitrators' decision should
         be reversed or modified. The opposing party shall file with the AAA and
         serve on the appealing party within twenty (20) days of receiving the
         appeal brief, and opposition brief not to exceed twenty (20) pages. The
         appellate arbitrator shall be appointed directly by the AAA without
         submission of a list by the parties, and shall be a retired judge of a
         court of record of the State in which the arbitration is conducted.

                           (F) If no appeal is filed, the arbitrators' decision
         shall be final and binding upon the parties. If an appeal is filed, the
         decision of the appellate arbitrator's decision shall be final and
         binding upon the parties. Judgment upon the award of the arbitrators,
         if no appeal was made, or upon the decision of the appellate
         arbitrator, if an appeal was filed, may be ordered and enforced by a
         court of competent Jurisdiction.

         7.8 COUNTERPARTS. This Agreement may be executed in counterparts, each
of which shall be deemed an original, but all of which together shall constitute
one and the same instrument.

         7.9 NO THIRD-PARTY BENEFICIARIES. No provision of this Agreement is
intended to confer upon any Person other than the Parties hereto any rights or
remedies hereunder, other than wholly-owned subsidiaries of the Parties hereto,
which shall be considered third party beneficiaries hereof.

         7.10 INTERPRETATION. The article and section headings contained in this
Agreement are solely for the purpose of reference, are not part of the agreement
of the parties and shall not in any way affect the meaning or interpretation of
this Agreement.

         7.11 ENTIRE AGREEMENT. This Agreement, including the documents,
instruments and agreements referred to herein, and the agreements and documents
executed contemporaneously herewith embody the entire agreement and
understanding of the parties hereto in respect of the subject matter hereof.
There are no restrictions, promises, representations, warranties, covenants, or
undertakings, other than those expressly set forth or referred to herein or
therein. This Agreement supersedes all prior agreements and understandings
between the parties with respect to such subject matter. Notwithstanding the
foregoing, this Agreement does not supersede the Confidentiality Agreement
between the Parties dated February 15, 1999.

         7.12 ATTORNEYS' FEES. In the event any party hereto institutes a
lawsuit against any other party hereto for a claim arising out of or to
specifically enforce this Agreement, the losing party shall pay the reasonable
attorneys' fees incurred by the prevailing party in connection with such
lawsuit.




                                       17

<PAGE>   19




         7.13 FURTHER ASSURANCES. The parties hereto agree (i) to furnish upon
request to each such further information, (ii) to execute and deliver to each
other such other documents, and (iii) to do such other acts and things, all as
the other party hereto may at any time reasonably request, for the purpose of
carrying out the intent of this Agreement and the documents referred herein.



                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]





                                       18

<PAGE>   20




         IN WITNESS WHEREOF, each of the parties hereto has executed this
Agreement as of the date first above written.

                                     BRIGHAM EXPLORATION COMPANY

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

                                     VERITAS DGC LAND, INC.

                                     By: /s/ Deanna Goodwin
                                        ----------------------------------------
                                     Name: Deanna Goodwin
                                          --------------------------------------
                                     Title: Vice President Finance
                                           -------------------------------------

Appendix A - Definitions


Schedule 1.1 -  Extinguished Liabilities
Schedule 2.4 -  Draft Annual Report on Form 10-K for fiscal year ended December
                31, 1998 
Schedule 2.9 -  Absence of Certain Changes




                                       19

<PAGE>   21




                                   APPENDIX A
                                   DEFINITIONS

        For the purposes of this Agreement, the following terms shall have the
meanings specified or referred to below whether or not capitalized when used in
this Agreement. Where a defined term in this Agreement derives its meaning from
a statutory reference, for the purposes of this Agreement any regulatory
definition promulgated pursuant to the applicable statute shall be deemed to be
applicable to the extent its definition is broader than the statutory reference
and any reference or citation to a statute or regulation shall be deemed to
include any amendments to that statute or regulation and judicial and
administrative interpretations of it. Any specific references to a law shall
include any amendments to it promulgated from time to time.

        "Affiliate" means, with respect to a specified Person, (a) any Entity of
which such Person is an executive officer, director, partner, trustee or other
fiduciary or is directly or indirectly the Beneficial Owner of ten percent (10%)
or more of any class of equity security thereof or other financial interest
therein; (b) if such Person is an individual, any relative or spouse of such
individual, or any relative of such spouse (such relative being related to the
individual in question within the second degree) and any Entity of which any
such relative, spouse, or relative of spouse is an executive officer, director,
partner, trustee or other fiduciary or is directly or indirectly the Beneficial
Owner of ten percent (10%) or more of any class of equity security thereof or
other financial interest therein; (c) if such Person is an Entity, any director,
executive officer, partner, trustee or other fiduciary or any direct or indirect
Beneficial Owner of ten percent (10%) or more of any class of equity security
of, or other financial interest in, such Entity; or (d) any Person that
directly, or indirectly through one or more intermediaries, controls, is
controlled by, or is under common control with the Person specified. For
purposes of this definition, "executive officer" means the president, any vice
president in charge of a principal business unit, division or function such as
sales, administration, research and development, or finance, and any other
officer, employee or other Person who performs a policy making function or has
the same duties as those of a president or vice president. For purposes of this
definition, "control" (including "controlling", "controlled by" and "under
common control with") means the possession, direct or indirect, of the power to
direct or cause the direction of the management and policies of a Person,
whether through the ownership of voting securities, by contract or otherwise.
When used without reference to a particular Person, "Affiliate" means an
Affiliate of the Company or the Shareholders.

        "Agreement" means this Exchange Agreement, including the schedules and
exhibits attached hereto, which are hereby incorporated herein

        "Alliance Agreement I" means that certain Anadarko Basin Seismic
Operation Agreement, dated February 15, 1996, by and between BOG and Veritas
predecessor, as amended.

        "Alliance Agreement II" means that certain Anadarko Basin Seismic
Operation Agreement, dated April 1, 1997, by and between BOG and VERITAS'
predecessor, as amended.

        "BOG" means Brigham Oil & Gas, L.P.



                                  Appendix A-1

<PAGE>   22




        "Best Efforts" means those efforts which a prudent individual desirous
of achieving a result would exert in similar circumstances to ensure that such
result is achieved as expeditiously as possible.

        "Closing " shall have the meaning set forth in Section 1.2.

        "Closing Date" means the date and time as of which the Closing actually
takes place.

         "Common Stock" means any class or series of the common stock, $.01 per
share par value, of the Company.

        "Encumbrance" means any lien, pledge, hypothecation, charge, mortgage,
deed of trust, security interest, encumbrance, equity, trust, equitable
interest, claim, easement, right-of-way, servitude, right of possession, lease
tenancy, license, encroachment, burden, intrusion, covenant, infringement,
interference, proxy, option, right of first refusal, community property
interest, legend, defect, impediment, exception, condition, restriction,
reservation, limitation, impairment, imperfection of title, restriction on or
condition to the voting of any security, restriction on the transfer of any
security or other asset, restriction on the receipt of any income derived from
any security or other asset, and restriction on the possession, use, exercise or
transfer of any other attribute of ownership, whether based on or arising from
common law, constitutional provision, statute or contract.

        "Entity" means any Company (including any non-profit Company), general
partnership, limited partnership, joint venture, joint stock association,
estate, trust, cooperative, foundation, union, syndicate, league, consortium,
coalition, committee, society, firm, company or other enterprise, association,
organization or entity of any nature.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, as
amended.

        "GAAP" means generally accepted United States accounting principles,
consistently applied. As applied to the Company, GAAP means those accounting
principles and practices (a) which are recognized as such by the Financial
Accounting Standards Board, (b) which are applied for all periods after the date
hereof in a manner consistent with the manner in which such principles and
practices were applied to the most recent audited financial statements of the
Company furnished to the Purchaser, and (c) which are consistently applied for
all periods after the date hereof so as to reflect properly the financial
condition, and results of operations and cash flows, of the Company.

        "Governmental Authority" means any foreign governmental authority, the
United States of America, any State of the United States, any local authority
and any political subdivision of any of the foregoing, any multi-national
organization or body, any agency, department, commission, board, bureau, court
or other authority thereof, or any quasi-governmental or private body
exercising, or purporting to exercise, any executive, legislative, judicial,
administrative, police, regulatory or taxing authority or power of any nature.




                                  Appendix A-2

<PAGE>   23




        "Governmental Authorization" means any permit, license, franchise,
approval, certificate, consent, ratification, permission, confirmation,
endorsement, waiver, certification, registration, qualification or other
authorization issued, granted, given or otherwise made available by or under the
authority of any Governmental Authority or pursuant to any Legal Requirement.

        "Legal Requirement" means any law, statute, ordinance, decree,
requirement, Order, treaty, proclamation, convention, rule or regulation (or
interpretation of any of the foregoing) of, and the terms of any Governmental
Authorization issued by, any Governmental Authority.

        "Liability" means any debt, obligation, duty or liability of any nature
(including any unknown, undisclosed, unfixed, unliquidated, unsecured,
unmatured, unaccrued, unasserted, contingent, conditional, inchoate, implied,
vicarious, joint, several or secondary liability), regardless of whether such
debt, obligation, duty or liability would be required to be disclosed on a
balance sheet prepared in accordance with GAAP.

        "Material Adverse Effect" means any material adverse change in the
condition (financial or otherwise), business, operations, properties, prospects,
assets or Liabilities of the Company or any Subsidiaries considered as a whole
(whether or not covered by insurance).

        "Order" means any order, judgment, injunction, edict, decree, ruling,
pronouncement, determination, decision, opinion, sentence, subpoena, writ or
award issued, made, entered or rendered by any court, administrative agency or
other Governmental Authority or by any arbitrator.

        "Organizational Documents" means, with respect to a Company, the
certificate of incorporation, articles of incorporation and bylaws of such
Company; with respect to a general partnership, the partnership agreement
establishing such partnership; with respect to a joint venture, the joint
venture agreement establishing such joint venture; with respect to a limited
partnership, the limited partnership agreement and the certificate of limited
partnership of such limited partnership; with respect to a trust, the instrument
establishing such trust; and with respect to any other Entity, any charter
document or other document executed, adopted, approved, ratified or filed in
connection with the formation, creation, constitution or organization of such
Entity, in each case including any and all amendments or modifications thereof.

        "Person" means any individual, Entity or Governmental Authority.

        "Proceeding" means any action, suit, litigation, arbitration, lawsuit,
claim, proceeding (including any civil, criminal, administrative, investigative
or appellate proceeding and any informal proceeding), prosecution, contest,
hearing, inquiry, inquest, audit, examination, investigation, challenge,
controversy or dispute commenced, brought, conducted or heard by or before, or
otherwise involving, any Governmental Authority or any arbitrator.

        "Public Offering" means an underwritten public offering of Common Stock
of the Company pursuant to an effective registration statement under the
Securities Act.




                                  Appendix A-3

<PAGE>   24




        "Securities Act" shall mean the Securities Act of 1933, as amended.

        "Subsidiary" means, with respect to any Person, any Company,
partnership, joint venture, joint stock association, business trust or other
Entity which is, directly or indirectly, owned or controlled by another Person
or any other Person which is itself a Subsidiary within the meaning of this
definition, including, without limitation, all Persons the majority of the
Capital Stock or voting stock of which is directly or indirectly owned by the
Company.

        "Threatened" - A Proceeding, dispute or other matter shall be deemed to
have been "threatened" if any demand or statement shall have been made (orally
or in writing) or any notice shall have been given (orally or in writing), or if
any other event shall have occurred or any other circumstances shall exist, that
might lead a prudent Person to conclude that such a Proceeding, dispute or other
matter might be asserted, commenced, taken or otherwise pursued in the future;
provided, however, when used in the context of "threatened releases", each term
shall have the meaning ascribed to it under Environmental Laws.

        Terms which are defined in the body of this Agreement shall have the
meanings specified therein.





                                  Appendix A-4


<PAGE>   1
                                                                   EXHIBIT 10.42

                          REGISTRATION RIGHTS AGREEMENT


         This Registration Rights Agreement (this "Agreement") is made and
entered into as of March 30, 1999, by and among Brigham Exploration Company, a
Delaware corporation (the "Company"), and Veritas DGC Land, Inc., a Delaware
corporation ("Veritas").

         This Agreement is made pursuant to the Exchange Agreement between the
Company and Veritas of even date herewith (the "Exchange Agreement"). In order
to induce Veritas to enter into the Exchange Agreement, the Company has agreed
to provide the registration and other rights set forth in this Agreement.
Pursuant to the Exchange Agreement, the Company will issue Veritas shares of
Common Stock (as defined below).

         The parties agree as follows:


                                    ARTICLE I

         Section 1.01. Definitions. Capitalized terms used herein without
definition shall have the meanings given to them in the Exchange Agreement. The
terms set forth below are used herein as so defined:

         "Commission" has the meaning specified therefor in Section 1.02 of this
Agreement.

         "Common Stock" means the common stock, par value $0.01 per share, of
the Company.

         "Exchange Act" shall mean the Securities Exchange Act of 1934, as
amended, and the rules and regulations promulgated thereunder.

         "Holder" means the record holder of any Registrable Securities.

         "Inspector" has the meaning specified therefor in Section 2.03 this
Agreement.

         "Losses" has the meaning specified therefore in Section 2.07 of this
Agreement.

         "Other Holders" has the meaning specified therefor in Section 2.01 of
this Agreement.

         "Person" means any individual, corporation, limited liability company,
partnership, joint venture, association, joint-stock company, business trust,
trust or unincorporated entity.

         "Records" has the meaning specified therefor in Section 2.03 of this
Agreement.

         "Registrable Securities" means the Acquired Shares until such time as
such securities cease to be Registrable Securities pursuant to Section 1.02
hereof.




<PAGE>   2





         "Registration Statement" has the meaning specified therefor in Section
2.01 of this Agreement.

         "Securities Act" has the meaning specified therefor in Section 1.02 of
this Agreement.

         "Selling Holder" means a Holder who is selling Registrable Securities
pursuant to a Registration Statement.

         Section 1.02. Registrable Securities. Any Registrable Security will
cease to be a Registrable Security when (i) a Registration Statement covering
such Registrable Security has been declared effective by the Securities and
Exchange Commission (the "Commission") and such Registrable Security has been
sold or disposed of pursuant to such effective Registration Statement; (ii)
such Registrable Security is disposed of pursuant to Rule 144 (or any similar
provision then in force) under the Securities Act of 1933, as amended (the
"Securities Act"); (iii) such Registrable Security is eligible to be, and at
the time of determination can be, disposed of pursuant to paragraph (k) of Rule
144 (or any similar provision then in force) under the Securities Act; or (iv)
such Registrable Security is held by the Company or one of its subsidiaries.

                                   ARTICLE II

         Section 2.01. Registration.

                  (a) The Company shall register on a Form S-3 (or Form S-1 or
successor form to either) Registration Statement all of the Registrable
Securities that are held by the Holder(s) so that such Registration Statement
is declared effective within 180 days of the closing under the Exchange
Agreement. The Company shall use its best efforts to keep such Registration
Statement effective until the second anniversary of such closing. With respect
to shares issued pursuant to the Exchange Agreement at the end of, or after,
such 180-day period, the Company shall register such shares on a Form S-3 (or
Form S-1 or successor form to either) Registration Statement within 30 days of
such shares' issuance. Each such Registration Statement referred to herein is a
"Registration Statement."

                  (b) The Company and the parties to the Registration Rights
Agreements with the Company dated February 26, 1997 and August 20, 1998,
respectively, who are entitled to piggy-back registration rights ("Other
Holders") with respect to a Registration Statement filed pursuant to Section
2.01 may include securities of the Company in such Registration Statement.

         Section 2.02. Piggy-Back Registration. If the Company proposes to
register any of its equity securities under the Securities Act for sale to the
public, whether for its own account or for the account of Other Holders or both
(except with respect to Registration Statements filed pursuant to demand under
the Registration Rights Agreement dated August 20, 1998 and Registration
Statements on Forms S-4 or S-8 or for purposes permissible under such forms as
of the date hereof), each such time it will give written notice to all Holders
of its intention to do so no less than 20 days prior to the anticipated filing
date. Upon the written request received by the Company from any Holder no later
than the 15th day after receipt by such holder of the notice sent by the
Company (which request shall state the intended method of disposition thereof),
the Company will use best efforts to cause the Registrable Securities as to



                                       -2-

<PAGE>   3




which registration shall have been so requested to be included in the
securities to be covered by such Registration Statement, all to the extent
required to permit the sale or other disposition by each Holder (in accordance
with its written request) of such Registrable Securities so registered;
provided, however, that the Company may at any time prior to the effectiveness
of any such Registration Statement, in its sole discretion and without the
consent of any Holder, abandon any proposed offering by the Company in which
any Holder had requested to participate. The number of Registrable Securities
to be included in such a registration may be reduced or eliminated if and to
the extent, in the case of an underwritten offering, the managing underwriter
shall advise the Company that such inclusion would materially jeopardize the
successful marketing of the securities (including the Registrable Securities)
proposed to be sold therein; provided, however, that such number of shares of
Registrable Securities shall not be reduced if any securities included in such
registration are included other than for the account of the Company unless the
shares included in the Registration for the account of such Persons are also
reduced on a pro rata basis, provided, in the case of a Registration Statement
filed pursuant to the exercise of demand registration rights of any Other
Holders, priority shall be given first to the Other Holders that demand such
registration.

         Section 2.03. Registration Procedures. If and whenever the Company is
required pursuant to this Agreement to effect the registration of any of the
Registrable Securities under the Securities Act, the Company will, as
expeditiously as possible:

                  (a) prepare and file with the Commission such amendments and
supplements to such Registration Statement and the prospectus used in
connection therewith as may be necessary to keep such Registration Statement
effective for the distribution period and as may be necessary to comply with
the provisions of the Securities Act with respect to the disposition of all
securities covered by such Registration Statement in accordance with the
Holders intended method of disposition;

                  (b) furnish to each Selling Holder and to each underwriter
such number of copies of the Registration Statement and the prospectus included
therein (including each preliminary prospectus and each document incorporated
by reference therein to the extent then required by the rules and regulations
of the Commission) as such Persons may reasonably request in order to
facilitate the public sale or other disposition of the Registrable Securities
covered by such Registration Statement;

                  (c) if applicable, use best efforts to register or qualify
the Registrable Securities covered by such Registration Statement under the
securities or blue sky laws of such jurisdictions as the Selling Holders shall
reasonably request, provided that the Company will not be required to qualify
generally to transact business in any jurisdiction where it is not then
required to so qualify or to take any action that would subject it to general
service of process in any such jurisdiction where it is not then so subject;

                  (d) immediately notify each Selling Holder, at any time when
a prospectus relating thereto is required to be delivered under the Securities
Act, of the happening of any event as a result of which the prospectus
contained in such Registration Statement, as then in effect, includes an untrue
statement of a material fact or omits to state any material fact required to be
stated therein or necessary to make the statements therein not misleading in
the light of the circumstances then existing and as promptly as practicable
amend or supplement the



                                       -3-

<PAGE>   4




prospectus or take other appropriate action so that the prospectus does not
include an untrue statement of a material fact or omit to state a material fact
required to be stated therein or necessary to make the statements therein not
misleading in the light of the circumstances then existing;

                  (e) make available for inspection by the Selling Holders
designated by a majority thereof, and any attorney, accountant or other agent
retained by such representative of the Selling Holders (the "Inspectors"), all
financial and other records, pertinent corporate documents and properties of
the Company (collectively, the "Records"), and cause the Company's officers,
directors and employees to supply all information reasonably requested by any
such Inspector in connection with such Registration Statement;

                  (f) cause the Registrable Securities to be listed on New York
Stock Exchange, American Stock Exchange or on the NASDAQ National Market if the
Common Stock is or becomes so listed;

                  (g) use best efforts to keep effective and maintain for the
period of distribution, qualification, approval or listing obtained to cover
the Registrable Securities as may be necessary for the Selling Holders to
dispose thereof and shall from time to time amend or supplement any prospectus
used in connection therewith to the extent necessary in order to comply with
applicable law;

                  (h) use best efforts to cause the Registrable Securities to
be registered with or approved by such other governmental agencies or
authorities as may be necessary by virtue of the business and operations of the
Company to enable the Selling Holders to consummate the disposition of such
Registrable Securities; and

                  (i) take such other actions as are reasonably requested by
the Selling Holders or the underwriters, if any, in order to expedite,
facilitate or consummate the disposition of such Registrable Securities.

         Section 2.04. Restrictions on Public Sale by Selling Holders of
Registrable Securities. To the extent not inconsistent with applicable law,
including insurance codes, each Selling Holder whose Registrable Securities are
included in a Registration Statement pursuant to this Agreement agrees not to
effect any public sale or distribution of the issue being registered (or any
securities of the Company convertible into or exchangeable or exercisable for
securities of the same type as the issue being registered) during the 14 days
before, and during the 90-day period beginning on, the effective date of such
Registration Statement (except as part of such registration), but only in the
case of an underwritten public offering by the Company of securities of the
same type as the Registrable Securities, and even then only if and to the
extent requested in writing (with reasonable prior notice) by the managing
underwriter or underwriters provided that the duration of the foregoing
restrictions shall be no longer than the duration of the shortest restriction
imposed by the underwriters on the officers or directors or any other
stockholder of the Company; and provided further, that the period of time for
which the Company is required to keep such registration statement which
includes Registrable Securities continuously effective shall be increased by a
period equal to such requested holdback period.




                                       -4-

<PAGE>   5





         Section 2.05. [Reserved]

         Section 2.06. Expenses.

                  (a) "Registration Expenses" means all expenses incident to
the Company's performance under or compliance with this Agreement, including
without limitation, all registration and filing fees, blue sky fees and
expenses, printing expenses, listing fees, fees and disbursements of counsel
and independent public accountants for the Company, fees of the National
Association of Securities Dealers, Inc., transfer taxes, fees of transfer
agents and registrars, costs of insurance and reasonable out-of-pocket expenses
(including without limitation, reasonable legal fees of one counsel for all
Selling Holders), but excluding any Selling Expenses. "Selling Expenses" means
all underwriting fees, discounts and selling commissions allocable to the sale
of the Registrable Securities.

                  (b) The Company will pay all Registration Expenses in
connection with each Registration Statement filed pursuant to this Agreement,
whether or not the Registration Statement becomes effective, and the Selling
Holders shall pay all Selling Expenses in connection with any Registrable
Securities registered pursuant to this Agreement.

         Section 2.07. Indemnification.

                  (a) In the event of a registration of any Registrable
Securities under the Securities Act pursuant to this Agreement, the Company
will indemnify and hold harmless each Selling Holder thereunder and each
Person, if any, who controls such Selling Holder within the meaning of the
Securities Act and the Exchange Act, against any losses, claims, damages or
liabilities (including reasonable attorneys' fees) ("Losses"), joint or
several, to which such Selling Holder or controlling Person may become subject
under the Securities Act, the Exchange Act or otherwise, insofar as such Losses
(or actions in respect thereof) arise out of or are based upon any untrue
statement or alleged untrue statement of any material fact contained in any
Registration Statement under which such Registrable Securities were registered
under the Securities Act pursuant to this Agreement, any preliminary prospectus
or final prospectus contained therein, or any amendment or supplement thereof,
or arise out of or are based upon the omission or alleged omission to state
therein a material fact required to be stated therein or necessary to make the
statements therein not misleading, and will reimburse each such Selling Holder
and each such controlling Person for any legal or other expenses reasonably
incurred by them in connection with investigating or defending any such Loss or
actions; provided, however, that the Company will not be liable in any such
case if and to the extent that any such loss, claim, damage or liability arises
out of or is based upon an untrue statement or alleged untrue statement or
omission or alleged omission so made in conformity with information furnished
by such Selling Holder, such underwriter or such controlling Person in writing
specifically for use in such Registration Statement or prospectus.

                  (b) Each Selling Holder agrees to indemnify and hold harmless
the Company, its directors, officers, employees and agents and each Person, if
any, who controls the Company within the meaning of the Securities Act or of
the Exchange Act to the same extent as the foregoing indemnity from the Company
to such Selling Holder, but only with respect to information regarding such
Selling Holder furnished in writing by or on behalf of such Selling Holder
expressly for inclusion in any Registration Statement or prospectus relating to
the



                                       -5-

<PAGE>   6




Registrable Securities, or any amendment or supplement thereto; provided,
however, that the liability of such Selling Holder shall not be greater in
amount than the dollar amount of the proceeds (net of any Selling Expenses)
received by such Selling Holder from the sale of the Registrable Securities
giving rise to such indemnification.

                  (c) Promptly after receipt by an indemnified party hereunder
of notice of the commencement of any action, such indemnified party shall, if a
claim in respect thereof is to be made against the indemnifying party
hereunder, notify the indemnifying party in writing thereof, but the omission
so to notify the indemnifying party shall not relieve it from any liability
which it may have to any indemnified party. In case any such action shall be
brought against any indemnified party and it shall notify the indemnifying
party of the commencement thereof, the indemnifying party shall be entitled to
participate in and, to the extent it shall wish, to assume and undertake the
defense thereof with counsel reasonably satisfactory to such indemnified party
and, after notice from the indemnifying party to such indemnified party of its
election so to assume and undertake the defense thereof, the indemnifying party
shall not be liable to such indemnified party under this Section 2.07 for any
legal expenses subsequently incurred by such indemnified party in connection
with the defense thereof other than reasonable costs of investigation and of
liaison with counsel as so elected; provided, however, that, (i) if the
indemnifying party has failed to assume the defense and employ counsel or (ii)
if the defendants in any such action include both the indemnified party and the
indemnifying party and counsel to the indemnified party shall have concluded
that there may be reasonable defenses available to the indemnified party that
are different from or additional to those available to the indemnifying party
or that the interests of the indemnified party reasonably may be deemed to
conflict with the interests of the indemnifying party, then the indemnified
party shall have the right to select a separate counsel and to assume such
legal defense and otherwise to participate in the defense of such action, with
the expenses and fees of such separate counsel and other expenses related to
such participation to be reimbursed by the indemnifying party is incurred.

                  (d) If the indemnification provided for in this Section 2.07
is unavailable to the Company or the Selling Holders or is insufficient to hold
them harmless in respect of any Losses, then each such indemnifying party, in
lieu of indemnifying such indemnified party, shall contribute to the amount
paid or payable by such indemnified party as a result of such Losses as between
the Company on the one hand and each Selling Holder on the other, in such
proportion as is appropriate to reflect the relative fault of the Company on
the one hand and of each Selling Holder on the other in connection with the
statements or omissions which resulted in such Losses, as well as any other
relevant equitable considerations. The relative fault of the Company on the one
hand and each Selling Holder on the other shall be determined by reference to,
among other things, whether the untrue or alleged untrue statements of a
material fact or the omission or alleged omission to state a material fact has
been made by, or relates to, information supplied by such party, and the
parties' relative intent, knowledge, access to information and opportunity to
correct or prevent such statement or omission.

                  No person guilty of fraudulent misrepresentation (within the
meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any Person who is not guilty of such fraudulent
misrepresentation.





                                       -6-

<PAGE>   7




                                   ARTICLE III

         Section 3.01. Communications. All notices and other communications
provided for or permitted hereunder shall be made in writing by telecopy,
courier service or personal delivery;

                  (a) if to a Holder, at the most current address given by such
holder to the Company in accordance with the provisions of this Section 3.01,

                  (b) if to the Company, initially at its address set forth in
its Form 10-K filed with the Commission, and

                  (c) for each, thereafter at such other address, notice of
which is given in accordance with the provisions of this Section 3.01.

                  All such notices and communications shall be deemed to have
been received at the time delivered by hand, if personally delivered; when
receipt acknowledged, if telecopied; and on the next business day if timely
delivered to an air courier guaranteeing overnight delivery.

         Section 3.02. Successor and Assigns. This Agreement shall inure to the
benefit of and be binding upon the successors and assigns of each of the
parties, including subsequent holders of Registrable Securities.

         Section 3.03. Counterparts. This Agreement may be executed in any
number of counterparts and by different parties hereto in separate
counterparts, each of which counterparts, when so executed and delivered, shall
be deemed to be an original and all of which counterparts, taken together,
shall constitute but one and the same Agreement.

         Section 3.04. Headings. The headings in this Agreement are for
convenience of reference only and shall not limit or otherwise affect the
meaning hereof.

         Section 3.05. Governing Law. THE LAWS OF THE STATE OF TEXAS SHALL
GOVERN THIS AGREEMENT WITHOUT REGARD TO PRINCIPLES OF CONFLICT OF LAWS.

         Section 3.06. Severability of Provisions. Any provision of this
Agreement which is prohibited or unenforceable in any jurisdiction shall, as to
such jurisdiction, be ineffective to the extent of such prohibition or
unenforceability without invalidating the remaining provisions hereof or
affecting or impairing the validity or enforceability of such provision in any
other jurisdiction.

         Section 3.07. Entire Agreement. This Agreement, together with the
Exchange Agreement and the other documents provided for therein are intended by
the parties as a final expression of their agreement and intended to be a
complete and exclusive statement of the agreement and understanding of the
parties hereto in respect of the subject matter contained herein. There are no
restrictions, promises, warranties or undertakings, other than those set forth
or referred to herein with respect to the registration rights granted by the
Company with respect to the securities sold pursuant to the Exchange Agreement.
This Agreement, the Exchange



                                       -7-

<PAGE>   8




Agreement and the other documents provided for therein supersede all prior
agreements and understandings between the parties with respect to such subject
matter except as specified in the Exchange Agreement.

         Section 3.08. Attorneys' Fees. In any action or proceeding brought to
enforce any provision of this Agreement, the successful party shall be entitled
to recover reasonable attorneys' fees in addition to its costs and expenses and
any other available remedy.

         Section 3.09. Amendment. This Agreement may be amended only by means of
a written amendment signed by the Company and by the Holders of a majority of
the Registrable Securities.

         Section 3.10. Registrable Securities Held by the Company or Its
Affiliates. In determining whether the Holders of the required amount of
Registrable Securities have concurred in any direction, amendment, supplement,
waiver or consent, Registrable Securities owned by the Company or one of its
Affiliates shall be disregarded.

         Section 3.11. Assignment of Rights. The rights of any Holder under
this Agreement may be assigned to any Person who acquires any Registrable
Securities. Any assignment of registration rights pursuant to this Section 3.11
shall be effective only upon receipt by the Company of written notice from such
assigning Holder stating the name and address of any assignee. The rights of an
assignee under this Section 3.11 shall be the same rights granted to the
assigning Holder under this Agreement. In connection with any such assignment,
the term "Holder" as used herein shall, where appropriate to assign the rights
and obligations of the assigning Holder hereunder to such assignee, be deemed
to refer to the assignee.

         Section 3.12 Liquidated Damages. The parties hereto agree that upon
the failure of the Company to register shares of Registrable Securities held by
Veritas in the amounts and at the times required hereunder, and to meet its
obligations under Section 2.03(a) hereunder, Veritas shall be entitled to
liquidated damages from the Company in an amount equal to $0.25 per share of
Registrable Securities then held by Veritas. The parties agree that the
liquidated damages set forth herein are reasonable and not a penalty because of
the difficulty of ascertaining the actual damages that would be sustained by
Veritas in the event of such a material breach of this Agreement by the
Company. In the event of such a breach Veritas either may elect the liquidated
damages provided hereunder or, in the alternative, pursue its remedies at law.




                                       -8-

<PAGE>   9



         IN WITNESS WHEREOF, the parties have executed this Agreement as of the
date first written above.

                                  BRIGHAM EXPLORATION COMPANY


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

                                  VERITAS DGC LAND, INC.


                                  By:   /s/ Deanna Goodwin
                                        ----------------------------------------
                                        Name: Deanna Goodwin
                                             -----------------------------------
                                        Title: Vice President Finance
                                              ----------------------------------





                                      -9-

<PAGE>   1


                                                                    Exhibit 23.1


                       CONSENT OF INDEPENDENT ACCOUNTANTS


We hereby consent to the incorporation by reference in the Registration
Statements on Form S-8 (No. 333-56961 and No. 333-70137) of Brigham Exploration
Company of our report dated March 30, 1999 which appears on page F1-2 of this
Form 10-KA of Brigham Exploration Company. We also consent to the incorporation
by reference of our report on the financial statements of Brigham Oil & Gas LP;
Brigham Holdings I, LLC; Brigham Holdings II, LLC and Brigham Inc. which appears
on page F2-1 of this Form 10-KA.

/s/ PricewaterhouseCoopers LLP

PricewaterhouseCoopers LLP

Houston, Texas
April 14, 1999


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