FIRST AMENDMENT
                   TO AMENDED AND RESTATED GUARANTY AGREEMENT

     THIS FIRST AMENDMENT TO AMENDED AND RESTATED GUARANTY AGREEMENT (this
"AMENDMENT") dated as of October 31, 2000, 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
Amended and Restated Credit Agreement dated as of February 17, 2000, as amended
by First Amendment to Amended and Restated 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 Amended and Restated Guaranty Agreement dated
February 17, 2000, by Guarantor (the "GUARANTY AGREEMENT").

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

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

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

     SECTION 2. AMENDMENTS TO GUARANTY AGREEMENT.

     (a) Section 5.2(r) of the Guaranty Agreement 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 ratio set forth below for such period. INTEREST COVERAGE
     RATIO shall mean the ratio of (i) EBITDA to (ii) the sum of all required
     payments of interest (whether paid in cash or in kind) during such period
     on borrowed money:




        (i)    not less than .75 to 1.0 for the twelve (12) month period ending
               September 30, 2000;

        (ii)   not less than .80 to 1.0 for the twelve (12) month period ending
               December 31, 2000;

        (iii)  not less than .90 to 1.0 for the twelve (12) month period ending
               March 31, 2001;

        (iv)   not less than 1.3 to 1.0 for the twelve (12) month period ending
               June 30, 2001;

        (v)    not less than 1.5 to 1.0 for the twelve (12) month period ending
               September 30, 2001;

        (vi)   not less than 1.7 to 1.0 for the twelve (12) month period ending
               December 31, 2001;

        (vii)  not less than 2.0 to 1.0 for the twelve (12) month period ending
               March 31, 2002;

        (viii) not less than 2.25 to 1.0 for the twelve (12) month period
               ending June 30, 2002; and

        (ix)   thereafter, not less than 2.50 to 1.0 for the twelve (12) month
               period ending September 30, 2002, and each twelve (12) month
               period ending at the end of each fiscal quarter of Guarantor.

     (b) The phrase "; provided that Guarantor may pay dividends on its
preferred equity securities so long as they are paid in kind and not in cash"
shall be added to the end of subsection 5.2(d).

     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.


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     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.

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 ss.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
AGREEMENTS 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


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