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                                                                 EXHIBIT 10.33.2




                     FIRST AMENDMENT TO GUARANTY AGREEMENT


                 THIS FIRST AMENDMENT TO GUARANTY AGREEMENT (this "Amendment")
dated as of March 30, 1998 is between BRIGHAM EXPLORATION COMPANY, a Delaware
corporation (the "Guarantor") and BANK OF MONTREAL, as agent ("Agent") for the
lenders (the "Lenders") that are or become parties to the Credit Agreement
defined below.

                                    RECITALS

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

         B.      One of the terms and conditions stated in the Credit Agreement
for the making of the loans was the execution and delivery of that certain
Guaranty Agreement of even date therewith 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.  Section 5.2(s) is
hereby amended in its entirety to read as follows:

                 "(s)     Interest Coverage Ratio.  The Guarantor will not
         permit its Interest Coverage Ratio as of the end of the fiscal
         quarters of the Guarantor stated below (calculated quarterly at the
         end of each fiscal quarter) to be less than the ratios stated below.
         Interest Coverage Ratio shall mean the following ratios of (i) EBITDA
         to (ii) cash interest payments made during the following periods:

                 (i)      not less than 1.75 to 1 for the three (3) month
                          period ending June 30, 1998;

                 (ii)     not less than 3 to 1 for the three (3) month period
                          ending September 30, 1998;
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                 (iii)    not less than 3 to 1 for the three (3) month period
                          ending December 31, 1998; and

                 (iv)     thereafter, not less than 3 to 1 for the twelve (12)
                          month periods ending at the end of each fiscal
                          quarter of the Guarantor."

         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.

         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.


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         GUARANTOR:                                BRIGHAM EXPLORATION COMPANY



                                                   By: /s/ CRAIG M. FLEMING
                                                       -------------------------
                                                   Name:  Craig M. Fleming
                                                   Title: CEO

AGENT AND LENDER:                          BANK OF MONTREAL



                                                   By: /s/ J.B. WHITMORE 
                                                       -------------------------
                                                   Name:  J.B. Whitmore
                                                   Title: Director





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