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                                                                EXHIBIT 10.37.2



                     SECOND AMENDMENT TO GUARANTY AGREEMENT

         THIS SECOND AMENDMENT TO GUARANTY AGREEMENT (this "Amendment") dated
as of August 20,1998 is between BRIGHAM EXPLORATION COMPANY, a Delaware
corporation (the "Guarantor") and BANK OF MONTREAL, as agent ("Agent") for the
lenders (the "Lenders") that are or become parties to the Credit Agreement
defined below.

                                    RECITALS

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

         B. Pursuant to the terns and conditions stated in the Credit
Agreement, Guarantor executed that certain Guaranty Agreement of even date
therewith by Guarantor, as amended by First Amendment to Guaranty Agreement
dated as of March 30, 1998 (such Guaranty Agreement as amended called the
"Guaranty Agreement").

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

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

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

         Section 2.    Amendments to Guaranty Agreement.

                (a) Additional Defined Terms. Section 1.02 of the Guaranty
          Agreement is hereby amended and supplemented by adding the following
          new definitions, which are read in their entirety as follows:

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          "Indenture" shall mean that certain Indenture dated as of August 20,
     1998, between the Guarantor, as issuer of the Subordinated Debt, and Chase
     Bank of Texas, National Association, as trustee.

          "Securities Purchase Agreement" shall mean that certain Securities
     Purchase Agreement dated as of August 20, 1998 among the Guarantor, Enron
     Capital & Trade Resources Corp., and Joint Energy Development Investments
     II Limited Partnership regarding $50,000,000 Senior Subordinated Secured
     Notes due 2003.

          "Subordination Agreement" shall mean that certain Intercreditor and
     Subordination Agreement dated August 20, 1998, as from time to time
     amended, among Enron Capital and Trade Resources Corp., Joint Energy
     Development Investments II Limited Partnership, and Bank of Montreal.

          "Subordinated Debt" shall mean the Debt in the principal amount not
     to exceed $40,000,000 (plus up to an additional $10,000,000 for interest
     paid in kind pursuant to Section 9.02 of the Indenture) of Guarantor
     incurred under the Indenture and expressly subordinated to the
     Indebtedness pursuant to the Subordination Agreement.

          "Subordinated Guarantees" shall mean the Guarantees permitted under
     Section 5.2(a)(7).

     (b) Section 3.1(m) is hereby amended by adding the following phrase at the
end thereof. ", except for liens and security interests securing the
Liabilities or as permitted under Section 5.2(b)(4)."

     (c) Section 5.2. Section 5.2 is hereby amended as follows:

         (i) Section 5.2(a) is amended by adding the following new clauses (6)
     and (7):

         "(6) the Subordinated Debt."

         "(7) Guarantees by Subsidiaries of the Guarantor (which also are
     obligated upon or otherwise guarantee the Liabilities pursuant to
     documents in form and substance satisfactory to the Agent) which guarantee
     the Subordinated Debt permitted under Section 5.2(a)(6) above, which
     Guarantees are subordinated consistent with the Subordination Agreement
     and otherwise are in form and substance satisfactory to the Agent
     consistent with the Subordination Agreement."

     (ii) Section 5.2(b) is amended by adding the following new clause (4):

          "(4) Liens securing the Subordinated Debt or the Subordinated
     Guarantees on Properties upon which prior Liens have been granted to
     secure the Liabilities pursuant to documents in form and substance
     satisfactory to the Agent, provided that such Liens (i) are subordinated
     and otherwise are in form and substance satisfactory to the Agent
     consistent with


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     the Subordination Agreement and (ii) do not directly or indirectly secure
     any Hedging Agreements."

          (iii) Section 5.2(o) is hereby amended by deleting the parenthetical
     clause in the third line and inserting the following in lieu thereof:

          "(other than the Loan Documents, the Indenture and the documents
          described in Section 4.01(a) through (d) of the Indenture, and any
          other documents establishing Liens permitted under Section
          5.2(b)(4))"

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

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

               (i)   not less than 1.25 to 1 for the three (3) month period
                     ending December 31, 1998;

               (ii)  not less than 1.75 to I for the six (6) month period ending
                     March 31, 1999;

               (iii) not less than 2 to 1 for the nine (9) month period ending
                     June 30, 1999;

               (iv)  not less than 2.25 to 1 for the twelve (12) month period
                     ending September 30, 1999;

               (v)   not less than 2.75 to I for the twelve (12) month period
                     ending December 31, 1999; and


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

           (v) Section 5.2 is amended by adding the following new clauses (t)
     and (u):

                    "(t) Securities Purchase Agreement and Indenture. The
               Guarantor will not agree to any amendment or modification to the
               Securities Purchase Agreement or the Indenture without the
               express written consent of the Agent."

                    "(u) Payments on Subordinated Debt. No prepayments of
               principal will be made on the Subordinated Debt without prior
               written consent of the Lenders. No payments of interest will be
               made in cash on the Subordinated Debt if (i) an Event of Default
               or, with respect to Section 5.2(q), (r) or (s), Default, is in
               existence or would be created thereby; (ii) a Borrowing Base
               deficiency is in existence under the Credit Agreement; (iii)
               such payment will be in contravention of the Subordination
               Agreement or (iv) the Interest Coverage Ratio is less than the
               following ratios during the following periods:

                    (i)   1.5 to 1 for the twelve (12) month period ending
                          December 31, 1998;

                    (ii)  1.75 to 1 for the twelve (12) month periods ending
                          March 31, 1999 and June 30, 1999;

                    (iii) 2.5 to 1 for the twelve (12) month period ending
                          September 30, 1999;

                    (iv)  2.75 to 1 for the twelve month period ending December
                          30, 1999; and

                    (v)   thereafter, 3 to 1 for the twelve (12) month periods
                          ending at the end of each fiscal quarter of the
                          Guarantor."

         Section 4. Representations and Warranties. Guarantor hereby reaffirms
that as of the effective date of this Amendment, the representations and
warranties made by the Guarantor in Article III of the Guaranty Agreement will
be true and correct as though made on and as of the effective date of this
Amendment.

         Section 5. Ratification. Guarantor hereby expressly ratifies and
affirms its obligations under the Guaranty Agreement as amended by this
Amendment and agrees that the Guaranty Agreement as amended by this Amendment
remains in full force and effect.


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         Section 6. Governing Law. This Amendment and the rights and
obligations of the parties hereunder and under the Credit Agreement shall be
construed in accordance with and be governed by the laws of the State of Texas
and the United States of America.

         Section 7. Descriptive Headings. etc. The descriptive headings of the
several Sections of this Amendment are inserted for convenience only and shall
not be deemed to affect the meaning or construction of any of the provisions
hereof.

         Section 8. Counterparts. This Amendment may be executed in any number
of counterparts and by different parties on separate counterparts and all of
such counterparts shall together constitute one and the same instrument.


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


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

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


GUARANTOR:                       BRIGHAM EXPLORATION COMPANY



                                 By:            /s/ Craig M. Fleming
                                     -------------------------------------------
                                 Name:  Craig M. Fleming
                                 Title: Vice President & Chief Financial Officer


AGENT AND LENDER:                BANK OF MONTREAL



                                 By:           /s/ Robert Roberts
                                     -------------------------------------------
                                 Name:  Robert L. Roberts
                                 Title: Director, U.S. Corporate Banking



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