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                                                                 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.



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                  (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



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         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.



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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/ 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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