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                                                                   EXHIBIT 10.36




                                                                           DRAFT
                                                                 August 13, 1998

                     SECOND AMENDMENT TO GUARANTY AGREEMENT


         THIS SECOND AMENDMENT TO GUARANTY AGREEMENT (this "Amendment") dated as
of August ___, 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 terms 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 __, 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 __,
                  1998 among the Guarantor and the purchasers named therein
                  regarding $50,000,000 Senior Subordinated Secured Notes due
                  2003.

                           "Subordination Agreement" shall mean that certain
                  Intercreditor and Subordination Agreement dated August __,
                  1998, as from time to time amended, among _______________, 
                  ________________________, 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 Brigham Exploration incurred
                  under the Indenture and expressly subordinated to the
                  Indebtedness pursuant to agreements in form and substance
                  satisfactory to the Lenders consistent with 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, the Subordinated Guarantees or the
         Subordinated Debt which liens and security interests securing the
         Subordinated Guarantees or the Subordinated Debt shall be subordinated
         on terms satisfactory to the Agent consistent with the Subordination
         Agreement."

                  (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


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                           Subordination Agreement and otherwise are in form and
                           substance satisfactory to the Agent.

                           (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 are subordinated on terms satisfactory to
                           the Agent consistent with the Subordination
                           Agreement."

                           (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 during the following periods (for
                           purposes hereof only cash interest accrued during the
                           last fiscal quarter shall be included, but all
                           interest (whether or not paid in cash) accrued for
                           all other fiscal quarters included within the test
                           period shall be included):

                                    (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 1 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;



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

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

                                    (vi)     not less than 2.75 to 1 for the
                                             twelve (12) month period ending
                                             December 31, 1999; and

                           (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



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                                            (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.

         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.

         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:
                                        --------------------------------------
                                     Name:
                                     Title:

AGENT AND LENDER:                    BANK OF MONTREAL


                                     By:
                                        --------------------------------------
                                     Name:
                                     Title:



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