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                                                                    EXHIBIT 10.1

                                    AGREEMENT


         This AGREEMENT (this "Amendment") is executed as of the 16th day of
August, 1999, between Brigham Exploration Company (the "Company"), a Delaware
corporation, and Jon L. Glass ("Employee").

                                   WITNESSETH:

         WHEREAS, the Company and Employee entered into that certain Employee
Stock Ownership Agreement dated as of February 27, 1997 (the "Stock Agreement");

         WHEREAS, the Company and Employee entered into those two certain Option
Agreements, each dated as of March 4, 1999, as amended (collectively, the
"Option Agreements"); and

         WHEREAS, the parties hereto desire to enter into this Amendment in
order to amend the Stock Agreement, to amend each Option Agreement and to enter
into certain other agreements;

         WHEREAS, the amendment to each Option Agreement effected hereby extends
the period during which Employee may exercise certain stock options after
certain terminations of Employee's employment with the Company, and Employee is
therefore willing to extend the term of the noncompetition provisions provided
in the Stock Agreement for the benefit of the Company, its successors and
assigns and to agree to the other provisions in this Amendment;

         WHEREAS, the protections afforded by the Stock Agreement, as amended by
this Amendment, are necessary in order for the Company to protect the goodwill
and other business interests of the Company; and

         WHEREAS, Employee acknowledges and agrees that the Stock Agreement, as
amended hereby, places on him limitations as to the business or investment
activities he may pursue as well as the time during which and the geographic
area over which such limitations will remain in effect, which limitations are
deemed by him to be reasonable, ancillary to an otherwise enforceable agreement
and no greater than are necessary under the circumstances to protect the
goodwill and other business interests of the Company;

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements contained herein and in each Option Agreement and the
Stock Agreement and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Company and Employee hereby
agree as follows:

         1. Amendment to each Option Agreement. Subject to Section 3 of this
Amendment, Section 4(d) of each Option Agreement is amended in its entirety to
read as follows:

                  (d) If Optionee's employment by the Companies terminates
         voluntarily by Optionee or by action of the Companies for reasons other
         than as specified in subsection (c), this Option may be exercised, but
         only (i) within 360 days after such termination (if otherwise prior to
         the date of expiration of this Option), and


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         not thereafter, and (ii) to purchase the number of Shares, if any, that
         could be purchased upon exercise of this Option at the date of
         termination of Optionee's employment.

         2. Amendment to the Stock Agreement. The first sentence of Section 3 of
the Stock Agreement is amended by replacing the phrase "for a period of one year
thereafter" with "for a period of three years thereafter". In addition, and
without limiting the foregoing, Employee hereby agrees that the Company's
Angelton Project (as described on Exhibit A hereto) shall constitute a protected
Company "area of mutual interest" for purposes of Section 3 of the Stock
Agreement. However, in the event that the Company is acquired by or merges with
another company (the "Acquiring Company") and as a result of such merger or
acquisition (i) the Acquiring Company acquires more than 50% of the outstanding
common stock of the Company and (ii) Ben M. Brigham does not hold the position
of either President, CEO or Vice President in the surviving company, then in
such event the amendment provided for in this Section 2 shall be of no further
force and effect.

         3. Contingency of Amendment to each Option Agreement. In the event that
either (a) Employee voluntarily terminate his employment with the Company
effective prior to September 30, 1999 or (b) prior to the expiration of the
period provided in Section 4(d) of each Option Agreement (as amended hereby),
Employee breaches the provisions of Section 3 of the Stock Agreement, then at
the discretion of the Company the provisions of Section 1 of this Amendment
shall immediately be of no further force and effect.

         4. Forfeiture of Certain Options . Employee hereby forfeits all options
to purchase shares of common stock of the Company which have previously been
granted to Employee, to the extent that the rights to exercise such options have
not vested as of the date hereof.

         5. Ratification of Agreement. The Stock Agreement and each Option
Agreement, each as amended by this Amendment, are hereby ratified and confirmed
in all respects. Except as expressly set forth herein, the terms, provisions and
conditions of the Stock Agreement and each Option Agreement shall remain in full
force and effect.

         6. Counterparts. This Amendment may be signed in counterparts, each of
which shall be deemed an original and all of which shall constitute one and the
same agreement.

         7. Effect of Agreement. This Amendment shall not enlarge or otherwise
affect the terms of Employee's employment with the Company, if any, and the
Company or an affiliate employing Employee may terminate his employment as
freely and with the same effect as if this Amendment had not been established.

         IN WITNESS WHEREOF, the parties hereto have executed this Amendment as
of the date first set forth above, to be effective as of August 16, 1999.

                                    BRIGHAM EXPLORATION COMPANY


   /s/ Jon L. Glass                 By: /s/ Ben M. Brigham
-------------------------------        ------------------------------
Jon L. Glass                        Name:   Ben M. Brigham
                                    Title:  President and Chief
                                            Executive Officer