<PAGE>

                                                                   Exhibit 10.76

                           BRIGHAM EXPLORATION COMPANY
                          Stockholders Voting Agreement

      This STOCKHOLDERS VOTING AGREEMENT, dated March 1, 2001 (this
"Agreement"), is made and entered into by and among Brigham Exploration Company,
a Delaware corporation (the "Company"), "ES", "MB", "MBP" and "DOP", as ES, MB,
MBP and DOP (collectively, the "Investors") are each defined on Page 7(a)
hereof, and the following shareholders of the Company (the "Shareholders"): Ben
M. and Anne L. Brigham, individual residents of Travis County, Texas, Harold D.
Carter, a resident of Dallas County, Texas, General Atlantic Partners III, L.P.,
a Delaware limited partnership, GAP-Brigham Partners, L.P., a Delaware limited
partnership, GAP Coinvestment Partners II, L.P., a Delaware limited partnership,
Aspect Resources, LLC, a Colorado limited liability company, and the individual
officers of the Company listed on Schedule I hereto.

                              W I T N E S S E T H:

      WHEREAS, the Company and the Investors propose to enter into a Securities
Purchase Agreement concurrently with the execution hereof (the "Purchase
Agreement"), pursuant to which the Company will issue and sell to the Investors
an aggregate of up to 500,000 shares of its Series A Preferred Stock and
warrants (the "Warrants") to acquire 2,105,263 shares (the "Warrant Shares") of
its common stock (the "Common Stock");

      WHEREAS, the Company, ES and MB previously entered into a Securities
Purchase Agreement dated November 1, 2000 (the "Previous Purchase Agreement"),
pursuant to which the Company issued and sold to ES and MB an aggregate of
1,000,000 shares of its Series A Preferred Stock and warrants (the "Previous
Warrants") to acquire 6,666,667 shares (the "Previous Warrant Shares") of Common
Stock;

      WHEREAS, the issuance of the Previous Warrants has been approved by the
stockholders of the Company;

      WHEREAS, the Warrant Shares and the Previous Warrant Shares represent
greater than 30% of the outstanding Common Stock before issuance;

      WHEREAS, representatives of the Nasdaq Stock Market have informed the
Company that they believe that the issuance of the Warrants, if the
exercisability of the Warrants were not conditioned on stockholder approval of
the issuance of the Warrants and the terms thereof, would constitute a change of
control under the rules of the Nasdaq Stock Market, which would violate the
rules of the Nasdaq Stock Market if made without stockholder approval;
<PAGE>

      WHEREAS, the Company and the Investors have agreed pursuant to the terms
of the Warrants and the Purchase Agreement that the Warrants shall not be
exercisable until the stockholders of the Company approve the issuance of the
Warrants and the terms thereof, and the Company has agreed to seek such approval
at its annual stockholders' meeting to be held on or before May 31, 2001; and

      WHEREAS, as a condition to the agreement of the Investors to enter into
the Purchase Agreement, the Company and the Shareholders have agreed to enter
into this Agreement to provide for certain agreements relating to approval of
the issuance of the Warrants and the terms thereof;

      NOW, THEREFORE, in consideration of the foregoing and the mutual
agreements set forth herein, the parties to this Agreement hereby agree as
follows:

      1. Agreement to Vote Shares. Each Shareholder agrees that, at any special
or annual meeting of shareholders of the Company, such Shareholder shall vote
all shares of Common Stock registered in its, his or her name or beneficially
owned by it, him or her as of the date hereof and any and all other capital
stock of the Company legally or beneficially acquired by such Shareholder after
the date hereof to approve the Warrants and the issuance of the Warrants to the
Investors. In the event that the Purchase Agreement is terminated for any
reason, then this Agreement shall automatically terminate and none of the
parties hereto shall have any liability hereunder. Each Shareholder represents
to the Investors that as of the date hereof such Shareholder owns the number of
outstanding shares of Common Stock set forth opposite such Shareholder's name on
attached Schedule I.

      2. Successors, Assigns and Transferees. The terms and provisions of this
Agreement shall not bind, inure to the benefit of or be enforceable by or
against the successors, assigns or transferees of each of the parties hereto. No
party hereto may assign its rights under this Agreement.

      3. Entire Agreement; Amendments. This Agreement, and such additional
instruments as may be concurrently executed and delivered pursuant to this
Agreement, constitutes the entire understanding of the parties with respect to
its subject matter. There are no restrictions, agreements, promises,
representations, warranties, covenants or undertakings other than those
expressly set forth herein or in the documents delivered concurrently herewith.
This Agreement may be amended only by a written instrument duly executed by all
the parties hereto.

      4. Headings. The section headings contained in this Agreement are for
reference purposes only and shall not effect in any way the meaning or
interpretation of this Agreement.

      5. Notices. All notices, requests, claims, demands and other
communications hereunder shall be in writing and shall be given (and shall be
deemed to have been duly given if so given) by hand delivery, facsimile or by
mail (registered or certified, postage prepaid, return receipt requested) to the
respective parties as follows:


                                       2
<PAGE>

            If to Brigham:

                  Brigham Exploration Company
                  6300 Bridge Point Parkway
                  Building Two, Suite 500
                  Austin, Texas 78730
                  Attention: Ben M. "Bud" Brigham
                  Fax No: (512) 427-3400

            If to ESC, MB or MBP:

                  Donaldson Lufkin & Jenrette
                  277 Park Avenue
                  New York, New York 10172
                  Attention: Nicole Arnaboldi, Ivy Dodes
                  Fax No: 212-892-2689
                  and
                  Mr. Steve Webster
                  1000 Louisiana, Suite 4900
                  Houston, Texas  77002
                  Fax No: (713) 652-6050

                        with a copy to:

                              Gardere Wynne Sewell, LLP
                              1000 Louisiana, Suite 3400
                              Houston, Texas 77002
                              Attention: N.L. Stevens III
                              Telefax: 713-276-5807

            If to DOP:

                  DLJ Offshore Management N.V.
                  John B. Gorsiraweg 14
                  Willemstad, Curacao
                  Netherlands, Antilles
                  Fax No: 011-599-961-4129
                  and
                  Mr. Steve Webster
                  1000 Louisiana, Suite 4900
                  Houston, Texas 77002
                  Fax No: (713) 652-6050

                        with a copy to:

                              Gardere Wynne Sewell, LLP
                              1000 Louisiana, Suite 3400
                              Houston, Texas 77002
                              Attention: N.L. Stevens III
                              Telefax: 713-276-5807


                                       3
<PAGE>

            If to Ben M. Brigham:

                  Ben M. Brigham
                  Brigham Exploration Company
                  6300 Bridge Point Parkway
                  Building Two, Suite 500
                  Austin, Texas 78730
                  Fax No: (512) 427-3400

            If to Anne L. Brigham:

                  Anne L. Brigham
                  Brigham Exploration Company
                  6300 Bridge Point Parkway
                  Building Two, Suite 500
                  Austin, Texas 78730
                  Fax No: (512) 427-3400

            If to Harold D. Carter:

                  Harold D. Carter
                  5949 Sherry Lane, Suite 620
                  Dallas, Texas 75225
                  Fax No.: (214) 692-7820

            If to General Atlantic Partners III, L.P.:

                  General Atlantic Partners III, L.P.
                  c/o General Atlantic Service Corporation
                  3 Pickwick Plaza
                  Greenwich, CT 06830
                  Attention: Mr. Thomas J. Murphy
                  Fax No: (203) 622-8818

            If to GAP-Brigham Partners, L.P.:

                  GAP-Brigham Partners, L.P.
                  c/o General Atlantic Service Corporation
                  3 Pickwick Plaza
                  Greenwich, CT 06830
                  Attention:  Mr. Thomas J. Murphy
                  Fax No: (203) 622-8818

            If to GAP Coinvestment Partners II, L.P.:

                  GAP Coinvestment Partners II, L.P.
                  c/o General Atlantic Service Corporation
                  3 Pickwick Plaza
                  Greenwich, CT 06830
                  Attention: Mr. Thomas J. Murphy
                  Fax No: (203) 622-8818


                                       4
<PAGE>

            If to Aspect Resources, LLC:

                  Aspect Resources, LLC
                  511 16th Street, Suite 300
                  Denver, CO  80202
                  Attention:  Mr. Alex Cranberg
                  Fax No:  (303) 573-7340

            If to any of the officers of Brigham:

                  Brigham Exploration Company
                  6300 Bridge Point Parkway
                  Building Two, Suite 500
                  Austin, Texas 78730
                  Attention: [name of officer]
                  Fax No:  (512) 427-3400

or to such other address as the person to whom notice is given may have
previously furnished to the others in writing in the manner set forth above.

      6. Governing Law. This Agreement shall be governed by and construed and
enforced in accordance with the laws of the State of Delaware, without reference
to the conflict of laws principles thereof.

      7. Waiver. Any waiver by any party of a breach of any provision of this
Agreement shall not operate as or be construed to be a waiver of any other
breach of such provision or of any breach of any other provision of this
Agreement. The failure of a party to insist upon strict adherence to any term of
this Agreement on one or more occasions shall not be considered a waiver or
deprive that party of the right thereafter to insist upon strict adherence to
that term or any other term of this Agreement.

      8. Challenges to Agreement. In the event that any part of this Agreement
or any transaction contemplated hereby is temporarily, preliminarily or
permanently enjoined or restrained by court of competent jurisdiction, the
parties hereto shall use their reasonable best efforts to cause any such
injunction or restraining order to be vacated or dissolved or otherwise declared
or determined to be of no further force or effect.

      9. Specific Performance. Each of the Shareholders acknowledges and agrees
that irreparable harm would occur if any provision of this Agreement were not
performed in accordance with the terms thereof, or were otherwise breached, and
that such harm could not be remedied by an award of damages. Accordingly, each
of the Shareholders agrees that any non-breaching party shall be entitled to an
injunction to prevent breaches of this Agreement and to enforce specifically the
terms and provisions hereof.

      10. Counterparts. This Agreement may be executed in counterparts, each of
which shall be an original, but each of which together shall constitute one and
the same Agreement;


                                       5
<PAGE>

provided that signature pages from separate counterparts may be combined to form
one or more fully executed original counterpart(s).

                                    * * * * *


                                       6
<PAGE>

      IN WITNESS WHEREOF, and intending to be legally bound hereby, each of the
undersigned parties has executed or caused this Agreement to be executed on the
date first above written.

                                        BRIGHAM EXPLORATION COMPANY

                                        By: /s/ Karen E. Lynch
                                           -------------------------------------
                                           Name:  Karen E. Lynch
                                                --------------------------------
                                           Title: Vice President
                                                 -------------------------------

                                           /s/ Ben M. Brigham
                                           -------------------------------------
                                           Ben M. Brigham

                                           /s/ Anne L. Brigham
                                           -------------------------------------
                                           Anne L. Brigham

                                           /s/ Harold D. Carter
                                           -------------------------------------
                                           Harold D. Carter


                                       7
<PAGE>

                                        DLJ ESC II, L.P.
                                        a Delaware Limited Partnership ("ESC")

                                        By: DLJ LBO Plans Management Corporation
                                            General Partner

                                        By: /s/ Steven A. Webster
                                           -------------------------------------
                                        Name: Steven A. Webster
                                             -----------------------------------
                                        Title: Attorney-in-Fact
                                              ----------------------------------

                                        DLJMB FUNDING III, INC.
                                        a Delaware Corporation ("MB")

                                        By: /s/ Steven A. Webster
                                           -------------------------------------
                                        Name: Steven A. Webster
                                             -----------------------------------
                                        Title: Attorney-in-Fact
                                              ----------------------------------


                                        DLJ Merchant Banking Partners III, L.P.
                                        a Delaware Limited Partnership ("MBP")

                                        By: DLJ Merchant Banking III, Inc.
                                            Managing General Partner

                                        By: /s/ Steven A. Webster
                                           -------------------------------------
                                        Name: Steven A. Webster
                                             -----------------------------------
                                        Title: Attorney-in-Fact
                                              ----------------------------------


                                        DLJ Offshore Partners III, C.V.
                                        a Netherlands Antilles Limited
                                        Partnership ("DOP")

                                        By: DLJ Merchant Banking III, Inc.
                                            Managing General Partner

                                        By: /s/ Steven A. Webster
                                           -------------------------------------
                                        Name: Steven A. Webster
                                             -----------------------------------
                                        Title: Attorney-in-Fact
                                              ----------------------------------


                                       7(a)
<PAGE>

                                        GENERAL ATLANTIC PARTNERS III, L.P.
                                        By GAP III Investors, Inc.
                                        Its General Partner

                                        By: /s/ Stephen P. Reynolds
                                           -------------------------------------
                                        Name: Stephen P. Reynolds
                                             -----------------------------------
                                        Title: President
                                              ----------------------------------


                                        GAP-BRIGHAM PARTNERS, L.P.

                                        By: /s/ Stephen P. Reynolds
                                           -------------------------------------
                                        Name: Stephen P. Reynolds
                                             -----------------------------------
                                        Title: General Partner
                                              ----------------------------------


                                        GAP COINVESTMENT PARTNERS II, L.P.

                                        By: /s/ Thomas J. Murphy
                                           -------------------------------------
                                        Name: Thomas J. Murphy
                                             -----------------------------------
                                        Title: Attorney-in-Fact
                                              ----------------------------------


                                        ASPECT RESOURCES, LLC
                                        By Aspect Management Corporation
                                        Its Manager

                                        By: /s/ Alex M. Cranberg
                                           -------------------------------------
                                        Name: Alex M. Cranberg
                                             -----------------------------------
                                        Title: President
                                              ----------------------------------

                                        /s/ Curtis F. Harrell
                                        ----------------------------------------
                                        Curtis F. Harrell


                                       8
<PAGE>

                                        /s/ David T. Brigham
                                        ----------------------------------------
                                        David T. Brigham


                                        /s/ A. Lance Langford
                                        ----------------------------------------
                                        A. Lance Langford


                                        /s/ Jeffery E. Larson
                                        ----------------------------------------
                                        Jeffery E. Larson


                                        /s/ Karen E. Lynch
                                        ----------------------------------------
                                        Karen E. Lynch


                                        /s/ Christopher A. Phelps
                                        ----------------------------------------
                                        Christopher A. Phelps


                                       9
<PAGE>

                                   Schedule I

                                            Number of Outstanding
Shareholder                                 Shares of Common Stock
-----------                                 ----------------------

Ben M. and Anne L. Brigham, collectively    3,719,792
Harold D. Carter                            314,893
General Atlantic Partners III, L.P.         2,679,418
GAP-Brigham Partners, L.P.                  127,725
GAP Coinvestment Partners II, L.P.          975,610
Aspect Resources, LLC                       487,805
Brigham Officers*:                          233,186 (in the aggregate)
Curtis F. Harrell
David T. Brigham
Lance Langford
Jeffery E. Larson
Karen E. Lynch
Christopher A. Phelps

* other than Ben M. Brigham