Document:

<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<PAGE>

                                                                  Exhibit 10.8.2

                           BRIGHAM EXPLORATION COMPANY

                               1997 INCENTIVE PLAN

                           RESTRICTED STOCK AGREEMENT

      THIS AGREEMENT, made as of the 27th day of October, 2000, by and between
BRIGHAM EXPLORATION COMPANY, a Delaware corporation (the "Company"), and [See
Schedule I attached] ("Employee");

                              W I T N E S S E T H:

      WHEREAS, the Compensation Committee of the Board of Directors of the
Company (the "Committee"), acting under the Company's 1997 Incentive Plan (the
"Plan"), has determined that it is desirable to award shares of restricted stock
to Employee under the Plan; and

      WHEREAS, pursuant to the Plan, the Committee has determined that the
shares of restricted stock so awarded shall be subject to the restrictions,
terms and conditions of this Agreement;

      NOW, THEREFORE, in consideration of the premises and mutual covenants and
agreements herein contained, the receipt and sufficiency of which are hereby
acknowledged, the parties hereby agree as follows:

      1. Plan Provisions. Capitalized terms used and not otherwise defined
herein shall have the respective meanings given such terms in the Plan. By
execution of this Agreement, Employee agrees that the Restricted Stock covered
hereby shall be governed by and subject to all applicable provisions of the
Plan. This Agreement is subject to the Plan, and the Plan shall govern where
there is any inconsistency between the Plan and this Agreement.

      2. Restricted Stock. On the terms and conditions and subject to the
restrictions, including forfeiture, hereinafter set forth, the Company hereby
makes to Employee, and Employee hereby accepts, the awards of Restricted Stock
(each such issuance is herein called an "Award") set forth on Exhibit A hereto,
which awards are being issued by the Company pursuant to the Plan. The number of
shares of Restricted Stock of each Award covered hereby (the "Restricted
Shares"), the date of issuance of such shares (the "Issue Date"), and the
Restricted Period applicable to such shares, including the date on which such
Restricted Period is scheduled to terminate (the "Scheduled Termination Date"),
are set forth on Exhibit A attached hereto. A certificate or certificates
representing the Restricted Shares shall be issued in the name of Employee as of
the applicable Issue Date and delivered to Employee on such Issue Date or as
soon thereafter as practicable. Employee shall cause the certificate(s)
representing the Restricted Shares, upon receipt thereof by Employee, to be
deposited, together with stock powers and any other instrument of transfer
reasonably requested by the Company duly endorsed in blank, with the Company, to
be held by the Company in escrow for Employee's benefit until such time as any
Restricted Shares represented by such certificate(s) are forfeited to the
Company or the restrictions thereon terminate. Restricted Shares
<PAGE>

shall be delivered to Employee upon vesting or assigned and transferred to and
reacquired by the Company upon forfeiture, as hereinafter set forth.

3. Vesting/Forfeiture.

      (a) Subject to Sections 3(b) and 3(c), with respect to each Award of
Restricted Shares to Employee, the Restricted Shares subject of such Award shall
be forfeited to the Company at no cost to the Company if Employee's employment
with the Company or a subsidiary of the Company terminates prior to the
termination of the Restricted Period applicable to such Restricted Shares.

      (b) Upon (i) Employee's termination of employment during the Restricted
Period due to death or Disability (as defined below), or (ii) the involuntary
termination of Employee's employment with the Company and its subsidiaries by
action of the Company (or its subsidiary, if Employee is employed by a
subsidiary of the Company) during the Restricted Period for reasons other than
Just Cause (as defined below) (each, a "Termination Event"), then, with respect
to the Award covered hereby with the earliest Scheduled Termination Date after
such Termination Event, (A) a ratable portion of the number of Restricted Shares
applicable to such Scheduled Termination Date (the "Next Vested Shares") shall
be deemed to have vested as of the date of such Termination Event, determined by
multiplying the number of Next Vested Shares by a fraction with a numerator
equal to the number of full months which have then elapsed since the last date
of termination of a Restricted Period pursuant to this Agreement (or Issue Date
in the event that no shares had previously vested) and a denominator equal to
the total number of months between the last date of termination of a Restricted
Period pursuant to this Agreement (or Issue Date in the event that no shares had
previously vested) and the next Scheduled Termination Date under this Agreement,
and rounding to the closest whole number, and (B) the Restricted Period
applicable to such ratable portion of Next Vested Shares shall terminate.

      (c) If as a result of any merger or acquisition transaction involving the
Company or any transaction involving the issuance or redemption of equity
interests in the Company, more than fifty percent (50%) of such equity interests
is owned by parties other than those listed on Exhibit B attached hereto (such
event is referred to herein as a "Fundamental Change"), then immediately before
the consummation of the Fundamental Change, the Restricted Shares shall become
fully vested and all Restricted Periods shall terminate.

      (d) Unless and until Restricted Shares are delivered to Employee upon
vesting, such Restricted Shares shall not be sold, assigned, transferred,
discounted, exchanged, pledged, or otherwise encumbered or disposed of by
Employee in any manner. Transfer of employment without interruption of service
between or among the Company and any of its subsidiaries shall not be considered
a termination of employment.

      (e) With respect to each Award of Restricted Shares to Employee, upon the
termination of the Restricted Period applicable to such shares, the restrictions
applicable to the Restricted Shares that have not theretofore been forfeited
shall terminate, and as soon as practicable thereafter a stock certificate for
the number of Restricted Shares with respect to which the restrictions have
terminated, together with any dividends or other distributions with respect to
such shares then being held by the

                                       2
<PAGE>

Company pursuant to the provisions of this Agreement, shall be delivered, free
of all such restrictions, to Employee or Employee's beneficiary or estate, as
the case may be.

      (f) Notwithstanding anything contained herein to the contrary, the
Committee shall have the right to cancel all or any portion of any outstanding
restrictions prior to the termination of such restrictions with respect to any
or all of the Restricted Shares on such terms and conditions as the Committee
may, in writing, deem appropriate.

      (g) For purposes of this Agreement, the following terms shall have the
indicated meanings:

      Disability: The "Disability" of Employee shall be deemed to have occurred
if, in the good faith judgment of the Committee, Employee shall become unable to
continue the proper performance of Employee's duties as an employee of the
Company or a subsidiary thereof on a full-time basis as a result of Employee's
physical or mental incapacity.

      Just Cause: The term "Just Cause" shall mean any of the following: (i)
conduct by Employee that constitutes willful misconduct or gross negligence in
the performance of his duties; (ii) conduct by the Employee that constitutes
fraud, dishonesty, or a criminal act, whether or not with respect to the
Company; (iii) embezzlement of funds or misappropriation of other property by
Employee, (iv) any act or conduct by Employee that, in the good faith opinion of
the Board of Directors or the President of the Company, is materially
detrimental to the Company or reflects unfavorably on the Company or the
Employee to such an extent that the Company's best interests reasonably require
the Employee's discharge.

      4. Rights as Stockholder. Upon the issuance of a certificate or
certificates representing any Restricted Shares to Employee, Employee shall
become the owner thereof for all purposes and shall have all rights as a
stockholder, including voting rights and the right to receive dividends and
distributions, with respect to such Restricted Shares, subject to the provisions
hereof. If the Company shall pay or declare a dividend or make a distribution of
any kind, whether due to a reorganization, recapitalization or otherwise, with
respect to the shares of Common Stock constituting Restricted Shares, then the
Company shall pay or make such dividend or other distribution with respect to
such Restricted Shares; provided, however, that the cash, stock or other
securities and other property constituting such dividend or other distribution
shall be held by the Company subject to the restrictions applicable to any
Restricted Shares until such Restricted Shares with respect to which such
dividend or other distribution was paid or made are either vested or forfeited.
If any Restricted Shares with respect to which such dividend or distribution was
paid or made do not vest but instead are forfeited pursuant to the provisions
hereof, then Employee shall not be entitled to receive such dividend or
distribution with respect to such forfeited shares and such dividend or
distribution with respect to such forfeited shares shall likewise be forfeited
and automatically transferred to and reacquired by the Company. If any
Restricted Shares with respect to which such dividend or distribution was paid
or made become vested pursuant to the provisions hereof, then Employee shall be
entitled to receive such dividend or distribution with respect to such vested
shares, without interest, and such dividend or distribution with respect to such
vested shares shall likewise be delivered to Employee.

                                       3
<PAGE>

      5. Withholding Taxes.

      (a) With respect to each Award of shares of Restricted Stock to Employee,
Employee may elect, within 30 days of the Issue Date of such shares and on
notice to the Company, to realize income for federal income tax purposes equal
to the fair market value of the shares on the Issue Date. In such event,
Employee shall make arrangements satisfactory to the Compensation Committee to
pay in the year of the Award any federal, state, or local taxes required to be
withheld with respect to such shares. If Employee fails to make such payments,
then any provision of this Agreement to the contrary notwithstanding, the
Company and its subsidiaries shall, to the extent permitted by law, have the
right to deduct from any payments of any kind otherwise due from the Company or
its subsidiaries to or with respect to Employee, whether or not pursuant to this
Agreement or the Plan and regardless of the form of payment, any federal, state,
or local taxes of any kind required by law to be withheld with respect to such
shares.

      (b) (i) No later than the date of the termination of the restrictions on
any of the shares of Restricted Stock covered hereby, Employee will pay to the
Company or its subsidiaries, or make arrangements satisfactory to the
Compensation Committee regarding payment of, any federal, state, or local taxes
of any kind required by law to be withheld with respect to the shares of
Restricted Stock with respect to which such restrictions have terminated.

            (ii) Employee shall, to the extent permitted by law, have the right
to deliver to the Company or its subsidiaries shares of Restricted Stock to
which Employee shall be entitled upon the vesting thereof (or other unrestricted
shares of Common Stock owned by Employee), valued at the fair market value of
such shares at the time of such delivery to the Company or its subsidiaries, to
satisfy the obligation of Employee under Section 5(b)(i) hereof.

            (iii) Any provision of this Agreement to the contrary
notwithstanding, if Employee does not otherwise satisfy the obligation of
Employee under Section 5(b)(i) hereof, then the Company and its subsidiaries
shall, to the extent permitted by law, have the right to deduct from any
payments of any kind otherwise due from the Company or its subsidiaries to or
with respect to Employee, whether or not pursuant to this Agreement or the Plan
and regardless of the form of payment, any federal, state, or local taxes of any
kind required by law to be withheld with respect to the shares of Restricted
Stock with respect to which the restrictions on the Restricted Stock have
terminated.

      6. Legend. Each certificate representing shares of Restricted Stock
covered hereby shall conspicuously set forth on the face or back thereof, in
addition to any legends required by applicable law or other agreement, a legend
in substantially the following form:

                                       4
<PAGE>

      THE SHARES REPRESENTED BY THIS CERTIFICATE HAVE BEEN ASSIGNED AND
      TRANSFERRED TO THE RECORD HOLDER HEREOF PURSUANT TO THE TERMS OF THE
      BRIGHAM EXPLORATION COMPANY 1997 INCENTIVE PLAN AND MAY NOT BE SOLD,
      ASSIGNED, TRANSFERRED, DISCOUNTED, EXCHANGED, PLEDGED, OR OTHERWISE
      ENCUMBERED OR DISPOSED OF IN ANY MANNER EXCEPT AS SET FORTH IN THE TERMS
      OF THE AGREEMENT EMBODYING THE AWARD OF SUCH SHARES DATED OCTOBER 27,
      2000. A COPY OF SUCH PLAN AND AGREEMENT IS ON FILE IN THE OFFICES OF THE
      CORPORATION.

      7. Governing Law. This Agreement shall be governed by and construed and
enforced in accordance with the laws of the State of Texas, without regard to
the principles of conflicts of laws thereof.

      8. Binding Effect. This Agreement shall be binding upon and inure to the
benefit of the parties hereto and their respective heirs, personal
representatives, successors, and permitted assigns; provided, however, that
Employee shall not assign or otherwise transfer this Agreement or any of
Employee's rights or obligations hereunder.

      9. Entire Agreement; Amendment. This Agreement, together with the exhibits
hereto and any other writings referred to herein or delivered pursuant hereto,
constitute the entire agreement between the parties hereto with respect to the
subject matter hereof and supersede all prior agreements and understandings,
whether written or oral, between the parties with respect to the subject matter
hereof. To the fullest extent provided by applicable law, this Agreement may be
amended, modified, and supplemented by mutual consent of the parties hereto at
any time, with respect to any of the terms contained herein, in such manner as
may be agreed upon in writing by such parties.

      10. Notices. All notices and other communications hereunder shall be in
writing and shall be deemed given:

      (a) If to the Company, when delivered by hand or on the third business day
after being deposited in the United States mail (certified mail with postage
prepaid) to:

            Brigham Exploration Company
            6300 Bridge Point Parkway
            Building 2, Suite 500
            Austin, Texas 78730
            Attention: Vice President Administration

      (b) If to Employee, when delivered by hand or on the third business day
after being deposited in the United States mail (certified mail with postage
prepaid) to the address for Employee contained in the Company's records.

                                       5
<PAGE>

Either party may at any time give to the other notice in writing of any change
of address of the party giving such notice and from and after the giving of such
notice the address or addresses therein specified will be deemed to be the
address of such party for the purposes of giving notice hereunder.

      11. Counterparts. This Agreement may be executed by the parties hereto in
any number of counterparts, each of which shall be deemed an original, but all
of which shall constitute one and the same agreement. Each counterpart may
consist of a number of copies hereof each signed by less than all, but together
signed by all, the parties hereto.

      IN WITNESS WHEREOF, the Company and Employee have executed this Agreement
as of the date first above written.

                                        BRIGHAM EXPLORATION COMPANY

                                        By: /s/ Ben M. Brigham
                                           -------------------------------------
                                        Name: Ben M. Brigham
                                             -----------------------------------
                                        Title: President
                                              ----------------------------------

                                        /s/ [See Schedule I attached]
                                        ----------------------------------------
                                            [See Schedule I attached]

                                       6
<PAGE>

                                   EXHIBIT A

                            RESTRICTED STOCK AWARDS

<TABLE>
<CAPTION>
               Number of
               Shares of                             Duration of
              Restricted                             Restricted                      Scheduled
  Award          Stock        Issue Date               Period                     Termination Date
  -----       ----------      ----------             -----------                  ----------------
<C>       <C>               <C>                <S>                           <C>
1.        [See Schedule I]  October 27, 2000   Commencing on October 27,     Midnight on October 26, 2001
                                               2000 and ending at midnight
                                               on October 26, 2001

2.        [See Schedule I]  October 27, 2000   Commencing on October 27,     Midnight on October 26, 2002
                                               2000 and ending at midnight
                                               on October 26, 2002

3.        [See Schedule I]  October 27, 2000   Commencing on October 27,     Midnight on October 26, 2003
                                               2000 and ending at midnight
                                               on October 26, 2003

4.        [See Schedule I]  October 27, 2000   Commencing on October 27,     Midnight on October 26, 2004
                                               2000 and ending at midnight
                                               on October 26, 2004
</TABLE>
<PAGE>

                                    EXHIBIT B

BRIGHAM EXPLORATION COMPANY, A Delaware corporation

BRIGHAM OIL & GAS, L.P., A Delaware limited partnership

BRIGHAM, INC. (f/k/a Brigham Exploration Company), a Nevada corporation

GENERAL ATLANTIC PARTNERS III, L.P., a Delaware limited partnership

GAP-BRIGHAM PARTNERS, L.P., a Delaware limited partnership

BEN M. BRIGHAM

ANNE L. BRIGHAM

HAROLD D. CARTER

RIMCO PARTNERS, L.P. II

RIMCO PARTNERS, L.P. III

RIMCO PARTNERS, L.P. IV
<PAGE>

                                  SCHEDULE I

Name of Employee         Award 1     Award 2      Award 4      Award 5
----------------         -------     -------      -------      -------

David T. Brigham         15,664       15,663       15,663       15,663

Alan Lance Langford      14,873       14,873       14,873       14,872

Karen E. Lynch            5,000        5,000        5,000        5,000

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00021-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00021-of-00352.parquet"}]]