<PAGE>

                                                                  Exhibit 10.70

                         SECURITIES PURCHASE AGREEMENT

      This SECURITIES PURCHASE AGREEMENT (this "Agreement"), is entered into as
of March 5, 2001, between Brigham Exploration Company, a Delaware corporation
(the "Company"), DLJMB Funding III, Inc., a Delaware corporation ("MB"), DLJ
Merchant Banking Partners III, LP, a Delaware limited partnership, ("MBP"), DLJ
Offshore Partners III, CV, a Netherlands Antilles limited partnership ("DOP")
and DLJ ESC II, LP, a Delaware limited partnership ("ESC") (collectively
referred to as "Investors").

      WHEREAS, the Company has authorized the sale and issuance of an aggregate
of up to 500,000, shares of its Series A Preferred Stock (the "Shares") and
warrants to acquire 2,105,263 shares of its Common Stock, (the "Warrants"), in
the form attached hereto as Exhibit A;

      WHEREAS, Investors desire to purchase the Shares and the Warrants on the
terms and conditions set forth herein; and

      WHEREAS, the Company desires to issue and sell the Shares and the Warrants
to Investors on the terms and conditions set forth herein;

      NOW, THEREFORE, in consideration of the premises and the mutual covenants
and agreements herein contained, and intending to be legally bound hereby, the
Company and Investors hereby agree as follows:

                                    ARTICLE I
                            TERMS OF THE TRANSACTION

      1.1 Authorization of Shares. On or prior to the Closing (as defined in
Section 2.1 below), the Company shall have authorized (a) the sale and issuance
to Investors of the Shares and the Warrants and (b) the issuance of such shares
of Common Stock to be issued upon exercise of the Warrants (the "Warrant
Shares"). The Shares shall have the rights, preferences, privileges and
restrictions set forth in the Certificate of Designations of the Company, in the
form attached hereto as Exhibit B as amended by the Certificate of Amendment of
Certificate of Designations in the form attached hereto as Exhibit C (as so
amended, the "Certificate of Designations").

      1.2 Sale and Purchase. Subject to the terms and conditions hereof, at the
Closing the Company hereby agrees to issue and sell to Investors, and Investors
agree to purchase from the Company, 500,000 Units at a purchase price of Twenty
Dollars ($20.00) per Unit, with each such Unit consisting of (i) one Share and
(ii) Warrants to purchase 4.210526 Warrant Shares and such Shares and Warrants
shall be allocated among the Investors as follows:

                                      Preferred
         Investor                       Stock                  Warrants
         --------                       -----                  --------

         MBP                           362,699                1,527,154
         Offshore                       15,307                   64,451
         MB                             33,694                  141,869
         ESC                            88,300                  371,789
                                       -------                ---------
         TOTAL                         500,000                2,105,263
<PAGE>

                                   ARTICLE II
                                     CLOSING

      2.1 Closing. The closing of the sale and purchase of the Shares and
Warrants under this Agreement (the "Closing") shall take place at the offices of
Brigham Exploration Company, 6300 Bridge Point Parkway, Building 2, Suite 500,
Austin, Texas 70730, at 10:00 a.m., local time, on the date of this Agreement or
at such other time or place as the Company and Investors may mutually agree (the
"Closing Date"). All closing transactions at the Closing shall be deemed to have
occurred simultaneously.

      2.2 Closing into Escrow.

            (a) At the Closing, subject to the terms and conditions hereof, (i)
      the Company will deliver to Chase Manhattan Bank, a New York state bank
      (the "Escrow Agent"), as escrow agent under an Escrow Agreement of even
      date herewith in the form of Exhibit D hereto (the "Escrow Agreement"),
      certificates issued in the name of each Investor representing the
      applicable Shares and Warrants representing the applicable Warrants to
      purchase Warrant Shares, and (ii) each Investor will deliver to the Escrow
      Agent by wire transfer payment of the purchase price for its Shares and
      Warrants.

            (b) The Escrow Agreement shall provide that the Escrow Agent shall
      release the certificates representing the applicable Shares and Warrants
      to each Investor, and shall release the purchase price for such Shares and
      Warrants to the Company, along with all interest accruing thereon while on
      deposit under the Escrow Agreement, upon receipt of a certificate executed
      by the Investors and the Company stating either of the following:

                  (i) That

                        (A) the Company filed preliminary proxy materials with
                  the Securities and Exchange Commission (the "SEC") in
                  accordance with applicable rules under the Exchange Act
                  seeking stockholder approval at the Company's annual
                  stockholder's meeting to be held on or before May 31, 2001
                  (the "Annual Meeting") of the matters described in the
                  Stockholders' Voting Agreement dated March 1, 2001 by and
                  among the Company and certain of its stockholders (the
                  "Stockholders' Voting Agreement"), as more fully described in
                  Section 5.7 hereof,

                        (B) either (1) the SEC has notified (whether orally or
                  in writing) the Company or its representative that it will not
                  review such proxy materials (which notice, if telephonic,
                  shall be certified to the Investors by the Company or its
                  representative in writing), (2) the SEC has notified the
                  Company that it will review such proxy materials, the SEC has
                  completed such review and the Company has responded to all
                  comments from the SEC to the SEC's satisfaction, or (3) as of
                  the date of mailing of the proxy materials to stockholders of
                  the Company the Company has not received any notice, written
                  or otherwise, from the SEC that the SEC intends to review such
                  proxy materials, and upon the occurrence of any of the events
                  described


                                       2
<PAGE>

                  in subsection 1, 2 or 3, above, the Company shall promptly
                  certify the occurrence of such event in writing to the
                  Investors, and

                        (C) as of the record date for the annual meeting to be
                  held in accordance with Section 5.7 hereof, the parties to the
                  Stockholders' Voting Agreement held at least a majority of the
                  outstanding shares of Common Stock of the Company; or

                  (ii) That holders of a majority of the outstanding shares of
            Common Stock have voted in favor of the matters described in the
            Stockholders' Voting Agreement at the Annual Meeting.

            (c) The Escrow Agreement shall provide that the Escrow Agent shall
      release the certificates representing the applicable Shares and Warrants
      to the Company, and shall release the purchase price for such Shares and
      Warrants to the Investors in the amounts originally deposited with the
      Escrow Agent by each such Investor, along with all interest accruing
      thereon while on deposit under the Escrow Agreement, upon receipt of a
      certificate executed by the Investors and the Company stating that holders
      of a majority of the outstanding shares of Common Stock have failed to
      vote in favor of the matters described in the Stockholders' Voting
      Agreement at the Annual Meeting.

            (d) The Escrow Agreement shall provide that the Escrow Agent shall
      release the certificates representing the applicable Shares and Warrants,
      and shall release the purchase price for such Shares and Warrants, as set
      forth in either paragraph (b) or (c) above upon receipt of a certificate
      as set forth in paragraph (b) or (c), respectively, signed by only the
      Company or the Investors, if (i) the party signing such certificate also
      certifies that they have provided a copy of such certificate to the other
      parties to the Escrow Agreement in accordance with the notice provisions
      of the Escrow Agreement and (ii) ten (10) calendar days shall have elapsed
      between the date on which the Escrow Agent shall have received the
      certificate required by paragraph (b) or (c) and the Escrow Agent shall
      not have received any notice in accordance with the notice provisions of
      the Escrow Agreement from another party to the Escrow Agreement protesting
      or otherwise disputing, challenging or disagreeing with any assertion
      contained in the certificate.

            (e) In the event of any dispute under paragraph (d) above, the
      parties agree to resolve such dispute by binding arbitration pursuant to
      Section 10.8 hereof. Upon receipt of a certificate from the prevailing
      party directing the Escrow Agent to make a distribution of the Shares,
      Warrants, purchase price for such Shares and Warrants, and interest
      thereon, all as specified in such certificate, which certificate is
      accompanied by an arbitral order or award which states on its face that it
      is rendered pursuant to this Agreement and provides for such distribution
      as set forth in the certificate, the Escrow Agent shall distribute such
      Shares, Warrants, purchase price for the Shares and Warrants and interest
      thereon as directed by such certificate and final arbitral order or award.
      Any such certificate and final arbitral order or award shall override any
      notice or other document received by the Escrow Agent pursuant to
      paragraph (d) above, except to the extent that Escrow Agent has previously
      acted in accordance with the terms of paragraphs (b) or (c) above.


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<PAGE>

            (f) In the event that the Escrow Agent has not received a
      certificate under paragraph (b), (c), (d) or (e) on or before June 15,
      2001, the Escrow Agent shall release the certificates representing the
      applicable Shares and Warrants to the Company, and shall release the
      purchase price for such Shares and Warrants to the Investors in the
      amounts originally deposited with the Escrow Agent by each such Investor,
      along with all interest accruing thereon while on deposit under the Escrow
      Agreement, upon receipt of a certificate on or after June 15, 2001
      executed by the Investors requesting such distribution.

            (g) If the Shares and Warrants are released to the Company and the
      purchase price for the Shares and the Warrants, along with interest
      accruing thereon while on deposit under the Escrow Agreement, is released
      to the Investors pursuant to the terms of the Escrow Agreement, then the
      Shares and the Warrants shall not be deemed to have been issued by the
      Company or to have been purchased by Investors hereunder, and this
      Agreement and the Ancillary Documents shall terminate; provided, however
      that the termination shall not release any party hereto from liability for
      any breach of any provision, covenant or agreement herein or in the
      Ancillary Documents prior to the termination of this Agreement and the
      Ancillary Documents.

            (h) The parties agree to deliver to the Escrow Agent the
      certificates and such other instructions as may be required under the
      Escrow Agreement in order to implement the provisions of this Section 2.2.

                                   ARTICLE III
                  REPRESENTATIONS AND WARRANTIES OF THE COMPANY

      The Company represents and warrants to Investors, as of the date hereof,
that:

      3.1 Corporate Organization. The Company is a corporation duly organized,
validly existing, and in good standing under the laws of the State of Delaware
and has all requisite corporate power and authority in all material respects to
own, lease, and operate its properties and to carry on its business as now being
conducted. No actions or proceedings to dissolve the Company are pending or, to
the best knowledge of the Company, threatened. The Company is duly qualified to
do business as a foreign corporation and is in good standing in each
jurisdiction where such qualification is necessary, except where the failure to
so qualify or to be in good standing would not reasonably be expected to have a
Material Adverse Effect.

      3.2 Capitalization of the Company.

      (a) On the Closing Date, the authorized capital stock of the Company will
consist of 50,000,000 shares of Common Stock and 10,000,000 shares of preferred
stock, $.01 par value, 2,250,000 of which are designated as Series A Preferred
Stock. As of the date hereof, (i) 15,979,544 shares of Common Stock are
outstanding and 1,013,334 shares of preferred stock are outstanding and (ii)
1,393,920 shares of Common Stock are reserved for issuance upon exercise of
outstanding employee, officer and director stock options and 15,129,143 shares
of Common Stock are reserved for issuance upon exercise of outstanding warrants
or conversion rights. All outstanding shares of capital stock of the Company
have been validly issued and are fully paid and nonassessable, and no


                                       4
<PAGE>

shares of capital stock of the Company are subject to, nor have any been issued
in violation of, preemptive or similar rights. On the Closing Date, the rights,
preferences, privileges and restrictions of the Shares will be as stated in the
Certificate of Designations.

      (b) Except as set forth above in subparagraph (a) of this Section 3.2,
there are outstanding (i) no shares of capital stock or other voting securities
of the Company; (ii) no securities of the Company convertible into or
exchangeable for shares of capital stock or other voting securities of the
Company; (iii) no options or other rights to acquire from the Company, and no
obligation of the Company to issue or sell, any shares of capital stock or other
voting securities of the Company or any securities of the Company convertible
into or exchangeable for such capital stock or voting securities; and (iv) no
equity equivalents, interests in the ownership or earnings, or other similar
rights of or with respect to the Company.

      (c) Neither the execution of this Agreement nor the performance of the
Company's obligations hereunder, nor the consummation of any other transaction
currently contemplated by the Company or any of its Subsidiaries, will trigger
or cause any adjustment under any anti-dilution provisions or any other similar
provisions contained in any agreement as currently in effect that have the
effect of (i) causing a decrease in any exercise price or conversion price in
any security exercisable for or convertible into shares of Common Stock (a
"Common Stock Equivalent"), or (ii) causing an increase in the number of shares
of Common Stock that may be acquired upon conversion or exercise of a Common
Stock Equivalent.

      3.3 Authority Relative to This Agreement. The Company has full corporate
power and authority to execute, deliver, and perform this Agreement and to
execute, deliver, and where applicable, perform the Ancillary Documents to which
it is a party and to consummate the transactions contemplated hereby and
thereby. The execution, delivery and performance by the Company of this
Agreement and the execution, delivery, and where applicable, performance by it
of the Ancillary Documents to which it is a party, and the consummation by it of
the transactions contemplated hereby and thereby, have been (or prior to the
Closing will have been) duly authorized by all necessary corporate action of the
Company. This Agreement has been duly executed and delivered by the Company and
constitutes, and each Ancillary Document executed or to be executed by the
Company has been, or when executed will be, duly executed and delivered by the
Company and constitutes, or when executed and delivered will constitute, a valid
and legally binding obligation of the Company, enforceable against the Company
in accordance with its terms, except that such enforceability may be limited by
(i) applicable bankruptcy, insolvency, reorganization, moratorium, and similar
laws affecting creditors' rights generally and (ii) general equitable principles
(regardless of whether such enforceability is considered in a proceeding in
equity or at law).

      3.4 Noncontravention. The execution, delivery, and performance by the
Company of this Agreement and the execution, delivery, and where applicable, the
performance by it of Ancillary Documents to which it is a party and the
consummation by it of the transactions contemplated hereby and thereby do not
and will not (i) conflict with or result in a violation of any provision of the
Company's Certificate of Incorporation, as amended, or the Company's Bylaws, as
amended, or the charter, bylaws, partnership agreement or other governing
instruments of any Subsidiary, (ii) conflict with or result in a violation of
any provision of, or constitute (with or without the giving of notice or the
passage of time or both) a default under, or give rise (with or without the
giving of notice or the passage of time or both) to any loss of material
benefit, or of any right of termination, cancellation, or acceleration under,
any Material Agreement, (iii) result in the creation or imposition


                                       5
<PAGE>

of any Encumbrance upon the properties of the Company or any Subsidiary or (iv)
assuming compliance with the matters referred to in Section 3.5, violate any
Applicable Law binding upon the Company or any Subsidiary, except, in the case
of clauses (ii), (iii) and (iv) above, for any such conflicts, violations,
defaults, terminations, cancellations, accelerations, or Encumbrances which
would not, individually or in the aggregate, have a Material Adverse Effect on
the Company.

      3.5 Consents and Approvals. No consent, approval, order, or authorization
of, or declaration, filing, or registration with, any Governmental Entity is
required to be obtained or made by the Company or any Subsidiary in connection
with the execution, delivery, or performance by the Company of this Agreement
and the execution, delivery, and where applicable, performance of Ancillary
Documents to which it is a party or the consummation of the transactions
contemplated hereby and thereby, other than (i) compliance with any applicable
requirements of the Securities Act; (ii) compliance with any applicable
requirements of the Exchange Act; (iii) compliance with any applicable state
securities laws; (iv) filing of the Certificate of Amendment of Certificate of
Designations with the Delaware Secretary of State; (v) compliance with any
applicable requirements of the HSR Act as a result of the exercise of any of the
Warrants; and (vi) such consents, approvals, orders, or authorizations which, if
not obtained, and such declarations, filings, or registrations which, if not
made, would not, individually or in the aggregate, have a Material Adverse
Effect on the Company. Except for such consents as are obtained before or
contemporaneously with consummation of the Closing, no consent or approval of
any person other than the Company, Investors or any Governmental Entity is
required to be obtained or made by the Company or any Subsidiary in connection
with the execution, delivery, or performance by the Company of this Agreement
and execution, delivery and, where applicable, performance of the Ancillary
Documents to which it is a party or the consummation of the transactions
contemplated hereby and thereby, other than such consents, approvals, orders, or
authorizations which, if not obtained, and such declarations, filings, or
registrations which, if not made, would not, individually or in the aggregate,
have a Material Adverse Effect on the Company.

      3.6 Authorization of Issuance; Reservation of Shares. When issued and
delivered pursuant to this Agreement and the Certificate of Designations against
payment therefor, the Shares and the Warrants will be validly issued, fully paid
and nonassessable. The Warrant Shares have been duly and validly reserved for
issuance. The issuances of the Shares and the Warrants are not subject to any
preemptive or similar rights.

      3.7 Financial Condition. The audited consolidated balance sheet of the
Company and its Subsidiaries as at December 31, 1999 and the related
consolidated statement of income, stockholders' equity and cash flow of the
Company and its Subsidiaries for the fiscal year ended on said date, with the
opinion thereon of Price Waterhouse heretofore furnished to the Investors and
the unaudited consolidated balance sheet of the Company and its Subsidiaries as
at September 30, 2000 and their related consolidated statements of income,
stockholders' equity and cash flow of the Company and its Subsidiaries for the
six-month period ended on such date heretofore furnished to the Investors, are
complete and correct and fairly present the consolidated financial condition of
the Company and its Subsidiaries as at said dates and the results of its
operations for the fiscal year and the nine-month period on said dates, all in
accordance with GAAP, as applied on a consistent basis (subject, in the case of
the interim financial statements, to normal year-end adjustments). Neither the
Company nor any Subsidiary has on the Closing Date any debt, trade payables,
contingent liabilities, liabilities for taxes, unusual forward or long-term
commitments or unrealized or anticipated losses from any unfavorable
commitments, except as referred to or reflected or provided


                                       6
<PAGE>

for in the Company's financial statements provided to the Investors as set forth
in this Section 3.7 or in Schedule 3.7 or except to the extent that the
existence of any of the foregoing would not have a Material Adverse Effect
relative to the Company. Since December 31, 1999, there has been no change or
event having a Material Adverse Effect relative to the Company, except as
disclosed to the Investors in writing. Since the date of the Financial
Statements, neither the business nor the properties of the Company's
Subsidiaries, taken as a whole, have been materially and adversely affected as a
result of any fire, explosion, earthquake, flood, drought, windstorm, accident,
strike or other labor disturbance, embargo, requisition or taking of property or
cancellation of contracts, permits or concessions by any Governmental Entity,
riot, activities of armed forces or acts of God or of any public enemy.

      3.8 Litigation. Except as disclosed in Schedule 3.8 hereto, at the Closing
Date there is no litigation, legal, administrative or arbitral proceeding,
investigation or other action of any nature pending or, to the knowledge of the
Company, threatened against or affecting the Company or any Subsidiary which
both (a) involves the possibility of any judgment or liability against the
Company or any Subsidiary not fully covered by insurance (except for normal
deductibles), and (b) would be more likely than not to have a Material Adverse
Effect relative to the Company.

      3.9 ERISA. The Company and each ERISA Affiliate have complied in all
material respects with ERISA and, where applicable, the Code regarding each
Plan. Each Plan is, and has been, maintained in substantial compliance with
ERISA and, where applicable, the Code.

      No act, omission or transaction has occurred which could result in
imposition on the Company or any ERISA Affiliate (whether directly or
indirectly) of an amount of $100,000 or more as (i) either a civil penalty
assessed pursuant to section 502(c), (i) or (1) of ERISA or a tax imposed
pursuant to Chapter 43 of Subtitle D of the Code or (ii) breach of fiduciary
duty liability damages under section 409 of ERISA.

      No Plan (other than a defined contribution plan) or any trust created
under any such Plan has been terminated since September 2, 1974. No liability to
the PBGC in excess of $100,000 (other than for the payment of current premiums
which are not past due) by the Company or any ERISA Affiliate has been or is
expected by the Company or any ERISA Affiliate to be incurred with respect to
any Plan. No ERISA Event with respect to any Plan has occurred which could
reasonably be expected to result in liabilities of $100,000 or more.

      Full payment when due has been made of all amounts which the Company or
any ERISA Affiliate is required under the terms of each Plan or applicable law
to have paid as contributions to such Plan, and no accumulated funding
deficiency in an amount of $100,000 or more (as defined in section 302 of ERISA
and section 412 of the Code), whether or not waived, exists with respect to any
Plan.

      The actuarial present value of the benefit liabilities under each Plan
which is subject to Title IV of ERISA does not, as of the end of the Company's
most recently ended fiscal year, exceed the current value of the assets
(computed on a plan termination basis in accordance with Title IV of ERISA) of
such Plan allocable to such benefit liabilities by $100,000 or more. The term
"actuarial present value of the benefit liabilities" shall have the meaning
specified in section 4041 of ERISA.


                                       7
<PAGE>

      None of the Company or any ERISA Affiliate sponsors, maintains, or
contributes to an employee welfare benefit plan, as defined in section 3(1) of
ERISA, including, without limitation, any such plan maintained to provide
benefits to former employees of such entities, that may not be terminated by the
Company or any ERISA Affiliate in its sole discretion at any time without any
material liability.

      None of the Company or any ERISA Affiliate sponsors, maintains or
contributes to, or has at any time in the preceding six calendar years,
sponsored, maintained or contributed to, any Multiemployer Plan.

      None of the Company or any ERISA Affiliate is required to provide security
under section 401(a)(29) of the Code due to a Plan amendment that results in an
increase in current liability for the Plan.

      3.10 Taxes. The Company has filed all United States Federal income tax
returns and all other tax returns which are required to be filed by it and has
paid all material taxes due pursuant to such returns or pursuant to any
assessment received by the Company, except for any taxes which are being
contested in good faith and by proper proceedings and against which adequate
reserves are being maintained. The charges, accruals and reserves on the books
of the Company in respect of taxes and other governmental charges are, in the
opinion of the Company, adequate. No tax lien has been filed and, to the
knowledge of the Company, no claim is being asserted with respect to any such
tax, fee or other charge, except for any taxes, fees or other charges which are
not material or which are being contested in good faith and by proper
proceedings and against which adequate reserves are being maintained.

      3.11 Titles, etc.

      (a) Subject to the matters set out in Schedule 3.11, each of the Company
and the Subsidiaries has good and defensible title, in all material respects, to
the material Oil and Gas Properties that are evaluated in the most recently
delivered reserve report, free and clear of all Liens, other than Excepted
Liens. Except for immaterial divergences, after giving full effect to the
Excepted Liens, the Company owns, in all material respects, the net interests in
production attributable to the Hydrocarbon Interests that are evaluated in the
most recently delivered reserve report, and the ownership of such Hydrocarbon
Interests shall not in any material respect obligate the Company to bear the
costs and expenses relating to the maintenance, development and operations of
each such Hydrocarbon Interest in an amount in excess of the working interest of
such Hydrocarbon Interest (without a corresponding increase in net revenue
interest). The Company does not believe, based upon information in its
possession, that its most recently delivered reserve report materially
overstates its oil and gas reserves, bearing in mind that reserves are evaluated
based upon estimates and assumptions with respect to which reasonable minds of
competent reserve engineers may differ.

      (b) All leases and agreements necessary for the conduct of the business of
the Company and the Subsidiaries are valid and subsisting, in full force and
effect and there exists no default or event or circumstance which with the
giving of notice or the passage of time or both would give rise to a default
under any such lease or leases, which would have a Material Adverse Effect on
the conduct of the business of the Company and the Subsidiaries.


                                       8
<PAGE>

      (c) The Oil and Gas Properties presently owned, leased or licensed by the
Company and the Subsidiaries, including, without limitation, all easements and
rights of way, include all properties necessary to permit the Company and the
Subsidiaries to conduct their business in all material respects in the same
manner as its business has been conducted prior to the Closing Date.

      (d) All of the properties of the Company and the Subsidiaries which are
reasonably necessary for the operation of their business are in good working
condition in all material respects and are maintained in accordance with prudent
business standards.

      3.12 No Material Misstatements. Taken as a whole, the written information,
statements, exhibits, certificates, documents and reports furnished to Investors
by the Company or any Subsidiary in connection with the negotiation of this
Agreement do not contain any material misstatement of fact or omit to state a
material fact or any fact necessary to make the statements contained therein not
materially misleading in the light of the circumstances in which made and with
respect to the Company or any Subsidiary. As of the Closing Date, there is no
fact peculiar to the Company or Subsidiary which has a Material Adverse Effect
relative to the Company or in the future is reasonably likely to have (so far as
the Company can now foresee) a Material Adverse Effect and which has not been
set forth in this Agreement or the other documents, certificates and statements
furnished to Investors by or on behalf of the Company or any Subsidiary prior
to, or on, the Closing Date in connection with the transactions contemplated
hereby.

      3.13 Investment Company Act. Neither the Company nor any Subsidiary is an
"investment company" or a company "controlled" by an "investment company,"
within the meaning of the Investment Company Act of 1940, as amended.

      3.14 Public Utility Holding Company Act. Neither the Company nor any
Subsidiary is a "holding company," or a "subsidiary company" of a "holding
company," or an "affiliate" of a "holding company" or of a "subsidiary company"
of a "holding company," or a "public utility" within the meaning of the Public
Utility Holding Company Act of 1935, as amended.

      3.15 Subsidiaries. Except as set forth on Schedule 3.15, the Company has
no Subsidiaries. Each Subsidiary is a corporation or limited partnership, duly
incorporated or organized, validly existing and in good standing under the laws
of its jurisdiction of incorporation or organization, if applicable, and has all
requisite corporate power and authority in all material respects to own, lease,
and operate its properties and to carry on its business as now being conducted.
Each Subsidiary is duly qualified to do business as a foreign corporation or
limited partnership, if applicable, and is in good standing in each jurisdiction
where such qualification is necessary, except where the failure to so qualify or
to be in good standing would not reasonably be expected to have a Material
Adverse Effect. There are outstanding (i) no securities of any Subsidiary of the
Company convertible into or exchangeable for shares of capital stock or other
voting securities of any Subsidiary of the Company and (ii) no options or other
rights to acquire from any Subsidiary of the Company, and no obligation of any
Subsidiary of the Company to issue or sell, any shares of capital stock or other
voting securities of any Subsidiary of the Company or any securities of any
Subsidiary of the Company convertible into or exchangeable for such capital
stock or voting securities.

      3.16 Defaults. Neither the Company nor any Subsidiary is in default nor
has any event or circumstance occurred which, but for the expiration of any
applicable grace period or the giving of notice, or both, would constitute a
default under any material agreement or instrument to which


                                       9
<PAGE>

the Company is a party or by which the Company is bound, which default would
have a Material Adverse Effect.

      3.17 Environmental Matters. Except for matters which are more likely than
not to not to have a Material Adverse Effect (or with respect to (c), (d) and
(e) below, where the failure to take such actions is more likely than not to not
have a Material Adverse Effect):

      (a) Neither any Oil and Gas Property of the Company or any of its
Subsidiaries nor the operations conducted thereon violate any order or
requirement of any court or Governmental Entity or any Environmental Laws;

      (b) Without limitation of clause (a) above, no Oil and Gas Property of the
Company or any of its Subsidiaries nor the operations currently conducted
thereon or, to the best knowledge of the Company, by any prior owner or operator
of such property or operation, are in violation of or subject to any existing,
pending or threatened action, suit, investigation, inquiry or proceeding by or
before any court or Governmental Entity or to any remedial obligations under
Environmental Laws;

      (c) All notices, permits, licenses or similar authorizations, if any,
required to be obtained or filed by the Company or any of its Subsidiaries in
connection with the operation or use of any and all Property of the Company and
each of its Subsidiaries, including without limitation present, or to the best
of Company's knowledge, past treatment, storage, disposal or release of a
hazardous substance or solid waste into the environment, have been duly obtained
or filed, and the Company and each Subsidiary thereof are in compliance with the
terms and conditions of all such notices, permits, licenses and similar
authorizations;

      (d) All hazardous substances, solid waste, and oil and gas exploration and
production wastes, if any, generated at any and all Oil and Gas Property of the
Company and each of its Subsidiaries have in the past, during the tenure of
ownership of the Company and its Subsidiaries and to the best of the Company's
knowledge, prior thereto, been transported, treated and disposed of in
accordance with Environmental Laws and so as not to pose an imminent and
substantial endangerment to public health or welfare or the environment, and, to
the best knowledge of the Company, all such transport carriers and treatment and
disposal facilities have been and are operating in compliance with Environmental
Laws and so as not to pose an imminent and substantial endangerment to public
health or welfare or the environment, and are not the subject of any existing,
pending or threatened action, investigation or inquiry by any Governmental
Entity in connection with any Environmental Laws;

      (e) The Company has taken all steps reasonably necessary to determine and
has determined that no hazardous substances, solid waste, or oil and gas
exploration and production wastes, have been disposed of or otherwise released
and there has been no threatened release of any hazardous substances on or to
any Oil and Gas Property of the Company or any of its Subsidiaries except in
compliance with Environmental Laws and so as not to pose an imminent and
substantial endangerment to public health or welfare or the environment; and

      (f) To the extent applicable, all Oil and Gas Property of the Company and
each of its Subsidiaries currently satisfies all design, operation, and
equipment requirements imposed by the OPA or scheduled as of the Closing Date to
be imposed by OPA during the term of this Agreement, and the Company does not
have any reason to believe that such Oil and Gas Property, to the extent


                                       10
<PAGE>

subject to OPA, will not be able to maintain compliance with the OPA
requirements during the term of this Agreement; and

      (g) Neither the Company nor any of its Subsidiaries has any known
contingent liability in connection with any release or threatened release of any
oil, hazardous substance or solid waste into the environment.

      3.18 Compliance with the Law. Neither the Company nor any Subsidiary has
violated any Governmental Requirement or failed to obtain any license, permit,
franchise or other governmental authorization necessary for the ownership of any
of its Oil and Gas Properties or the conduct of its business, which violation or
failure would have (in the event such violation or failure were asserted by any
Person through appropriate action) a Material Adverse Effect. Except for such
acts or failures to act as would not have a Material Adverse Effect, the Oil and
Gas Properties (and properties unitized therewith) have been maintained,
operated and developed in a good and workmanlike manner and in conformity with
all applicable laws and all rules, regulations and orders of all duly
constituted authorities having jurisdiction and in conformity with the
provisions of all leases, subleases or other contracts comprising a part of the
Hydrocarbon Interests and other contracts and agreements forming a part of the
Oil and Gas Properties; specifically in this connection, but subject to the
Material Adverse Effect qualification set forth above, (i) after the Closing
Date, no Oil and Gas Property is subject to having allowable production reduced
below the full and regular allowable (including the maximum permissible
tolerance) because of any overproduction (whether or not the same was
permissible at the time) prior to the Closing Date and (ii) none of the wells
comprising a part of the Oil and Gas Properties (or properties unitized
therewith) are deviated from the vertical more than the maximum permitted by
applicable laws, regulations, rules and orders, and such wells are, in fact,
bottomed under and are producing from, and the well bores are wholly within, the
Oil and Gas Properties (or in the case of wells located on properties unitized
therewith, such unitized properties).

      3.19 Insurance. Schedule 3.19 attached hereto contains an accurate and
complete description of all material policies of fire, liability, workmen's
compensation and other forms of insurance owned or held by the Company and each
Subsidiary as of the Closing Date. All such policies are in full force and
effect, all premiums with respect thereto covering all periods up to and
including the Closing Date have been paid, and no notice of cancellation or
termination has been received with respect to any such policy. Such policies are
sufficient for compliance with all requirements of law and of all agreements to
which the Company or any Subsidiary is a party; are valid, outstanding and
enforceable policies; provide adequate insurance coverage in at least such
amounts and against at least such risks (but including in any event public
liability) as are usually insured against in the same general area by companies
engaged in the same or a similar business for the assets and operations of the
Company and each Subsidiary; will remain in full force and effect through the
respective dates set forth in Schedule 3.19 with the payment of additional
premiums; and will not in any way be affected by, or terminate or lapse by
reason of, the transactions contemplated by this Agreement. Schedule 3.19
identifies all material risks, if any, which the Company, the Subsidiaries and
their respective Board of Directors or officers have designated as being self
insured. Neither the Company nor any Subsidiary has been refused any insurance
with respect to its assets or operations, nor has its coverage been limited
below usual and customary policy limits, by an insurance carrier to which it has
applied for any such insurance or with which it has carried insurance during the
last three years.


                                       11
<PAGE>

      3.20 Hedging Agreements. Schedule 3.20 sets forth, as of the Closing Date,
a true and complete list of all Hedging Agreements (including commodity price
swap agreements, forward agreements or contracts of sale which provide for
prepayment for deferred shipment or delivery of oil, gas or other commodities)
of the Company and each Subsidiary.

      3.21 Material Agreements. Set forth on Schedule 3.21 hereto is a complete
and correct list of all material agreements, leases, indentures, purchase
agreements, obligations in respect of letters of credit, guarantees, joint
venture agreements, and other instruments in effect or to be in effect as of the
Closing Date (other than Hedging Agreements) providing for, evidencing, securing
or otherwise relating to any material Debt of the Company or any Subsidiary, and
all obligations of the Company or any Subsidiary to issuers of surety or appeal
bonds (excluding operator's bonds, plugging and abandonment bonds, and similar
surety obligations obtained in the ordinary course of business) issued for
account of the Company or any such Subsidiary.

      3.22 Gas Imbalances. As of the Closing Date, except as set forth in the
most recent Reserve Report furnished to Investors, on a net basis there are no
gas imbalances, take or pay or other prepayments with respect to the Company's
or any Subsidiary's Hydrocarbon Interests which would require the Company or
such Subsidiary to deliver five percent (5%) or more of the monthly production
from the Company's and its Subsidiaries' Hydrocarbons produced on a monthly
basis from the Hydrocarbon Interests, at some future time without then or
thereafter receiving full payment therefor.

      3.23 Brokerage Fees. The Company has not retained any financial advisor,
broker, agent, or finder or paid or agreed to pay any financial advisor, broker,
agent, or finder on account of the sale by the Company and the purchase by
Investors of the Shares pursuant to this Agreement.

      3.24 SEC Filings. The Company has complied in all material respects with
its obligations to file with the Securities and Exchange Commission all forms,
reports, schedules, statements and other documents required to be filed by it
since May 9, 1997 under the Securities Act and the Exchange Act. All forms,
reports, schedules, statements, and other documents (including all amendments
thereto) filed by the Company with the Securities and Exchange Commission since
such date are herein collectively referred to as the "SEC Filings". The SEC
Filings, at the time filed, complied in all material respects with all
applicable requirements of federal securities laws. None of the SEC Filings,
including, without limitation, any financial statements or schedules included
therein, at the time filed or as same may have been amended, contained any
untrue statement of a material fact or omitted to state any material fact
required to be stated therein or necessary in order to make the statements
contained therein, in light of the circumstances under which they were made, not
misleading.

      3.25 Stockholder Approval. Neither the execution of this Agreement nor the
consummation of the transactions contemplated hereunder require the approval of
the stockholders of the Company under the applicable listing rules of the Nasdaq
Stock Market, Inc.; provided, however, that the Warrants shall not be
exercisable until after approval of the stockholders of the Company as set forth
therein.

                                   ARTICLE IV
                   REPRESENTATIONS AND WARRANTIES OF INVESTORS


                                       12
<PAGE>

      Each Investor represents and warrants to the Company that:

      4.1 Organization. MB is a corporation duly organized, validly existing and
in good standing under the laws of the State of Delaware. Each of ESC and MBP is
a limited partnership duly organized, validly existing and in good standing
under the laws of the State of Delaware. DOP is a limited partnership
(commanditaire vennootschap), duly organized, validly existing and in good
standing under the laws of the Netherlands Antilles. Each Investor has all
requisite corporate power and authority in all material respects to own, lease,
and operate its properties and to carry on its business as now being conducted.
No actions or proceedings to dissolve either Investor are pending or, to the
best knowledge of any Investor, threatened.

      4.2 Authority Relative to This Agreement. Each Investor has full corporate
or (if applicable) other power and authority to execute, deliver, and perform
this Agreement and execute, deliver and, where applicable, perform the Ancillary
Documents to which it is a party and to consummate the transactions contemplated
hereby and thereby. The execution, delivery, and performance by each Investor of
this Agreement and execution, delivery, and, where applicable, performance of
the Ancillary Documents to which it is a party, and the consummation by it of
the transactions contemplated hereby and thereby, have been duly authorized by
all necessary corporate (if applicable) action of such Investor. This Agreement
has been duly executed and delivered by each Investor and constitutes, and each
Ancillary Document executed or to be executed by each Investor has been, or when
executed will be, duly executed and delivered by such Investor and constitutes,
or when executed and delivered will constitute, a valid and legally binding
obligation of such Investor, enforceable against such Investor in accordance
with its terms, except that such enforceability may be limited by (i) applicable
bankruptcy, insolvency, reorganization, moratorium, and similar laws affecting
creditors' rights generally and (ii) general equitable principles (regardless of
whether such enforceability is considered in a proceeding in equity or at law).

      4.3 Noncontravention. The execution, delivery, and performance by each
Investor of this Agreement and the execution, delivery and, where applicable,
performance of Ancillary Documents to which it is a party and the consummation
by it of the transactions contemplated hereby and thereby do not and will not
(i) conflict with or result in a violation of any provision of MB's Certificate
of Incorporation or Bylaws or ESC's or MBP's Certificate of Limited Partnership
or partnership agreement, or DOP's Agreement of Limited Partnership, (ii)
conflict with or result in a violation of any provision of, or constitute (with
or without the giving of notice or the passage of time or both) a default under,
or give rise (with or without the giving of notice or the passage of time or
both) to any right of termination, cancellation, or acceleration under, any
bond, debenture, note, mortgage, indenture, lease, agreement or other instrument
or obligation to which any Investor is a party or by which Investor or any of
its properties may be bound, (iii) result in the creation or imposition of any
Encumbrance upon the properties of any Investor, or (iv) violate any Applicable
Law binding upon any Investor, except, in the case of clauses (ii), (iii) and
(iv) above, for any such conflicts, violations, defaults, terminations,
cancellations, accelerations, or Encumbrances which would not, individually or
in the aggregate, have a Material Adverse Effect on any Investor.

      4.4 Consents and Approvals. No consent, approval, order, or authorization
of, or declaration, filing, or registration with, any Governmental Entity is
required to be obtained or made by Investors in connection with the execution,
delivery, or performance by Investors of this Agreement. No consent or approval
of any person other than any Governmental Entity is required to be obtained or
made by any Investor in connection with the execution, delivery or performance


                                       13
<PAGE>

by Investors of this Agreement and the execution, delivery and, where
applicable, performance of the Ancillary Documents to which it is a party.

      4.5 Purchase for Investment. Each Investor understands that none of the
Shares, the Warrants or the Warrant Shares have been registered under the
Securities Act. Each Investor also understands that the Shares, the Warrants and
the Warrant Shares are being offered and sold pursuant to an exemption from
registration contained in the Securities Act based in part upon Investors'
representations contained in the Agreement. Each Investor hereby represents and
warrants as follows:

      (a) Investor Bears Economic Risk. Each Investor has substantial experience
in evaluating and investing in private placement transactions of securities in
companies similar to the Company so that it is capable of evaluating the merits
and risks of its investment in the Company and has the capacity to protect its
own interests. Without limiting the generality of the foregoing, each Investor
further represents that it has such knowledge regarding the oil and gas industry
and the business of the Company and the current circumstances surrounding such
industry and business that it is capable of evaluating the merits and risks of
the acquisition of the Shares, the Warrants and the Warrant Shares. Each
Investor must bear the economic risk of this investment indefinitely unless the
Shares, the Warrants or the Warrant Shares are registered pursuant to the
Securities Act, or an exemption from registration is available. Each Investor
understands that the Company has no present intention of registering the Shares,
the Warrants or the Warrant Shares. Each Investor also understands that there is
no assurance that any exemption from registration under the Securities Act will
be available and that, even if available, such exemption may not allow an
Investor to transfer all or any portion of the Shares, Warrants or Warrant
Shares under the circumstances, in the amounts or at the times an Investor might
propose.

      (b) Acquisition for Own Account. Each Investor is acquiring the Shares,
the Warrants and Warrant Shares for such Investor's own account for investment
only, and not with a view towards their distribution.

      (c) Investor Can Protect Its Interest. Each Investor represents that by
reason of its, or of its management's, business or financial experience, such
Investor has the capacity to protect its own interests in connection with the
transactions contemplated in this Agreement and the Ancillary Agreements.
Further, neither Investor is aware of no publication of any advertisement in
connection with the transactions contemplated in the Agreement.

      (d) Accredited Investor. Each Investor represents that it is an accredited
investor within the meaning of Regulation D under the Securities Act.

      (e) Company Information. Each Investor has had access to the Company's SEC
Filings and has had an opportunity to discuss the Company's business, management
and financial affairs with directors, officers and management of the Company and
has had the opportunity to review the Company's operations and facilities. Each
Investor has also had the opportunity to ask questions of, and receive answers
from, the Company and its management regarding the terms and conditions of this
investment. Each Investor hereby acknowledges and affirms that it has completed
its own independent investigation, analysis, and evaluation of the Company and
its subsidiaries, that it has made all such reviews and inspections of the
business, assets, results of operations, condition (financial or otherwise), and
prospects of the Company and its subsidiaries as it has deemed


                                       14
<PAGE>

necessary or appropriate, and that in making its decision to enter into this
Agreement and to consummate the transactions contemplated hereby it has relied
solely on its own independent investigation, analysis, and evaluation of the
Company and its subsidiaries, or that of its own independent advisers in
evaluating its investment in the Shares, Warrants and Warrant Shares.

      (f) Rule 144. Each Investor acknowledges and agrees that the Shares and
the Warrants, and, if issued, the Warrant Shares, must be held indefinitely
unless they are subsequently registered under the Securities Act or an exemption
from such registration is available. Each Investor has been advised or is aware
of the provisions of Rule 144, which permits limited resale of shares purchased
in a private placement subject to the satisfaction of certain conditions,
including, among other things: the availability of certain current public
information about the Company, the resale occurring following the required
holding period under Rule 144 and the number of shares being sold during any
three-month period not exceeding specified limitations.

      (g) Transfer Restrictions. Each Investor acknowledges and agrees that the
Shares, the Warrants and the Warrant Shares are subject to restrictions on
transfer as set forth in Section 5.5, below, and further understands that the
Shares, the Warrants and the Warrant Shares will not have been registered
pursuant to the Securities Act or any applicable state securities laws, that the
Shares, the Warrants and the Warrant Shares will be characterized as "restricted
securities" under federal securities laws, and that under such laws and
applicable regulations the Shares, the Warrants and the Warrant Shares cannot be
sold or otherwise disposed of without registration under the Securities Act or
an exemption therefrom. In this connection, each Investor represents that it is
familiar with Rule 144 promulgated under the Securities Act, as currently in
effect, and understands the resale limitations imposed thereby and by the
Securities Act. Appropriate stop transfer instructions may be issued to the
transfer agent for securities of the Company (or a notation may be made in the
appropriate records of the Company) in connection with the Shares, the Warrants
or the Warrant Shares.

      (h) Confirmation. The acquisition of the Shares by an Investor at the
Closing shall constitute such Investor's confirmation of the foregoing
representations.

      4.6 No Other Shares. Except for such rights as may be conferred on an
Investor under the First Purchase Agreement or by this Agreement and the
Ancillary Documents, Investors do not beneficially own, directly or indirectly,
any shares of capital stock or other securities of the Company or any of its
Subsidiaries.

      4.7 Financial Resources. Each Investor has the financial resources
available to it as are necessary to perform its obligations to acquire the
Shares pursuant to the terms of this Agreement.

      4.8 Brokerage Fees. No Investor has retained any financial advisor,
broker, agent, or finder or paid or agreed to pay any financial advisor, broker,
agent, or finder on account of the sale by the Company and the purchase by
Investors of the Shares pursuant to this Agreement.

                                    ARTICLE V
                              ADDITIONAL AGREEMENTS

      5.1 Reasonable Best Efforts.


                                       15
<PAGE>

      (a) Each party hereto agrees that it will use its reasonable best efforts
to take, or cause to be taken, all action and to do, or cause to be done, all
things reasonably necessary, proper, or advisable under Applicable Laws to
consummate the transactions contemplated by this Agreement, including, without
limitation, (i) cooperation in determining whether any consents, approvals,
orders, authorizations, waivers, declarations, filings, or registrations of or
with any Governmental Entity or third party are required in connection with the
consummation of the transactions contemplated hereby; (ii) reasonable best
efforts to obtain any such consents, approvals, orders, authorizations, and
waivers and to effect any such declarations, filings, and registrations; (iii)
reasonable best efforts to cause to be lifted or rescinded any injunction or
restraining order or other order adversely affecting the ability of the parties
to consummate the transactions contemplated hereby; (iv) reasonable best efforts
to defend, and cooperation in defending, all lawsuits or other legal proceedings
challenging this Agreement or the consummation of the transactions contemplated
hereby; and (v) the execution of any additional instruments necessary to
consummate the transactions contemplated hereby.

      (b) Without limiting the generality of Section 5.1(a), to the extent
required by the HSR Act, each of the parties hereto shall (i) file or cause to
be filed, as promptly as practicable but in no event later than five (5)
consecutive Business Days after the execution and delivery of this Agreement,
with the Federal Trade Commission and the United States Department of Justice,
all reports and other documents required to be filed by such party under the HSR
Act concerning the transactions contemplated hereby and (ii) promptly comply
with or cause to be complied with any requests by the Federal Trade Commission
or the United States Department of Justice for additional information concerning
such transactions, in each case so that the waiting period applicable to this
Agreement and the transactions contemplated hereby under the HSR Act shall
expire as soon as practicable after the execution and delivery of this
Agreement. Each party hereto agrees to request, and to cooperate with the other
party or parties in requesting, early termination of any applicable waiting
period under the HSR Act. Notwithstanding the foregoing, if any report or other
document is required to be filed by any Investor under the HSR Act solely as a
result of the purchase and sale of the Shares or the Warrants (with no regard to
any other securities held by such Investor or its Affiliates), the Company shall
pay any and all fees and expenses, including filing fees and legal expenses,
incurred by such Investor in connection with the filing of such reports or other
documents and any other actions required to comply with the provisions of the
HSR Act.

      5.2 Press Releases. Except as may be required by Applicable Law or by the
rules of any national securities exchange or registered securities association,
prior to the Closing, neither Investors nor the Company shall issue any press
release with respect to this Agreement or the transactions contemplated hereby
without the prior consent of the other party (which consent shall not be
unreasonably withheld under the circumstances). Any such press release required
by Applicable Law or by the rules of any national securities exchange or
registered securities association shall only be made after reasonable notice to
the other party.

      5.3 Fees and Expenses. Except as otherwise expressly provided in this
Agreement, all fees and expenses, including fees and expenses of counsel,
financial advisors and accountants, incurred in connection with this Agreement
and the transactions contemplated hereby shall be paid by the party incurring
such fee or expense.

      5.4 Survival. The representations and warranties made herein shall survive
the Closing, regardless of any investigation made by or on behalf of any party,
until the second anniversary of the Closing Date; provided, however, the
representations and warranties contained in Sections 3.9,


                                       16
<PAGE>

3.10 and 3.18 shall survive until the expiration of the applicable statute
limitations relating to the subject matters of such representations and
warranties (the "Survival Date".) All statements as to factual matters contained
in any certificate or other instrument delivered by or on behalf of the Company
pursuant hereto in connection with the transactions contemplated hereby shall be
deemed to be representations and warranties by the Company herein for purposes
of this Section 5.5. No action may be brought with respect to a breach of any
representation or warranty after the Survival Date unless, prior to such time,
the party seeking to bring such an action has notified the other parties of such
claim, specifying in reasonable detail the nature of the loss suffered.

      5.5 Transfer Restrictions.

      (a) Notwithstanding any provision contained in this Agreement to the
contrary, each Investor agrees that it will not, directly or indirectly, sell,
assign, transfer, pledge, encumber, or otherwise dispose of any of the Shares,
Warrants or Warrant Shares except:

            (i) In compliance with Rule 144; provided, however, that the
      Investor shall provide the Company with copies of all filings made with
      the Securities and Exchange Commission with respect to sales of securities
      under Rule 144 and with such other information and documents as the
      Company shall reasonably require in order to assure full compliance with
      Rule 144; or

            (ii) Pursuant to a no-action letter or other interpretive statement
      or release of the Securities and Exchange Commission to the effect that
      the proposed sale or other disposition may be effected without
      registration under the Securities Act; or

            (iii) Pursuant to an applicable exemption (other than Rule 144)
      under the Securities Act; provided, however, that the Investor shall have
      furnished the Company with an opinion of counsel, which opinion and
      counsel shall be reasonably acceptable to the Company, to the effect that
      such disposition does not require registration of such securities under
      the Securities Act; provided further, however, that no opinion of counsel
      shall be required in the case of a transfer to an affiliate (as defined in
      Rule 405 of the Securities Act) of Investor if such affiliate shall have
      furnished the Company with the representations contained in Section 4.5 of
      this Agreement and shall have agreed with the Company to be subject to the
      terms of this Agreement to the same extent as if an original holder of
      securities pursuant hereto.

            (iv) Pursuant to an effective registration statement filed under the
      Securities Act.

      (b) It is agreed and understood by each Investor that the certificates or
instruments representing the Shares, Warrants and Warrant Shares shall each be
stamped or otherwise imprinted with a legend in substantially the following
form:

      "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY APPLICABLE STATE SECURITIES
LAWS, AND MAY NOT BE SOLD OR TRANSFERRED IN THE ABSENCE OF SUCH REGISTRATION OR
AN EXEMPTION THEREFROM. SUCH SECURITIES ARE SUBJECT TO THE RESTRICTIONS AND
PRIVILEGES SPECIFIED IN A SECURITIES PURCHASE AGREEMENT, DATED AS OF


                                       17
<PAGE>

MARCH 5, 2001, BETWEEN BRIGHAM EXPLORATION COMPANY AND THE INITIAL HOLDERS OF
SECURITIES NAMED THEREIN, A COPY OF WHICH IS ON FILE WITH THE SECRETARY OF
BRIGHAM EXPLORATION COMPANY AND WILL BE FURNISHED WITHOUT CHARGE TO THE HOLDER
HEREOF UPON WRITTEN REQUEST, AND THE HOLDER OF THIS CERTIFICATE AGREES TO BE
BOUND THEREBY."

      5.6 Transaction Fee. The sum of One Hundred Thousand Dollars ($100,000),
plus all reasonable out-of-pocket expenses incurred by the Investors, including
attorneys fees, shall be paid by the Company to Investors on the Closing Date
upon Closing.

      5.7 Action at Annual Meeting of Stockholders.

      (a) The Company shall take all action necessary in accordance with
applicable law and the Company's Certificate of Incorporation and Bylaws to have
the Company's common stockholders, at the Annual Meeting to be held on or before
May 31, 2001, consider and approve the matters described in the Stockholders
Voting Agreement dated March 1, 2001, by and among the Company and certain of
its stockholders, such approval, when so obtained, shall be referred to as the
"Stockholder Approval". The Company shall not mail or otherwise distribute the
proxy statement or information statement (or any related proxy materials or
amendments or supplements thereto, if any) relating to the Annual Meeting to its
stockholders without consultation with Investors and their counsel, and such
proxy statement or information statement and such other items shall, to the
extent same relate to the subject matter of the Stockholders Voting Agreement,
be in such form as Investors and their counsel shall approve (such approval not
to unreasonably withheld).

      (b) The Company shall provide a certificate signed by a duly authorized
officer of the Company to each holder of Warrants promptly after the Annual
Meeting certifying whether the Stockholder Approval has been obtained at the
Annual Meeting and whether the Warrants are then exercisable.

      5.8 Capitalization Certification. The Company shall provide, immediately
after the Closing, a schedule reflecting the capitalization of the Company as of
immediately after the transactions contemplated by this Agreement, including at
least the information provided in the representation in Section 3.2 and
indicating the number of fully-diluted shares of Common Stock, and certified by
the Chief Financial Officer of the Company (the "Certificate"). Until the second
anniversary of the Closing Date, the Company shall amend the Certificate at any
time after the Closing to reflect any changes to the Certificate (which in all
cases shall reflect the capitalization of the Company as of immediately after
the transactions contemplated by this Agreement) if the Company learns that the
Certificate is incorrect or not complete in any respect. Notwithstanding any
provision contained in this Agreement, the Registration Rights Agreement and the
Warrant Certificate, if the number of fully-diluted shares of Common Stock as
reflected in the Certificate at any time is more than 34,608 shares in excess of
34,607,870 shares of Common Stock, then the number of shares purchasable upon
exercise of the Warrant shall be increased to a number of shares equal to 6.08%
of the fully-diluted shares of Common Stock. Upon any such adjustment to the
number of shares to be acquired upon exercise of the Warrant, the holder of the
Warrant shall deliver to the Company the Warrant Certificate for cancellation
and immediately thereupon the Company shall issue a new Warrant Certificate
reflecting the adjusted number of shares purchasable thereunder. For purposes of
this Section 5.8, the term "fully-diluted shares of Common Stock" means the sum
of shares of Common Stock outstanding, plus all shares of Common Stock issuable


                                       18
<PAGE>

pursuant to (i) the conversion or exchange of securities that are convertible
into or exchangeable for shares of Common Stock or the exercise of any option,
warrant or other right to acquire shares of Common Stock from the Company, (ii)
the conversion or exchange of any security that is convertible into or
exchangeable for any securities referenced in 5.8(i) or the exercise of any
security that is exercisable for any securities referenced in 5.8(i), and (iii)
the exercise of any rights under any agreement regarding equity equivalents,
interests in the ownership or earnings, or other similar rights of or with
respect to the Company.

      5.9 Restrictions on Certain Actions. Investors hereby agree (subject to
the occurrence of the Closing ) that for a period of one year from the Closing
Date, Investors shall not, without the prior written approval of the Board of
Directors of the Company, in any manner, directly or indirectly, acquire for
their own accounts any Voting Securities (or beneficial ownership thereof),
except by way of stock dividends or other distributions or offerings made
available to holders of Voting Securities generally and except for acquisitions
of Common Stock upon exercise of the Warrants (as defined herein) or upon
exercise of the Warrants (as defined in the First Purchase Agreement). The
parties acknowledge that various Affiliates of the Investors are brokers or
investment advisors or are otherwise engaged in transactions in securities
generally as part of their ordinary course of business. The parties agree that
actions taken by Affiliates of the Investors as such in the ordinary course of
their business, such as acting as broker for clients acquiring shares of Voting
Securities, shall not be deemed a violation of any of the provisions of this
Section 5.9.

                                   ARTICLE VI
                    CONDITIONS TO OBLIGATIONS OF THE COMPANY

      The obligations of the Company to consummate the transactions contemplated
by this Agreement shall be subject to the fulfillment on or prior to the Closing
Date of each of the following conditions:

      6.1 Representations and Warranties. All the representations and warranties
of Investors contained in this Agreement shall be true and correct in all
material respects, except as affected by transactions contemplated or permitted
by this Agreement.

      6.2 Covenants and Agreements. Investors shall have performed and complied
with in all material respects all covenants and agreements required by this
Agreement to be performed or complied with by them on or prior to the Closing
Date.

      6.3 HSR Act. All waiting periods (and any extensions thereof) applicable
to this Agreement and the transactions contemplated hereby under the HSR Act
shall have expired or been terminated.

      6.4 Legal Proceedings. No Proceeding shall, on the Closing Date, be
pending or threatened seeking to restrain, prohibit or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

      6.5 Consents. All consents, approvals, orders, authorizations and waivers
of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for


                                       19
<PAGE>

the consummation of the transactions contemplated hereby, shall have been
obtained or made, and all thereof shall be in full force and effect at the time
of Closing.

                                   ARTICLE VII
                     CONDITIONS TO OBLIGATIONS OF INVESTORS

      The obligations of Investors to consummate the transactions contemplated
by this Agreement shall be subject to the fulfillment on or prior to the Closing
Date of each of the following conditions:

      7.1 Representations and Warranties. All the representations and warranties
of the Company contained in this Agreement shall be true and correct in all
material respects, except as affected by transactions contemplated or permitted
by this Agreement (or the announcement thereof).

      7.2 Covenants and Agreements. The Company shall have performed and
complied with in all material respects all covenants and agreements required by
this Agreement to be performed or complied with by it on or prior to the Closing
Date.

      7.3 HSR Act. All waiting periods (and any extensions thereof) applicable
to this Agreement and the transactions contemplated hereby under the HSR Act
shall have expired or been terminated.

      7.4 Legal Proceedings. No Proceeding shall, on the Closing Date, be
pending or threatened seeking to restrain, prohibit or obtain damages or other
relief in connection with this Agreement or the consummation of the transactions
contemplated hereby.

      7.5 Consents. All consents, approvals, orders, authorizations and waivers
of, and all declarations, filings and registrations with, third parties
(including Governmental Entities) required to be obtained or made by or on the
part of the parties hereto, or otherwise reasonably necessary for the
consummation of the transactions contemplated hereby, shall have been obtained
or made, and all thereof shall be in full force and effect at the time of
Closing.

      7.6 Legal Opinion. Thompson & Knight, L.L.P., counsel to the Company,
shall have delivered to the Investors a legal opinion satisfactory in form and
substance to the Investors.

      7.7 Closing Deliveries. The Escrow Agent shall have received the
certificates, instruments and documents required to be delivered by the Company
by Section 2.2.

                                  ARTICLE VIII
                                    COVENANTS

      8.1 Affirmative Covenants. The Company covenants and agrees that, so long
as any of the Shares are outstanding:

            (a) Financial Statements and Other Reports. The Company shall
      deliver, or shall cause to be delivered, to the Investors:

                  (i) Annual Financial Statements. As soon as available and in
            any event within 90 days after the end of each fiscal year of the
            Company and its consolidated


                                       20
<PAGE>

            Subsidiaries for such fiscal year, and the related consolidated and
            unaudited consolidating balance sheets of the Company and its
            consolidated Subsidiaries as at the end of such fiscal year, and
            setting forth in each case in comparative form the corresponding
            figures for the preceding fiscal year, and accompanied by the
            related opinion of independent public accountants which opinion
            shall state that said financial statements fairly present the
            consolidated financial condition and results of operations of the
            Company and its consolidated Subsidiaries as at the end of, and for,
            such fiscal year and that such financial statements have been
            prepared in accordance with GAAP except for such changes in such
            principles with which the independent public accountants shall have
            concurred.

                  (ii) Quarterly Financial Statements. As soon as available and
            in any event within 60 days after the end of each of the first three
            fiscal quarterly periods of each fiscal year of the Company,
            consolidated statements of income, stockholders' equity, changes in
            financial position and cash flow of the Company and its consolidated
            Subsidiaries for such period and for the period from the beginning
            of the respective fiscal year to the end of such period, and the
            related consolidated and consolidating balance sheets as at the end
            of such period.

                  (iii) Monthly Financial Statements. As soon as available and
            in any event within forty-five (45) days after the end of each
            calendar month that is not also the end of one of the Company's
            first three fiscal quarterly periods or of the Company's fiscal
            year, consolidated statements of income and changes in financial
            position of the Company and its consolidated Subsidiaries for such
            period and for the period from the beginning of the respective
            fiscal year to the end of such period, and the related consolidated
            balance sheets as at the end of such period and beginning statements
            setting forth in each case in comparative form the corresponding
            figures for the corresponding period in the preceding fiscal year.

            (b) SEC Filings, Etc. Promptly, upon its becoming available, each
      financial statement, report, notice or proxy statement sent by the Company
      to stockholders generally.

            (c) Engineering Reports. Not later than April 30 and October 30 of
      each year, the Company shall furnish to the Investors a Reserve Report as
      of the preceding December 31 and June 30, respectively. The Reserve Report
      to be furnished in April of each year shall be prepared by certified
      independent petroleum engineers or other independent petroleum
      consultant(s) and the Reserve Reports to be furnished in October of each
      year shall be prepared by or under the supervision of the chief engineer
      or Vice President of Operations of the Company who shall certify such
      Reserve Report to have been prepared in accordance with the procedures
      used in the immediately preceding April Reserve Report. At Company's
      option, the Reserve Report to be furnished in October of each year may
      instead consist of a report from the independent petroleum engineers
      referred to above on any new wells and a roll-forward by Company on any
      wells previously reported in the Reserve Report described in the
      immediately preceding April.

            (d) Exchange Act Reports. At all times (i) timely file all reports
      required to be filed by the Company under Section 13(d) or Section 15 of
      the Exchange Act and the rules and regulations thereunder, and (ii) if the
      Company is no longer subject to the requirements


                                       21
<PAGE>

      of the Exchange Act, provide holders of the Shares reports in
      substantially the same form and at the same times as would be required if
      the Company were subject to the Exchange Act.

            (e) Nasdaq Listing. Maintain at all times a valid listing for the
      Common Stock on a national securities exchange or the National Market
      System or SmallCap Market of the Nasdaq Stock Market, Inc.

            (f) Further Assurances. The Company at its expense will promptly
      execute and deliver to the Investors upon request all such other
      documents, agreements and instruments to comply with or accomplish the
      covenants and agreements of the Company in this Agreement or any other
      agreements and documents executed by and between the Company and the
      Investors.

      8.2 Negative Covenants. The Company covenants and agrees that, so long as
at least 10% of the Shares are outstanding, without the prior written consent of
the persons holding 75% of the then outstanding Shares:

            (a) Dividends, Distributions and Redemptions. The Company will not
      declare or pay any dividend, purchase, redeem, or otherwise acquire for
      value any, other than those issued under the First Purchase Agreement,
      Parity Security or Junior Security now or hereafter outstanding, return
      any capital or make a distribution of its assets to its stockholders.

            (b) Nature of Business. Neither the Company nor Brigham Oil & Gas,
      L.P. will allow any material change to be made in the character of its
      business as an independent oil and gas exploration and production company.

            (c) Environmental Matters. Neither the Company nor any Subsidiary
      will knowingly cause or permit any of its Property to be in violation of,
      or knowingly do anything or permit anything to be done which will subject
      any such Property to any remedial obligations under any Environmental
      Laws, assuming disclosure to the applicable Governmental Authority of all
      relevant facts, conditions and circumstances, if any, pertaining to such
      Property where such violations or remedial obligations would have a
      Material Adverse Effect.

            (d) Transactions with Affiliates. Neither the Company nor any
      Subsidiary will enter into any transaction, including, without limitation,
      any purchase, sale, lease or exchange of Property or the rendering of any
      service, with any Affiliate unless such transactions are otherwise not in
      violation of this Agreement, and are upon fair and reasonable terms no
      less favorable to it than it would obtain in a comparable arm's length
      transaction with a Person not an Affiliate.

                                   ARTICLE IX
                              AMENDMENT AND WAIVER

      9.1 Amendment. This Agreement may not be amended except by an instrument
in writing signed by or on behalf of all the parties hereto.


                                       22
<PAGE>

      9.2 Waiver. No failure or delay by a party hereto in exercising any right,
power, or privilege hereunder shall operate as a waiver thereof nor shall any
single or partial exercise thereof preclude any other or further exercise
thereof or the exercise of any other right, power, or privilege. The provisions
of this Agreement may not be waived except by an instrument in writing signed by
or on behalf of the party against whom such waiver is sought to be enforced.

                                    ARTICLE X
                                  MISCELLANEOUS

      10.1 Notices. All notices, requests, demands, and other communications
required or permitted to be given or made hereunder by any party hereto shall be
in writing and shall be deemed to have been duly given or made if (i) delivered
personally, (ii) sent by prepaid overnight courier service, or (iii) sent by
telecopy or facsimile transmission, answer back requested, to the parties at the
following addresses (or at such other addresses as shall be specified by the
parties by like notice):

      (a)   If to the Company:
            Brigham Exploration Company
            6300 Bridge Point Parkway
            Building 2, Suite 500
            Austin, TX  78730
            Attention: Chief Financial Officer
            Telefax:  512-427-3400

      with a copy to:

            Thompson & Knight L.L.P.
            1700 Pacific Avenue, Suite 3300
            Dallas, Texas 75201
            Attention: Joe Dannenmaier
            Telefax: 214-969-1751

      (b)   If to MB, MBP or ESC, to such Investor at:
            277 Park Avenue
            New York, New York 10172
            Attention: Nicole Arnaboldi, Ivy Dodes
            Telefax: 212-892-7272

      with a copy to:

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

      (c)   If to DOP:
            c/o DLJ Offshore Management N.V.
            John B. Gorsiraweg 14


                                       23
<PAGE>

            Willemstad, Curacao
            Netherlands, Antilles
            Fax: 011-599-961-4129

      with a copy to:

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

Such notices, requests, demands, and other communications shall be effective (i)
if delivered personally or sent by courier service, upon actual receipt by the
intended recipient, or (ii) if sent by telecopy or facsimile transmission, when
the answer back is received.

      10.2 Entire Agreement. This Agreement, together with the Schedules,
Exhibits, Annexes, and other writings referred to herein or delivered pursuant
hereto, constitutes the entire agreement between the parties hereto with respect
to the subject matter hereof and supersedes all prior agreements and
understandings, both written and oral, between the parties and their Affiliates
with respect to the subject matter hereof.

      10.3 Binding Effect; Assignment; No Third Party Benefit. This Agreement
shall be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns. Except as otherwise expressly
provided in this Agreement, neither this Agreement nor any of the rights,
interests or obligations hereunder shall be assigned by any of the parties
hereto without the prior written consent of the other party. Nothing in this
Agreement, express or implied, is intended to or shall confer upon any person
other than the parties hereto, and their respective heirs, legal
representatives, successors, and permitted assigns, any rights, benefits or
remedies of any nature whatsoever under or by reason of this Agreement.

      10.4 Severability. If any provision of this Agreement is held to be
unenforceable, then this Agreement shall be considered divisible and such
provision shall be deemed inoperative to the extent it is deemed unenforceable,
and in all other respects this Agreement shall remain in full force and effect
to the maximum extent permitted by Applicable Law.

      10.5 Injunctive Relief. The parties hereto acknowledge and agree that
irreparable damage would occur in the event any of the provisions of this
Agreement were not performed in accordance with their specific terms or were
otherwise breached. It is accordingly agreed that the parties shall be entitled
to an injunction or injunctions to prevent breaches of the provisions of this
Agreement, and shall be entitled to enforce specifically the provisions of this
Agreement, in any court of the United States or any state thereof having
jurisdiction, in addition to any other remedy to which the parties may be
entitled under this Agreement or at law or in equity.

      10.6 Governing Law. THIS AGREEMENT SHALL BE GOVERNED BY AND CONSTRUED AND
ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK, WITHOUT REGARD TO
THE PRINCIPLES OF CONFLICTS OF LAWS THEREOF.


                                       24
<PAGE>

      10.7 Jurisdiction. Except as otherwise expressly provided in this
Agreement, any suit, action or proceeding seeking to enforce any provision of,
or based on any matter arising out of or in connection with, this Agreement or
the transactions contemplated hereby may be brought in the United States
District Court for the Southern District of New York or any other New York State
court sitting in New York City, and each of the parties hereby consents to the
jurisdiction of such courts (and of the appropriate appellate courts therefrom)
in any such suit, action or proceeding and irrevocably waives, to the fullest
extent permitted by law, any objection which it may now or hereafter have to the
laying of the venue of any such suit, action or proceeding in any such court or
that any such suit, action or proceeding which is brought in any such court has
been brought in an inconvenient forum. Process in any such suit, action or
proceeding may be served on any party anywhere in the world, whether within or
without the jurisdiction of any such court. Without limiting the foregoing, each
party agrees that service of process on such party as provided in Section 10.01
shall be deemed effective service of process on such party.

      10.8 Binding Arbitration. In the event of any dispute, difference or
question arising out of relating to the release of the Shares, Warrants,
purchase price for the Shares and Warrants, and interest thereon accruing while
such amounts are deposited under the Escrow Agreement ("Dispute") between any of
the parties hereto ("Disputing Parties") which cannot be otherwise resolved by
the Disputing Parties themselves, the Dispute will be settled by arbitration by
an arbitrator mutually acceptable to the Disputing Parties in an arbitration
proceeding conducted in Houston, Texas in accordance with the rules existing at
the date hereof of the American Arbitration Association. If the Disputing
Parties hereto cannot agree on an arbitrator within ten (10) days of the
initiation of the arbitration proceeding, an arbitrator shall be selected for
the Disputing Parties by the American Arbitration Association. The Disputing
Parties shall use their best efforts to have the arbitral proceeding conclude
and a judgement rendered by the arbitrator within forty (40) business days of
the initiation of the arbitration proceeding. The decision of such arbitrator
shall be final and judgement upon the award rendered by the arbitration may be
entered in any court having jurisdiction thereof, and the costs (including,
without limitation, reasonable fees and expenses of counsel and experts for the
Disputing Parties) of such arbitration (including the cost to enforce or
preserve the rights awarded in the arbitration) shall be borne by the Disputing
Party whom the decision of the arbitrator is against. If the decision of the
arbitrator is not clearly against one of the Disputing Parties, or the decisions
of the arbitrator is against more than one Disputing Party on one or more
issues, costs of such arbitration shall be borne equally by the Disputing
Parties.

      10.9 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.

                                   ARTICLE XI
                                   DEFINITIONS

      11.1 Certain Defined Terms. As used in this Agreement, each of the
following terms has the meaning given it in this Article:


                                       25
<PAGE>

      "Affiliate" of any Person shall mean (i) any Person directly or indirectly
controlled by, controlling or under common control with such first Person, (ii)
any director or officer of such first Person or of any Person referred to in
clause (i) above and (iii) if any Person in clause (i) above is an individual,
any member of the immediate family (including parents, spouse and children) of
such individual and any trust whose principal beneficiary is such individual or
one or more members of such immediate family and any Person who is controlled by
any such member or trust. For purposes of this definition, any Person which owns
directly or indirectly 50% or more of the securities having ordinary voting
power for the election of directors or other governing body of a corporation or
50% or more of the partnership or other ownership interests of any other Person
(other than as a limited partner of such other Person) will be deemed to
"control" (including, with its correlative meanings, "controlled by" and "under
common control with") such corporation or other Person.

      "Ancillary Documents" means each agreement, instrument, and document
(other than this Agreement) executed or to be executed by the Company or any
Investor in connection with the sale and purchase of the Shares and Warrants and
the other transactions contemplated by this Agreement.

      "Applicable Law" means any statute, law, rule, or regulation or any
judgment, order, writ, injunction, or decree of any Governmental Entity to which
a specified person or property is subject.

      "Board Representative" means any representative of Investors on the Board,
to the extent (a) nominated to the Board pursuant to Article VIII of the First
Purchase Agreement and (b) acting in his or her capacity as a member of the
Board.

      "BOG" means Brigham Oil & Gas, L.P.

      "Business Day" shall mean any day other than a Saturday, a Sunday, or a
day on which banking institutions in Austin, Texas are authorized or obligated
by law or executive order to close.

      "Code" shall mean the Internal Revenue Code of 1986, as amended from time
to time and any successor statute.

      "Common Stock" means the common stock, par value of $.01 per share, of the
Company, and such other class of securities as shall represent the common equity
of the Company.

      "Debt" shall mean, for any Person the sum of the following (without
duplication): (i) all obligations of such Person for borrowed money or evidenced
by bonds, debentures, notes or other similar instruments (including principal,
interest, fees and charges); (ii) all obligations of such Person (whether
contingent or otherwise) in respect of bankers acceptances, letters of credit,
surety or other bonds and similar instruments; (iii) all obligations of such
Person to pay the deferred purchase price of Property or services (other than
for borrowed money) excluding Trade Payables; (iv) all obligations under leases
which shall have been, or should have been, in accordance with GAAP, recorded as
capital leases in respect of which such Person is liable (whether contingent or
otherwise); (v) all obligations under leases (other than capital leases and oil
and gas leases) which require such Person or its Affiliate to make payments
exceeding $100,000 over the term of such lease, including payments at
termination, which are substantially equal to at least eighty percent (80%) of
the purchase price of the Property subject to such lease plus interest at an
imputed market


                                       26
<PAGE>

rate of interest; (vi) all Debt (as described in the other clauses of this
definition) of others secured by a Lien on any asset of such Person, whether or
not such Debt is assumed by such Person; (vii) all Debt (as described in the
other clauses of this definition) of others guaranteed by such Person or in
which such Person otherwise assures a creditor against loss of the Debt of
others; (viii) all obligations or undertakings of such Person to maintain or
cause to be maintained the financial position or covenants of others including
without limitation agreements expressed as an agreement to purchase the Debt or
Property of others or otherwise; (x) obligations to pay for goods or services
whether or not such goods or services are actually received or utilized by such
Person; (xi) any capital stock of such Person in which such Person has a
mandatory obligation to redeem such stock; (xii) the undischarged balance of any
production payment created by such Person or for the creation of which such
Person directly or indirectly received payment; and (xiii) all obligations of
such Person under Hedging Agreements.

      "Encumbrances" means liens, charges, pledges, options, mortgages, deeds of
trust, security interests, claims, restrictions (whether on voting, sale,
transfer, disposition, or otherwise), easements, and other encumbrances of every
type and description, whether imposed by law, agreement, understanding, or
otherwise.

      "Environmental Laws" shall mean any and all Governmental Requirements
pertaining to the environment in effect in any and all jurisdictions in which
the Company or any Subsidiary is conducting or at any time has conducted
business, or where any Oil and Gas Property of the Company or any Subsidiary is
located, including without limitation, the Oil Pollution Act of 1990 ("OPA"),
the Clean Air Act, as amended, the Comprehensive Environmental, Response,
Compensation, and Liability Act of 1980 ("CERCLA"), as amended, the Federal
Water Pollution Control Act, as amended, the Occupational Safety and Health Act
of 1970, as amended, the Resource Conservation and Recovery Act of 1976
("RCRA"), as amended, the Safe Drinking Water ACT, as amended, the Toxic
Substances Control Act, as amended, the Superfund Amendments and Reauthorization
Act of 1986, as amended, the Hazardous Materials Transportation Act, as amended,
and other environmental conservation or protection laws. As used in the
provisions hereof relating to Environmental Laws, the term "oil" shall have the
meaning specified in OPA, the terms "hazardous substance" and "release" (or
"threatened release") have the meanings specified in CERCLA, and the terms
"solid waste" and "disposal" (or "disposal") have the meanings specified in
RCRA; provided that to the extent the laws of the state in which any Oil and Gas
Property of the Company or any Subsidiary is located establish a meaning for
"oil", "hazardous substance," "release," "solid waste" or "disposal" which is
broader than that specified in either OPA, CERCLA or RCRA, such broader meaning
shall apply.

      "ERISA" shall mean the Employee Retirement Income Security Act of 1974, as
amended from time to time and any successor statute.

      "ERISA Affiliate" shall mean each trade or business (whether or not
incorporated) which together with the Company or any Subsidiary of the Company
would be deemed to be a "single employer" within the meaning of section
4001(b)(1) of ERISA or subsections (b), (c), (m) or (o) of section 414 of the
Code.

      "Excepted Liens" shall mean: (i) Liens for taxes, assessments or other
governmental charges or levies not yet due or which are being contested in good
faith by appropriate action and for which adequate reserves have been maintained
in accordance with GAAP; (ii) Liens in connection with


                                       27
<PAGE>

workmen's compensation, unemployment insurance or other social security, old age
pension or public liability obligations not yet due or which are being contested
in good faith by appropriate action and for which adequate reserves have been
maintained in accordance with GAAP; (iii) operators', vendors', carriers',
warehousemen's, repairmen's, mechanics', workmen's, materialmen's, construction
or other like Liens arising by operation of law in the ordinary course of
business or incident to the exploration, development, operation and maintenance
of Oil and Gas Properties or customary landlord's liens, each of which is in
respect of obligations that have not been outstanding more than 90 days or which
are being contested in good faith by appropriate proceedings and for which
adequate reserves have been maintained in accordance with GAAP; (iv) any Liens
reserved in leases or farmout agreements for rent or royalties and for
compliance with the terms of the farmout agreements or leases in the case of
leasehold estates, to the extent that any such Lien referred to in this clause
does not materially impair the use of the property covered by such Lien for the
purposes for which such property is held or materially impair the value of such
property subject thereto; (v) encumbrances (other than to secure the payment of
borrowed money or the deferred purchase price of property or services),
easements, restrictions, servitudes, permits, conditions, covenants, exceptions
or reservations in any rights of way or other property for the purpose of roads,
pipelines, transmission lines, transportation lines, distribution lines for the
removal of gas, oil, coal or other minerals or timber, and other like purposes,
or for the joint or common use of real estate, rights of way, facilities and
equipment, and defects, irregularities, zoning restrictions and deficiencies in
title of any rights of way or other property which in the aggregate do not
materially impair the use of such rights of way or other property for the
purposes of which such rights of way and other property are held or materially
impair the value of such property subject thereto; (vi) deposits of cash or
securities to secure the performance of bids, trade contracts, leases, statutory
obligations and other obligations of a like nature incurred in the ordinary
course of business; and (vii) Liens (including "Excepted Liens") permitted by or
created pursuant to the Senior Credit Agreement and Liens permitted by or
created pursuant to the Subordinated Credit Agreement.

      "Exchange Act" means the Securities Exchange Act of 1934, as amended.

      "First Purchase Agreement" means that certain Securities Purchase
Agreement dated as of November 1, 2000, between the Company, MB and ESC.

      "Governmental Entity" means any court or tribunal in any jurisdiction
(domestic or foreign) or any public, governmental, or regulatory body, agency,
department, commission, board, bureau, or other authority or instrumentality
(domestic or foreign).

      "Governmental Requirement" shall mean any law, statute, code, ordinance,
order, determination, rule, regulation, judgment, decree, injunction, franchise,
permit, certificate, license, authorization or other directive or requirement
(in the case of banking regulatory authorities whether or not having the force
of law), including, without limitation, Environmental Laws, energy regulations
and occupational, safety and health standards or controls, of any Governmental
Entity.

      "Hedging Agreements" shall mean any commodity, interest rate or currency
swap, cap, floor, collar, forward agreement or other exchange or protection
agreements or any option with respect to any such transaction.

      "HSR Act" means the Hart-Scott-Rodino Antitrust Improvements Act of 1976,
as amended.


                                       28
<PAGE>

      "Hydrocarbon Interests" shall mean all rights, titles, interests and
estates now or hereafter acquired in and to oil and gas leases, oil, gas and
mineral leases, or other liquid or gaseous hydrocarbon leases, mineral fee
interests, overriding royalty and royalty interests, net profit interests and
production payment interests, including any reserved or residual interests of
whatever nature.

      "Hydrocarbons" shall mean oil, gas, casinghead gas, drip gasoline, natural
gasoline, condensate, distillate, liquid hydrocarbons, gaseous hydrocarbons and
all products refined or separated therefrom.

      "Lien" shall mean any interest in property securing an obligation owed to,
or a claim by, a person other than the owner of the property, whether such
interest is based on the common law, statute or contract, and whether such
obligation or claim is fixed or contingent, and including but not limited to (i)
the lien or security interest arising from a mortgage, encumbrance, pledge,
security agreement, conditional sale or trust receipt or a lease, consignment or
bailment for security purposes or (ii) production payments and the like payable
out of Oil and Gas Properties. The term "Lien" shall include reservations,
exceptions, encroachments, easements, rights of way, covenants, conditions,
restrictions, leases and other title exceptions and encumbrances affecting
property. For the purposes of this Agreement, a Person shall be deemed to be the
owner of any property which it has acquired or holds subject to a conditional
sale agreement, or leases under a financing lease or other arrangement pursuant
to which title to the Property has been retained by or vested in some other
Person in a transaction intended to create a financing.

      "Material Adverse Effect" means, relative to the Company or the Investors,
as the case may be, any change, development, or effect (individually or in the
aggregate) which is, or is reasonably likely to be, materially adverse (i) to
the business, assets, results of operations, condition (financial or otherwise),
or prospects of the Company and the Subsidiaries considered as a whole, or the
Investors, as the case may be, or (ii) to the ability of the Company or the
Investors, as the case may be, to perform on a timely basis any material
obligation of the Company or the Investors, as the case may be, under this
Agreement or any agreement, instrument, or document entered into or delivered in
connection herewith.

      "Material Agreement" means (a) any written agreement, contract, lease,
commitment, understanding, instrument or obligation to which the Company or any
Subsidiary is a party or by which the Company or any Subsidiary or any of their
respective properties may be bound involving total value or consideration or
liability in excess of $500,000, (b) any loan or credit agreement, bond,
debenture, note, mortgage or indenture by which the Company or any Subsidiary or
any of their respective properties may be bound, or (c) any agreement set forth
as an exhibit to the Company's Form 10-K for the fiscal year ended December 31,
1999.

      "Oil and Gas Properties" shall mean Hydrocarbon Interests; the Properties
now or hereafter pooled or unitized with Hydrocarbon Interests; all presently
existing or future unitization, pooling agreements and declarations of pooled
units and the units created thereby (including without limitation all units
created under orders, regulations and rules of any Governmental Authority) which
may affect all or any portion of the Hydrocarbon Interests; all operating
agreements, contracts and other agreements which relate to any of the
Hydrocarbon Interests or the production, sale, purchase, exchange or processing
of Hydrocarbons from or attributable to such Hydrocarbon Interests; all


                                       29
<PAGE>

Hydrocarbons in and under and which may be produced and saved or attributable to
the Hydrocarbon Interests, including all oil in tanks, the lands covered thereby
and all rents, issues, profits, proceeds, products, revenues and other incomes
from or attributable to the Hydrocarbon Interests; all tenements, hereditaments,
appurtenances and Properties in any manner appertaining, belonging, affixed or
incidental to the Hydrocarbon Interests; and all Properties, rights, titles,
interests and estates described or referred to above, including any and all
Property, real or personal, now owned or hereinafter acquired and situated upon,
used, held for use or useful in connection with the operating, working or
development of any of such Hydrocarbon Interests or Property (excluding drilling
rigs, automotive equipment or other personal property which may be on such
premises for the purpose of drilling a well or for other similar temporary uses)
and including any and all oil wells, gas wells, injection wells or other wells,
buildings, structures, fuel separators, liquid extraction plants, plant
compressors, pumps, pumping units, field gathering systems, tanks and tank
batteries, fixtures, valves, fittings, machinery and parts, engines, boilers,
meters, apparatus, appliances, tools, implements, cables, wires, towers, casing,
tubing and rods, similar equipment, surface leases, rights-of-way, easements and
servitudes together with all additions, substitutions, replacements, accessions
and attachments to any and all of the foregoing.

      "Person" or "person" means any individual, corporation, partnership, joint
venture, association, joint-stock company, trust, enterprise, unincorporated
organization, or Governmental Entity.

      "Plan" shall mean any employee pension benefit plan, as defined in Section
3(2) of ERISA, which (i) is currently or hereafter sponsored, maintained or
contributed to by the Company, any Subsidiary or an ERISA Affiliate or (ii) was
at any time during the preceding six calendar years sponsored, maintained or
contributed to, by the Company, any Subsidiary or an ERISA Affiliate.

      "Proceeding" means any action, suit or proceeding, whether civil,
criminal, administrative, arbitrative or investigative, any appeal in such an
action, suit or proceeding, and any inquiry or investigation that could lead to
such an action, suit or proceeding.

      "Reasonable best efforts" means a party's best efforts in accordance with
reasonable commercial practice and without the incurrence of unreasonable
expense.

      "Registration Rights Agreement" means that certain Registration Rights
Agreement, dated November 1, 2000, by and among the Company, MB and ESC, as
amended by that certain First Amendment to Registration Rights Agreement, dated
as of the date hereof, by and among the Company and the Investors.

      "Rule 144" means Rule 144 promulgated under the Securities Act.

      "Securities Act" means the Securities Act of 1933, as amended.

      "Senior Credit Agreement" means that certain Amended and Restated Credit
Agreement dated as of February 17, 2000, by and between BOG, Bank of Montreal,
as Agent, and the Lenders signatory thereto, as amended on October 31, 2000,
together with the "Loan Documents" described therein.


                                       30
<PAGE>

      "Subordinated Credit Agreement" means the Subordinated Credit Agreement
dated as of October 31, 2000 by and between BOG, Shell Capital, Inc., as Agent,
and the Lenders signatory thereto, together with the "Loan Documents" described
therein.

      "Subsidiaries" means Brigham Oil & Gas, L.P.; Brigham, Inc.; Brigham
Holdings I, LLC and Brigham Holdings II, LLC.

      "Voting Securities" means shares of Common Stock and any other securities
of the Company entitled to vote generally for the election of directors or any
other securities (including, without limitation, rights, warrants, and options)
convertible into or exchangeable or exercisable for any of the foregoing
(whether or not presently convertible, exchangeable, or exercisable).


                                       31
<PAGE>

      IN WITNESS WHEREOF, the parties have executed this Agreement, or caused
this Agreement to be executed by their duly authorized representatives, all as
of the day and year first above written.

                                        THE COMPANY:

                                        BRIGHAM EXPLORATION COMPANY
Address:
6300 Bridge Point Parkway
Building 2, Suite 500                   By: /s/ Karen E. Lynch
Austin, TX 78730                           -------------------------------------

                                        INVESTORS:


Address:                                DLJ ESC II, LP
277 Park Avenue
New York, NY 10172                      By: DLJ LBO Plans Management Corporation
Attn: Ivy Dodes/Nicole Arnaboldi            General Partner

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


Address:                                DLJMB FUNDING III, INC.
277 Park Avenue
New York, NY  10172                     By: /s/ Steven A. Webster
                                           -------------------------------------
                                           Steven A. Webster, Attorney in Fact


Address:                                DLJ MERCHANT BANKING PARTNERS  III, L.P.
277 Park Avenue
New York, NY 10172                      By: DLJ Merchant Banking III, Inc.
                                            Managing General Partner

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


Address:                                DLJ OFFSHORE PARTNERS III, C.V.
c/o DLJ Offshore Management N.V.
John B. Gorsiraweg 14                   By: DLJ Merchant Banking III, Inc.
Willemstad, Curacao                         Managing General Partner
Netherlands, Antilles
                                        By: /s/ Steven A. Webster
                                           -------------------------------------
                                            Steven A. Webster, Attorney in Fact


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