<PAGE>   1
                                                                 EXHIBIT 10.1.4


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                              AMENDED AND RESTATED
                        AGREEMENT OF LIMITED PARTNERSHIP




                              -------------------




                            BRIGHAM OIL & GAS, L.P.




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                         Dated as of December 30, 1997





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<PAGE>   2

                               TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                    PAGE
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<S>                                                                                 <C>
ARTICLE I -- Formation of Partnership..................................................2
         Section 1.1.  Formation.......................................................2
         Section 1.2.  Name............................................................2
         Section 1.3.  Business........................................................3
         Section 1.4.  Place of Business and Registered Agent..........................3
         Section 1.5.  Names and Addresses of Partners.................................3
         Section 1.6.  Term............................................................3
         Section 1.7.  Filings.........................................................4
         Section 1.8.  Title to Partnership Property...................................4

ARTICLE II -- Definitions and References...............................................4
         Section 2.1.  Defined Terms...................................................4
         Section 2.2.  References and Titles...........................................6

ARTICLE III -- Capitalization..........................................................6
         Section 3.1.  Capital Contributions of Partners...............................6
         Section 3.2.  Additional Capital Contributions................................6
         Section 3.3.  Non-payment of Capital Contributions............................7
         Section 3.4.  Return of Capital Contributions.................................7
         Section 3.5.  Payments and Advances by General Partner........................7

ARTICLE IV -- Allocations and Distributions............................................8
         Section 4.1.      Allocation of Profits and Losses. ..........................8
         Section 4.2.      Distributions...............................................8

ARTICLE V -- Management................................................................8
         Section 5.1.  Power and Authority of General Partner..........................8
         Section 5.2.  Contracts With Affiliates......................................10
         Section 5.3.  Tax Elections..................................................10
         Section 5.4.  Tax Returns; Tax Matters Partner...............................11
         Section 5.5.  Reimbursement of Expenses......................................11

ARTICLE VI -- Rights of Limited Partner...............................................11
         Section 6.1.  Rights of Limited Partner......................................11
         Section 6.2.  Limitations on Limited Partner.................................11
         Section 6.3.  Liability of Limited Partner...................................12
         Section 6.4.  Withdrawal and Return of Capital Contributions.................12

ARTICLE VII -- Books, Records and Bank Accounts.......................................12
         Section 7.1.  Capital Accounts, Books and Records............................12
         Section 7.2.  Reports........................................................13
         Section 7.3.  Bank Accounts..................................................13
         Section 7.4.  Information Relating to the Partnership........................13
</TABLE>



                                      (ii)
<PAGE>   3


<TABLE>
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                                                                                    PAGE
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<S>                                                                                 <C>
ARTICLE VIII -- Dissolution, Liquidation and Termination..............................13
         Section 8.1.  Dissolution....................................................13
         Section 8.2.  Liquidation and Termination....................................14
         Section 8.3.  Reconstitution.................................................15

ARTICLE IX -- Assignments of Interests................................................15
         Section 9.1.  Assignment by Partners.........................................15

ARTICLE X -- Miscellaneous............................................................16
         Section 10.1.  Notices.......................................................16
         Section 10.2.  Amendment.....................................................16
         Section 10.3.  Partition.....................................................16
         Section 10.4.  Entire Agreement..............................................16
         Section 10.5.  Severability..................................................16
         Section 10.6.  No Waiver.....................................................16
         Section 10.7.  Applicable Law................................................16
         Section 10.8.  Meetings of the Partners......................................17
         Section 10.9.  Successors and Assigns........................................17
         Section 10.10.  Counterparts.................................................17
</TABLE>



                                     (iii)

<PAGE>   4

                              AMENDED AND RESTATED
                        AGREEMENT OF LIMITED PARTNERSHIP

                            BRIGHAM OIL & GAS, L.P.


         THIS AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP (this
"Agreement") dated as of December 30, 1997, is made by and between Brigham,
Inc., a Nevada corporation, as the general partner (the "General Partner"), and
Brigham Holdings I, LLC, a Nevada limited liability company ("BHILLC"), as a
limited partner, and Brigham Holdings II, LLC, a Nevada limited liability
company ("BHIILLC"), as a limited partner (BHILLC and BHIILLC shall
individually referred to herein as a "Limited Partner", and together shall be
referred to as the "Limited Partners").

                              W I T N E S S E T H:

         WHEREAS, Brigham Oil & Gas, L.P., a Delaware limited partnership (the
"Partnership") was formed on May 1, 1992 pursuant to an Agreement of Limited
Partnership by and among Brigham Exploration Company, a Texas corporation
(which subsequently changed its name to Brigham, Inc. ("BI") and was merged
with and into its parent, Brigham I, Inc., a Nevada corporation now know as
Brigham, Inc. ("Brigham Nevada") after the merger), as a general partner, and
certain additional parties, as general and limited partners;

         WHEREAS, the Agreement of Limited Partnership for the Partnership was
amended on three occasions for various purposes, including the admission of
certain additional parties as limited partners (the Agreement of Limited
Partnership as so amended herein called the "Original Agreement");

         WHEREAS, on February 26, 1997, in an exchange (the "Exchange") made
pursuant to an Exchange Agreement dated on such date, all of the shareholders
of BI contributed all of their stock in BI to a newly-organized corporation,
Brigham Exploration Company, a Delaware corporation ("BEC"), and all of the
other partners of the Partnership (the "Other Partners") contributed their
interests in the Partnership to BEC, all in exchange for common stock in BEC;

         WHEREAS, BI's interest in the profits and capital of the Partnership
at the time of the Exchange was approximately 54.00% and the interests of the
Other Partners in profits and capital was approximately 46.00%;

         WHEREAS, at the time of the Exchange, the Partnership was indebted to
RIMCO Partners, LP II, RIMCO Partners, LP III and RIMCO Partners, LP IV
(collectively "RIMCO") in the approximate amount of $16,486,000.00 (the "RIMCO
Debt");

         WHEREAS, RIMCO contributed the RIMCO Debt to BEC as a part of the
Exchange and received therefor common stock in BEC, whereupon BEC contributed
the RIMCO Debt to the Partnership as a contribution to capital;

<PAGE>   5

         WHEREAS, following the contribution of the RIMCO Debt by BEC to the
Partnership as a contribution to capital, the Partnership interests of the of
the partners were 43.23% for BI, and 56.77% for BEC;

         WHEREAS, pursuant to a prospectus dated May 8, 1997, BEC issued
additional shares in an initial public offering, the proceeds of which were
contributed by BEC to the capital of the Partnership, resulting in further
adjustments in the Partnership interests of the partners, with BI's interest
being reduced to 31.5% and BEC's interest being increased to 68.5%; and

         WHEREAS, the partners now wish to amend and restate the Original
Agreement to reflect the current percentage interests of the partners, to
convert BEC's interests in the Partnership into limited partner interests, to
convert BI's interest in the Partnership, which is now held by Brigham Nevada
due to the merger, into a 1% general partner interest and a 30.5% limited
partner interest, to admit Brigham Holdings I, LLC, a Nevada limited liability
company and assignee of BEC's 68.5% limited partner interest, as a limited
partner, to admit Brigham Holdings II, LLC, a Nevada limited liability company
and assignee of BI's 30.5% limited partner interest, as a limited partner, and
to make additional changes to eliminate certain obsolete provisions and
incorporate certain additional provisions to reflect current operations of the
Partnership;

         NOW, THEREFORE, in consideration of the premises, the mutual covenants
and agreements contained herein and other good and valuable consideration, the
receipt and sufficiency of which are hereby acknowledged, the General Partner
and Limited Partners agree as follows:


                                   ARTICLE I

                            Formation of Partnership

         Section 1.1. Formation. The Partnership was organized on May 1, 1992,
as a limited partnership pursuant to the provisions of the Delaware Revised
Uniform Limited Partnership Act (Del. Code Ann. tit. 6 Sections 17-101 to
17-1109), as amended from time to time, and any successor statute or statutes
(the "Act").

         Section 1.2. Name. The name of the Partnership shall be "Brigham Oil &
Gas, L.P." Subject to all applicable laws, the business of the Partnership
shall be conducted in the name of the Partnership unless under the law of some
jurisdiction in which the Partnership does business such business must be
conducted under another name. In such a case, the business of the Partnership
in such jurisdiction may be conducted under such other name or names (except
the name of the General Partner, any Affiliate of the General Partner or the
name of the Limited Partner) as the General Partner shall determine to be
necessary so long as it does not affect adversely the limited liability of the
Limited Partner hereunder or jeopardize in any manner the title to or ownership
of any Partnership assets. The General Partner shall cause to be filed on
behalf of the Partnership such partnership or


                                      -2-

<PAGE>   6

assumed or fictitious name certificate or certificates or similar instruments
as may from time to time be required by law.

         Section 1.3. Business. The business of the Partnership shall be (a) to
acquire and own or lease all types of real and personal property, specifically
including oil, gas and other mineral interests in real property (the "Oil & Gas
Properties"); (b) explore, drill, develop and operate such Oil & Gas
Properties; (c) produce, collect, store, treat, deliver, market, sell or
otherwise dispose of oil, gas and related hydrocarbons, minerals and other
products from such Oil & Gas Properties; (d) farmout, sell, abandon and
otherwise dispose of such Oil & Gas Properties and other Partnership assets;
(e) obtain and market seismic data; and (g) take all such other actions
incidental to any of the foregoing as the General Partner may determine to be
necessary or desirable.

         Section 1.4. Place of Business and Registered Agent.

         (a) The principal United States office and place of business of the
Partnership and its street address shall be 6300 Bridge Point Parkway, Bldg. 2,
Suite 500, Austin, Texas 78730. The General Partner, at any time and from time
to time, may change the location of the Partnership's principal United States
office and place of business and may establish such additional place or places
of business of the Partnership as the General Partner shall determine to be
necessary or desirable, provided notice thereof is concurrently given to the
Limited Partner.

         (b) The registered office of the Partnership in the State of Delaware
shall be The Corporation Trust Company, Corporation Trust Center, 1209 Orange
Street, Wilmington, Delaware 19801, and the registered agent for service of
process on the Partnership shall be The Corporation Trust Company, a
corporation whose business address is the same as the Partnership's registered
office. The General Partner, at any time and from time to time, may change the
Partnership's registered office or registered agent or both by complying with
the applicable provisions of the Act and giving concurrent notice thereof to
the Limited Partners and may establish, appoint and change additional
registered offices and registered agents of the Partnership in such other
states as the General Partner shall determine to be necessary or advisable.

         Section 1.5. Names and Addresses of Partners. The General Partner is
the sole general partner of the Partnership, and the mailing and street address
of its business is 6300 Bridge Point Parkway, Bldg. 2, Suite 500, Austin, Texas
78730. The Limited Partners are the only limited partners of the Partnership,
and the mailing and street address of each of their businesses, which is the
same for each, is 3773 Howard Hughes Parkway, Suite 300 North, Las Vegas,
Nevada 89109. The General Partner and the Limited Partners may agree to admit
additional Limited Partners to the Partnership, in which case any such
additional Limited Partner shall provide its mailing and street address to the
Partnership.

         Section 1.6. Term. The Partnership shall be formed and commence upon
the completion of filing for record an initial certificate of limited
partnership of the Partnership with the Secretary of State of the State of
Delaware and shall continue until terminated in accordance with Article VIII.


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<PAGE>   7

The General Partner shall not be required to deliver or mail a copy of the
certificate of limited partnership to the Limited Partners.

         Section 1.7. Filings. Upon the request of the General Partner, the
Limited Partners shall promptly execute and deliver all such certificates and
other instruments conforming hereto as shall be necessary for the General
Partner to accomplish all filing, recording, publishing and other acts
appropriate to comply with all requirements for the formation and operation of
the Partnership as a limited partnership under the laws of the State of
Delaware and for the qualification or reformation and operation of the
Partnership as a limited partnership (or a partnership in which the Limited
Partners have limited liability) in all other jurisdictions where the
Partnership shall propose to conduct business. Prior to the conducting of any
business in any jurisdiction, the General Partner shall to the full extent
necessary to establish limited liability for the Limited Partners under the
laws of such jurisdiction and otherwise to comply with the laws of such
jurisdiction, cause the Partnership to comply with all requirements for the
registration, qualification or reformation of the Partnership to conduct
business as a limited partnership (or a partnership in which the Limited
Partners have limited liability) in such jurisdiction. Thereafter, the General
Partner shall cause the Partnership to continue to comply with all such
requirements and all other requirements necessary to maintain the limited
liability of the Limited Partners in each jurisdiction where the Partnership
does business.

         Section 1.8. Title to Partnership Property. All property owned by the
Partnership, whether real or personal, tangible or intangible, shall be deemed
to be owned by the Partnership as an entity, and no Partner, individually,
shall have any ownership of such property. The Partnership shall hold its
property in its own name. The Partnership shall hold all of its assets in the
name of the Partnership unless under the law of some jurisdiction in which the
Partnership owns assets such assets must be held in another name. In such a
case, such assets in such jurisdiction shall be held under such other name or
names (except the name of the General Partner, any Affiliate of the General
Partner or the name of the Limited Partners) as the General Partner shall
determine to be necessary so long as it does not affect adversely the limited
liability of the Limited Partners hereunder or jeopardize in any manner the
title to or ownership of any Partnership assets.


                                   ARTICLE II

                           Definitions and References

         Section 2.1. Defined Terms. When used in this Agreement, the following
terms shall have the respective meanings set forth below:

         "Act" shall mean the Delaware Revised Uniform Limited Partnership Act
(Del. Code Ann. tit. 6 Sections 17-101 to 17-1109), as amended from time to
time, and any successor statute or statutes.


                                      -4-

<PAGE>   8

         "Affiliate" shall mean (a) any person directly or indirectly owning,
controlling or holding with power to vote 10% or more of the outstanding voting
securities of the General Partner, (b) any person 10% or more of whose
outstanding voting securities are directly or indirectly owned, controlled or
held with power to vote by the General Partner, (c) any person directly or
indirectly controlling, controlled by or under common control with the General
Partner, and (d) any officer, director or partner of the General Partner or any
person described in subsection (a), (b) or (c) of this paragraph. As used in
this Agreement, the term "person" shall include an individual, an estate, a
corporation, a partnership, an association, a joint stock company and a trust.

         "Agreed Rate" shall mean a rate per annum which is equal to the lesser
of (a) the rate of interest as published from time to time in the Wall Street
Journal as the "prime rate" (defined as the base rate on corporate loans posted
by at least 75% of the nation's 30 largest banks), adjusted from time to time
to reflect any changes in such rate determined hereunder, or (b) the maximum
rate from time to time permitted by applicable law.

         "BHILLC" shall mean Brigham Holdings I, LLC, a Nevada limited
liability company.

         "BHIILLC" shall mean Brigham Holdings II, LLC, a Nevada limited
liability company.

         "Capital Account" shall have the meaning set forth in Section 7.1(b)
hereof.

         "Capital Contributions" shall mean for any Partner at the particular
time in question the aggregate of the dollar amounts of any cash and the fair
market value of any property contributed to the capital of the Partnership, or,
if the context in which such term is used so indicates, the dollar amounts of
cash and the fair market value of any property agreed to be contributed, or
requested to be contributed, by such Partner to the capital of the Partnership.

         "General Partner" shall mean Brigham, Inc., a Nevada corporation, and
any person who becomes a substituted General Partner of the Partnership
pursuant to the terms hereof.

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

         "Limited Partner" shall mean each of BHILLC and BHIILLC, and any
person who becomes a substituted Limited Partner or an additional Limited
Partner of the Partnership pursuant to the terms hereof.

         "Partners" shall mean the General Partner and the Limited Partner.

         "Partnership" shall mean Brigham Oil & Gas, L.P., a Delaware limited
partnership.

         "Sharing Ratio" shall mean 1% for the General Partner, 30.5% for
BHIILLC and 68.5% for BHILLC.


                                      -5-
<PAGE>   9

         Section 2.2. References and Titles. All references in this Agreement
to articles, sections, subsections and other subdivisions refer to
corresponding articles, sections, subsections and other subdivisions of this
Agreement unless expressly provided otherwise. Titles appearing at the
beginning of any of such subdivisions are for convenience only and shall not
constitute part of such subdivisions and shall be disregarded in construing the
language contained in such subdivisions. The words "this Agreement," "herein,"
"hereof," "hereby," "hereunder" and words of similar import refer to this
Agreement as a whole and not to any particular subdivision unless expressly so
limited. Pronouns in masculine, feminine and neuter genders shall be construed
to include any other gender, and words in the singular form shall be construed
to include the plural and vice versa, unless the context otherwise requires.


                                  ARTICLE III

                                Capitalization

         Section 3.1. Capital Contributions of Partners. The General Partner
and the Limited Partners have already made Capital Contributions to the
Partnership in such amounts and at such times as are reflected in the books of
the Partnership. Notwithstanding anything to the contrary contained herein,
such Capital Contributions shall be the maximum contribution to the Partnership
that the Partners shall be required to make (unless the Partners otherwise
elect as provided in Section 3.2).

         Section 3.2. Additional Capital Contributions. At any time after the
making of the Capital Contributions referred to in Section 3.1, the General
Partner may request that each Partner make additional Capital Contributions to
the Partnership in accordance with each Partner's Sharing Ratio for the purpose
of (i) acquiring additional Oil & Gas Properties, or (ii) for such other uses
as are consistent with the purpose of the Partnership. No Partner shall be
obligated to make any such additional Capital Contributions unless and until
such time as each Partner agrees to make such additional Capital Contributions.

         In the event that a Partner shall decline to make all or any portion
of the additional Capital Contributions requested at any time, the General
Partner may elect to take any of the following actions:

         (a) The General Partner may borrow funds in the name of the
Partnership for expenditure for such purposes, subject to Section 5.2(a) ;

         (b) The Partners electing to make additional Capital Contributions may
pay their pro rata share of all of the additional Capital Contributions which a
Partner shall decline to make; and the General Partner shall adjust the Sharing
Ratios accordingly; or

         (c) The General Partner may cause the Partnership and/or the Partners
to take such other actions upon which the Partners shall agree.


                                      -6-

<PAGE>   10

         Section 3.3. Non-payment of Capital Contributions.

         (a) The Partnership shall have the right to pursue any remedy existing
at law or in equity for the collection of the unpaid amount of the Capital
Contributions agreed to be made in Section 3.l or hereafter agreed to be made
in accordance with Section 3.2, including without limitation the prosecution of
a suit against a defaulting Partner.

         (b) The Partnership may retain any revenues otherwise distributable to
a defaulting Partner pursuant to this Agreement in an amount equal to the
amount such Partner failed or refused to contribute as required pursuant to the
terms of this Agreement, together with interest on such past-due amounts at a
rate equal to the Agreed Rate. Any amount so withheld shall be deemed, for all
purposes of this Agreement, to have been distributed to the defaulting Partner
and, other than that portion of such amounts representing interest, be deemed
to have been recontributed by the defaulting Partner to the capital of the
Partnership for the purposes for which contributions were initially requested.
To the extent that a Partner has advanced funds to the Partnership as a result
of the default of a Partner, such Partner shall be entitled to be reimbursed
from the amounts so withheld from the defaulting Partner.

         Section 3.4. Return of Capital Contributions. Except as provided in
Section 3.5, no interest shall accrue on any contributions to the capital of
the Partnership; and no Partner shall have the right to withdraw or be repaid
any capital contributed by such Partner except as provided in Section 8.2 of
this Agreement. All interest which accrues on Partnership funds shall be
allocated and credited to the Partners in accordance with Section 4.1.

         Section 3.5. Payments and Advances by General Partner. The General
Partner shall have the right to pay any indebtedness or obligation of the
Partnership out of funds of the General Partner, and may bill the Partnership
in the same manner that the Partnership may bill the Limited Partners. Further,
if at any time the General Partner advances funds to or on behalf of the
Partnership or the General Partner is required to pay any indebtedness or
obligation of the Partnership in excess of the Capital Contributions of the
General Partner agreed to be made in this Article III, such advance or payment
shall constitute a loan by the General Partner to the Partnership. If any such
advance or payment is outstanding for more than sixty(60) days and except as
provided in Section 3.4, such advance or payment shall bear interest from the
date first made at a rate equal to the Agreed Rate. No such advance or payment
by the General Partner shall be deemed to be a contribution by the General
Partner to the capital of the Partnership. Any advances by the General Partner
(other than (i) for a required payment by the General Partner which is beyond
the control of the General Partner of any indebtedness or obligation of the
Partnership in excess of the Capital Contributions of the General Partner
agreed to be made in this Article III, or (ii) a payment by the General Partner
of any costs and expenses allocated and charged to a Limited Partner upon the
default by the Limited Partner in the payment of any Capital Contributions
previously agreed to be made by the Limited Partner) shall be subject to the
limitations on borrowing specified in Section 5.2(a). Any loan made by the
General Partner hereunder to pay any costs or expenses allocated and charged to
any Partner


                                      -7-

<PAGE>   11

shall be repaid (with payments to be applied first to the payment of interest
and then to the repayment of principal) from the revenues that would otherwise
be next distributed to such Partner hereunder.


                                   ARTICLE IV

                         Allocations and Distributions

         Section 4.1. Allocation of Profits and Losses. Except as may be
otherwise required under Section 704 of the Internal Revenue Code and the
Treasury Regulations promulgated thereunder (including those Regulations
governing allocations with respect to nonrecourse indebtedness and property
carried on the books of the Partnership at an amount which differs from its
adjusted tax basis), each item of income, gain, loss, deduction, and credit of
the Partnership shall be allocated and charged to the Partners in accordance
with their respective Sharing Ratios.

         Section 4.2. Distributions. All cash funds of the Partnership (other
than Capital Contributions and any borrowed funds) which the General Partner
reasonably determines are not needed for the payment of existing or foreseeable
(within 30 days) Partnership obligations and expenditures shall be distributed
to the Partners in proportion to their Sharing Ratios. Payment of all
distributions made by the Partnership to the Limited Partners shall be made by
transfer of immediately available funds in accordance with such written
instructions to the General Partner as may be provided by the Limited Partners
from time to time. All distributions in liquidation of a Partner's interest in
the Partnership shall be made in accordance with Section 8.2.


                                   ARTICLE V

                                   Management

         Section 5.1. Power and Authority of General Partner. The General
Partner shall have full and exclusive power and authority on behalf of the
Partnership to manage, control, administer and operate the properties, business
and affairs of the Partnership and to do or cause to be done any and all acts
deemed by the General Partner to be necessary or appropriate thereto, and the
scope of such power and authority shall encompass all matters in any way
connected with such business or incident thereto, including but not limited to,
the power and authority:

         (a) To purchase or otherwise acquire real or personal property of
every nature considered necessary or appropriate to carry on and conduct the
business of the Partnership;

         (b) To borrow monies for the purchase, development and maintenance of
Partnership assets and other aspects of the Partnership's business and from
time to time to draw, make, execute and issue promissory notes and other
negotiable or non-negotiable instruments and evidences of indebtedness; to
secure the payment of the sums so borrowed and to mortgage, pledge or assign in


                                      -8-

<PAGE>   12

trust all or any part of the property of the Partnership, and to assign any
monies owing or to be owing to the Partnership;

         (c) To enter into any agreements of joint venture or partnership or
for sharing of risks, expenses or profits, with any person, firm, corporation,
government or agency thereof engaged in any business or transaction in which
the Partnership is authorized to engage;

         (d) To maintain, develop, manage and defend Partnership property; to
contract with third parties for such purposes; and to do any and all other
things necessary or appropriate to carry out the terms and provisions of this
Agreement which would or might be done by a normal and prudent businessman in
the development and management of its own property;

         (e) To sell, assign, convey or otherwise dispose of, for such
consideration and upon such terms and conditions as the General Partner may
determine to be in the best interests of the Partnership, all or any part of
the Partnership property, any interest therein, or any interest payable
therefrom, and in connection therewith to execute and deliver such deeds,
assignments and conveyances containing such warranties as the General Partner
may determine to be appropriate;

         (f) To purchase, lease, rent or otherwise acquire or obtain the use of
facilities and all other kinds and types of real or personal property that may
in anyway be deemed necessary, convenient, or advisable in connection with
carrying on the business of the Partnership;

         (g) To pay any amounts necessary or appropriate to the maintenance or
operation of any Partnership property;

         (h) To make and to enter into such agreements and contracts with such
parties and to give such receipts, releases and discharges with respect to any
and all of the foregoing and any matters incident thereto as the General
Partner may deem advisable or appropriate;

         (i) To procure and maintain in force such insurance as the General
Partner shall deem prudent to serve as protection against liability for loss
and damage which may be occasioned by the activities to be engaged in by the
Partnership or the General Partner on behalf of the Partnership;

         (j) To sue and be sued, complain and defend in the name of and on
behalf of the Partnership;

         (k) To quitclaim, surrender, release or abandon any Partnership
property, with or without consideration therefor;

         (l) To execute and deliver all checks, drafts, endorsements and other
orders for the payment of Partnership funds;


                                      -9-

<PAGE>   13

         (m) To employ on behalf of the Partnership agents, employees and
officers (having such duties and titles and having such authority by delegation
from the General Partner as the General Partner shall designate), accountants,
attorneys, brokers, consultants and all other professionals, clerical help and
such other assistance and services as the General Partner may deem proper and
to pay therefor such remuneration as the General Partner may determine to be
reasonable and appropriate;

         (n) To appear and to represent the Partnership before any governmental
authority or regulatory agency and to make all necessary or appropriate filings
before such authority or agency; and

         (o) To take such other action, execute and deliver such other
documents and perform such other acts as may be deemed by the General Partner
to be appropriate to carry out the business and affairs of the Partnership in
accordance with this Agreement.

         Section 5.2. Contracts With Affiliates. The Partnership may enter into
contracts and agreements with the General Partner and its Affiliates for the
rendering of services, the sale and lease of supplies and equipment, provided
that the amount of the compensation, price or rental that can be charged to or
by the Partnership therefor must be no less favorable to the Partnership than
those available from unrelated third parties in the area engaged in the
business of rendering comparable services or selling or leasing comparable
properties, equipment and supplies which could reasonably be made available to
or by the Partnership.

         Section 5.3. Tax Elections. The General Partner shall make the
following elections on behalf of the Partnership:

         (a) To elect a fiscal year of the Partnership to be the calendar year;

         (b) To elect the accrual method of accounting if permitted by
applicable law;

         (c) To elect, in accordance with Sections 195 and 709 of the Internal
Revenue Code and applicable regulations and comparable state law provisions, to
treat all start-up and organization costs of the Partnership as deferred
expenses amortizable over sixty (60) months; and

         (d) To elect with respect to such other federal, state and local tax
matters as shall be deemed to be in the best interests of the Partnership and
the Partners.

         Section 5.4. Tax Returns; Tax Matters Partner. The General Partner
shall be the "tax matters partner" of the Partnership and shall prepare and
timely file all federal, state and local income and other tax returns and
reports as may be required as a result of the business of the Partnership.

         Section 5.5. Reimbursement of Expenses. All direct and indirect costs
and expenses incurred by the General Partner in organizing the Partnership and
in managing and conducting the business and


                                      -10-

<PAGE>   14

affairs of the Partnership, including, without limitation, (i) all costs and
expenses incurred in oil and gas exploration, development, operation,
production and marketing activities including all costs and expenses incurred
in connection with activities in support of or related to directly or
indirectly such oil and gas exploration, development, of operation, production
and marketing activities, (ii) all other costs and expenses incurred in any
business of the Partnership other than oil and gas exploration, development and
production, (iii) secretarial, telephone, office rent and other office
expenses, (iv) salaries and other compensation expenses of employees, officers
and directors, (v) other administrative expenses, (vi) travel expenses, (vii)
legal, accounting, geological, engineering and well supervision costs and
expenses and (viii) expenses incurred in providing or obtaining such other
professional, technical, administrative services and advice as the General
Partner may deem necessary or desirable, shall be paid or reimbursed by the
Partnership as a Partnership expense. The General Partner shall determine which
expenses are allocable to the Partnership in a manner which is fair and
reasonable to the General Partner and the Partnership, and if such allocation
is made by the General Partner in good faith it shall be conclusive in the
absence of manifest error.

                                   ARTICLE VI

                           Rights of Limited Partner

         Section 6.1. Rights of Limited Partner. Each of the Limited Partners
shall have the right to: (a) have the Partnership books and records (including,
without limitation, those required under the Act) kept at the principal United
States office of the Partnership and at all reasonable times to inspect and
copy any of them at the sole expense of such Partner; (b) have on demand true
and full information of all things affecting the Partnership and a formal
account of Partnership affairs whenever circumstances render it just and
reasonable; (c) have dissolution and winding up by decree of court as provided
for in the Partnership; and (d) exercise all rights of a limited partner under
the Partnership (except to the extent otherwise specifically provided herein).

         Section 6.2. Limitations on Limited Partner. Each of the Limited
Partners shall not: (a) be permitted to take part in the business or control of
the business or affairs of the Partnership; (b) have any voice in the
management or operation of any Partnership property; or (c) have the authority
or power to act as agent for or on behalf of the Partnership or any other
Partner, to do any act which would be binding on the Partnership or any other
Partner, or to incur any expenditures on behalf of or with respect to the
Partnership. No Partner shall hold out or represent to any third party that any
of the Limited Partners have any such power or right or that the Limited
Partners are anything other than a "limited partner" in the Partnership.

         Section 6.3. Liability of Limited Partner. Each of the Limited
Partners shall not be liable for the debts, liabilities, contracts or other
obligations of the Partnership except to the extent of any unpaid Capital
Contributions agreed to be made by a Limited Partner as set forth in Section
3.1, any additional Capital Contributions hereafter agreed to be made by a
Limited Partner in accordance with Section 3.2 and a Limited Partner's share of
the assets (including undistributed revenues) of the Partnership; and in all
events, a Limited Partner shall be liable and obligated to make payments of its


                                      -11-

<PAGE>   15

Capital Contributions only as and when such payments are due in accordance with
the terms of this Agreement, and a Limited Partner shall not be required to
make any loans to the Partnership. The Partnership shall indemnify and hold
harmless each of the Limited Partners in the event it (a) becomes liable for
any debt, liability, contract or other obligation of the Partnership except to
the extent expressly provided in the preceding sentence or (b) is directly or
indirectly required to make any payments with respect thereto.

         Section 6.4. Withdrawal and Return of Capital Contributions. Each of
the Limited Partners shall not be entitled to (a) withdraw from the Partnership
except upon the assignment by such Limited Partner of all of its interest in
the Partnership and the substitution of the Limited Partner's assignee as a
Limited Partner of the Partnership in accordance with Section 9.1, or (b) the
return of its Capital Contributions except to the extent, if any, that
distributions made pursuant to the express terms of this Agreement may be
considered as such by law or by unanimous agreement of the Partners, or upon
dissolution and liquidation of the Partnership, and then only to the extent
expressly provided for in this Agreement and as permitted by law.


                                  ARTICLE VII

                        Books, Records and Bank Accounts

         Section 7.1. Capital Accounts, Books and Records.

         (a) The General Partner shall keep books of account for the
Partnership in accordance with the terms of this Agreement. Such books shall be
maintained at the principal office of the Partnership.

         (b) An individual capital account (a "Capital Account") shall be
maintained by the Partnership for each Partner in accordance with the
requirements of the applicable Treasury Regulations under Section 704 of the
Internal Revenue Code.

         Section 7.2. Reports. The General Partner shall deliver to the Limited
Partners such reports and financial statements as the General Partner shall
determine or as the Limited Partners shall reasonably request from time to
time.

         Section 7.3. Bank Accounts. The General Partner shall cause one or
more accounts to be maintained in the name of the Partnership in one or more
banks which each have capital, surplus and undivided profits of at least
$200,000,000, which accounts shall be used for the payment of expenditures
incurred by the General Partner in connection with the business of the
Partnership and in which shall be deposited any and all receipts of the
Partnership. The General Partner may also temporarily invest the cash funds of
the Partnership in any manner it determines to be in the best interests of the
Partnership and the Partners. All amounts shall be and remain the property of
the


                                      -12-

<PAGE>   16

Partnership and shall be received, held and disbursed by the General Partner
for the purposes specified in this Agreement. There shall not be deposited in
any of such accounts any funds other than funds belonging to the Partnership,
and no other funds shall in any way be commingled with such funds.

         Section 7.4. Information Relating to the Partnership. Upon request,
the General Partner shall supply to the Limited Partners any information
requested regarding the Partnership or its activities. During ordinary business
hours, the Limited Partners and its authorized agents and representatives shall
have reasonable access to all books, records and materials in the Partnership's
offices regarding the Partnership or its activities.


                                  ARTICLE VIII

                    Dissolution, Liquidation and Termination

         Section 8.1. Dissolution. The Partnership shall be dissolved upon the
occurrence of any of the following:

         (a) The occurrence of December 31, 2025.

         (b) The sale, disposition or termination of all of the property then
owned by the Partnership.

         (c) The occurrence of an event of withdrawal from the Partnership by
the General Partner as provided for in the Partnership.

         (d) The consent in writing of the General Partner and all of the
Limited Partners.

         (e) The occurrence of any event which, under the Act, causes the
dissolution of a limited partnership.

         Section 8.2. Liquidation and Termination. Upon dissolution of the
Partnership, the General Partner or, if the withdrawal of the General Partner
caused the dissolution of the Partnership, a person selected by all of the
Limited Partners, shall act as liquidator or shall appoint one or more
liquidators who shall have full authority to wind up the affairs of the
Partnership and make final distribution as provided herein. The liquidator
shall continue to operate the Partnership properties with all of the power and
authority of the General Partner. The steps to be accomplished by the
liquidator are as follows:

         (a) As promptly as possible after dissolution and again after final
liquidation, the liquidator, if requested by any Partner, shall cause a proper
accounting to be made by the Partnership's independent accountants of the
Partnership's assets, liabilities and operations through


                                      -13-

<PAGE>   17

the last day of the month in which the dissolution occurs or the final
liquidation is completed, as appropriate.

         (b) The liquidator shall pay all of the debts and liabilities of the
Partnership (including all expenses incurred in liquidation) or otherwise make
adequate provision therefor (including without limitation the establishment of
a cash escrow fund for contingent liabilities in such amount and for such term
as the liquidator may reasonably determine). After making payment or provision
for all debts and liabilities of the Partnership, the Partners' Capital
Accounts shall then be adjusted by (i) assuming the sale of all remaining
assets of the Partnership for cash at their respective fair market values (as
determined by an appraiser selected by the liquidator) as of the date of
termination of the Partnership and (ii) debiting or crediting each Partner's
Capital Account with its respective share of the hypothetical gains or losses
resulting from such assumed sales in the same manner as each such Capital
Account would be debited or credited for gains or losses on actual sales of
such assets. The liquidator shall then by payment of cash or property (valued
as of the date of termination of the Partnership at its fair market value by
the appraiser selected in the manner provided above) distribute to the Partners
such amounts as are required to pay the positive balances of their respective
Capital Accounts. Such a distribution shall be in cash or in kind as determined
by the liquidator. Any distribution to the Partners in liquidation of the
Partnership shall be made by the latter of either the end of the taxable year
in which the liquidation occurs or on a date which is not more than ninety (90)
days after the date of such liquidation. For purposes of the preceding
sentence, the term "liquidation" shall have the same meaning as set forth in
Treasury Regulation Section 1.704-1(b)(2)(ii) as in effect at such time. Each
Partner shall have the right to designate another person to receive any
property which otherwise would be distributed in kind to that Partner pursuant
to this Section 8.2.

         (c) Except as expressly provided herein, the liquidator shall comply
with any applicable requirements of the Act and all other applicable laws
pertaining to the winding up of the affairs of the Partnership and the final
distribution of its assets.

         (d) Notwithstanding any provision in this Agreement to the contrary,
no Partner shall be obligated to restore a deficit balance in its Capital
Account at any time.

         The distribution of cash and/or property to the Partners in accordance
with the provisions of this Section 8.2 shall constitute a complete return to
the Partners of their Capital Contributions and a complete distribution to the
Partners of their interest in the Partnership and all Partnership property.

         Section 8.3. Reconstitution. Notwithstanding the foregoing or any
other provision of this Agreement, upon the occurrence of an event of
dissolution described in Section 8.1, the Partners may unanimously consent to
the reconstitution of the Partnership, and the business of the Partnership
shall be continued without being wound up as provided for in the Act.


                                      -14-

<PAGE>   18

                                   ARTICLE IX

                            Assignments of Interests

         Section 9.1. Assignment by Partners.

         (a) No Partner's interest in the Partnership shall be assigned,
mortgaged, pledged, subjected to a security interest or otherwise encumbered,
in whole or in part, without the prior written consent of all of the other
Partners, and any attempt by a Partner to assign its interest without such
consent shall be void ab initio.

         (b) Unless an assignee becomes a substituted Partner in accordance
with the provisions set forth below, such assignee shall not be entitled to any
of the rights granted to a Partner hereunder, other than the right to receive
allocations of income, gain, loss, deduction, credit and similar items and
distributions to which the assignor would otherwise be entitled, to the extent
such items are assigned.

         (c) An assignee of the interest of a Partner, or any portion thereof,
shall become a substituted Partner entitled to all of the rights of a Partner
if, and only if (i) the assignor gives the assignee such right, (ii) the
Partners consent to such substitution, the granting or denying of which shall
be in each Partner's sole discretion, and (iii) the assignee executes and
delivers such instruments, in form and substance satisfactory to the General
Partner, as the General Partner may deem necessary or desirable to effect such
substitution and to confirm the agreement of the assignee to be bound by all of
the terms and provisions of this Agreement. Upon the satisfaction of such
requirements, the General Partner shall concurrently (or as of such later date
as shall be provided for in any applicable written instruments furnished to the
General Partner) admit any such assignee as a substituted Partner of the
Partnership and reflect such admission and the date thereof in the records of
the Partnership.

         (d) The Partnership and the General Partner shall be entitled to treat
the record owner of any Partnership interest as the absolute owner thereof in
all respects and shall incur no liability for distributions of cash or other
property made in good faith to such owner until such time as a written
assignment of such interest that complies with the terms of this Agreement has
been received by the General Partner.


                                      -15-

<PAGE>   19

                                   ARTICLE X

                                 Miscellaneous

         Section 10.1. Notices. All notices, elections, demands or other
communications required or permitted to be made or given pursuant to this
Agreement shall be in writing and shall be considered as properly given or made
if given by (a) personal delivery, (b) prepaid telegram, telex or facsimile
(provided that such telegram, telex or facsimile is confirmed by expedited
delivery service), or (c) expedited delivery service with proof of delivery,
addressed to the respective addressee(s) specified in Section 1.5. Any Partner
may change its address by giving notice in writing to the other Partners of its
new address.

         Section 10.2. Amendment. This Agreement may be changed, modified or
amended only by an instrument in writing agreed upon by the General Partner and
the Limited Partner.

         Section 10.3. Partition. Each of the Partners hereby irrevocably
waives for the term of the Partnership any right that such Partner may have to
maintain any action for partition with respect to the Partnership property.

         Section 10.4. Entire Agreement. This Agreement constitutes the full
and complete agreement of the parties hereto with respect to the subject matter
hereof.

         Section 10.5. Severability. Every provision in this Agreement is
intended to be severable. If any term or provision hereof is illegal or invalid
for any reason whatsoever, such illegality or invalidity shall not affect the
validity of the remainder of this Agreement.

         Section 10.6. No Waiver. The failure of any Partner to insist upon
strict performance of a covenant hereunder or of any obligation hereunder,
irrespective of the length of time for which such failure continues, shall not
be a waiver of such Partner's right to demand strict compliance in the future.
No consent or waiver, express or implied, to or of any breach or default in the
performance of any obligation hereunder shall constitute a consent or waiver to
or of any other breach or default in the performance of the same or any other
obligation hereunder.

         Section 10.7. Applicable Law. This Agreement and the rights and
obligations of the parties hereunder shall be governed by and interpreted,
construed and enforced in accordance with the laws of the State of Delaware.

         Section 10.8. Meetings of the Partners. The General Partner may hold
meetings with the Limited Partners from time to time to inform and consult with
the Limited Partners concerning such matters as the General Partner deems
appropriate. Such meetings may be held by conference telephone and shall be
held at such times and places, as often and in such manner as shall be
determined by the General Partner. The General Partner shall give notice of the
time, place and topic of each such meeting at least ten business days prior
thereto. Notwithstanding the foregoing


                                      -16-

<PAGE>   20

provisions of this Section 10.8, the Limited Partners shall not be permitted to
take part in the business or control of the business of the Partnership; it
being the intention of the parties that the involvement of the Limited Partners
as contemplated in this Section 10.8 is for the purpose of informing the
Limited Partners with respect to various Partnership matters, explaining any
information furnished to the Limited Partners in connection therewith,
answering any question the Limited Partners may have with respect thereto and
receiving any ideas or suggestions the Limited Partners may have with respect
thereto; it being the further intention of the parties that the General Partner
shall have full and exclusive power and authority on behalf of the Partnership
to manage, control, administer and operate the property, business and affairs
of the Partnership in accordance with this Agreement.

         Section 10.9. Successors and Assigns. This Agreement shall be binding
upon and inure to the benefit of the parties hereto and their respective
successors and assigns; provided, however, that no Partner may sell, assign,
transfer or otherwise dispose of all or any part of its rights or interest in
the Partnership or under this Agreement except in accordance with Article IX.

         Section 10.10. Counterparts. This Agreement may be executed in one or
more counterparts, each of which shall be an original and all of which shall
constitute but one and the same document.


                                      -17-

<PAGE>   21

         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the day and year first above written.

SHARING RATIO:                       GENERAL PARTNER:

1%                                   BRIGHAM, INC.


                                     By: /s/ Ben M. Brigham
                                        -----------------------------------
                                        Ben M. Brigham,
                                        President


                                     LIMITED PARTNERS:

68.5%                                BRIGHAM HOLDINGS I, LLC



                                     By:      /s/ Ben M. Brigham
                                        -----------------------------------
                                        Ben M. Brigham,
                                        President


30.5%                                BRIGHAM HOLDINGS II, LLC



                                     By       /s/ Ben M. Brigham
                                        --------------------------------
                                        Ben M. Brigham,
                                        President


                                     -18-