<PAGE>   1
                                                                  EXHIBIT 10.40



                               GUARANTY AGREEMENT


                                       BY


                            [SEE SCHEDULE I HERETO]


                                  IN FAVOR OF


                   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION,
                                   AS TRUSTEE



                                AUGUST 20, 1998


<PAGE>   2

                               TABLE OF CONTENTS


<TABLE>
<CAPTION>
                                                                                                Page
                                                                                                ----
<S>                                                                                             <C>
ARTICLE 1
         GENERAL TERMS
         Section 1.1   Terms Defined Above or in the Indenture.....................................2
         Section 1.2   Certain Definitions.........................................................2

ARTICLE 2
         THE GUARANTY
         Section 2.1   Liabilities Guaranteed......................................................4
         Section 2.2   Nature of Guaranty..........................................................4
         Section 2.3   Trustee's Rights............................................................4
         Section 2.4   Guarantor's Waivers.........................................................5
         Section 2.5   Maturity of Liabilities; Payment............................................5
         Section 2.6   Trustee's, Agent's and Noteholders' Expenses................................5
         Section 2.7   Liability...................................................................5
         Section 2.8   Events and Circumstances Not Reducing or Discharging 
                       Guarantor's Obligations.....................................................6
         Section 2.9   Right of Subrogation and Contribution.......................................7

ARTICLE 3
         REPRESENTATIONS AND WARRANTIES
         Section 3.1   By Guarantor................................................................8
         Section 3.2   No Representation by Noteholders............................................9

ARTICLE 4
         SUBORDINATION OF INDEBTEDNESS
         Section 4.1   Subordination of All Guarantor Claims.......................................9
         Section 4.2   Claims in Bankruptcy.......................................................10
         Section 4.3   Payments Held in Trust.....................................................10
         Section 4.4   Liens Subordinate..........................................................10

ARTICLE 5
         MISCELLANEOUS
         Section 5.1   Successors and Assigns.....................................................11
         Section 5.2   Notices....................................................................11
         Section 5.3   Business and Financial Information.........................................11
         Section 5.4   Construction...............................................................11
         Section 5.5   Invalidity.................................................................11
         Section 5.6   Subordination Agreement....................................................11
         Section 5.7   ENTIRE AGREEMENT...........................................................12
</TABLE>


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<PAGE>   3

                               GUARANTY AGREEMENT


         THIS GUARANTY AGREEMENT by [see Schedule I hereto] (hereinafter called
"Guarantor"), is in favor of CHASE BANK OF TEXAS, NATIONAL ASSOCIATION in its
capacity as trustee under the Indenture (as hereinafter defined), and each and
every successor trustee under the Indenture (the "Trustee"), for the ratable
benefit of Agent and the Noteholders (each as hereinafter defined).

                              W I T N E S S E T H:

     A. Brigham Exploration Company, a Delaware corporation ("Borrower") has
executed an Indenture, dated as of August 20, 1998, by and among the Borrower
and Chase Bank of Texas, National Association (the "Indenture"), pursuant to
which the Borrower has issued and will issue its Senior Subordinated Secured
Notes in the aggregate face amount of $50,000,000, with final maturity on
August 20, 2003 (such notes, as from time to time supplemented, amended or
modified and all other notes given in substitution therefor or in modification,
renewal or extension thereof, in whole or in part, being hereinafter called the
"Notes"), to Joint Energy Development Investments II Limited Partnership, a
Delaware limited partnership ("JEDI-II") and Enron Capital & Trade Resources
Corp., a Delaware corporation ("ECT").

     B. Brigham Oil & Gas, L.P., a Delaware limited partnership ("BOG") and
Bank of Montreal, as Agent ("B-MO"; B-MO, together with any other parties from
time to time constituting lenders under the Senior Credit Agreement (as
hereinafter defined) are herein called the "Senior Lenders") have entered into
that certain Credit Agreement dated as of January 28, 1998 as heretofore and
hereafter amended (such agreement, as the same may from time to time be
modified, extended, renewed, restated, replaced, amended or supplemented, being
herein called the "Senior Credit Agreement") pursuant to which the Senior
Lenders made and continue to make loans to BOG as evidenced by and to be
evidenced by the notes in the aggregate original principal amount of
$75,000,000 (such notes, as the same may from time to time be modified,
extended, renewed, restated, amended, replaced or supplemented, being herein
called the "BMO Notes").

     C. The BMO Notes and all other obligations now or hereafter existing or to
exist under the Senior Credit Agreement are guaranteed by various guaranties
(such instruments, together with any others as may now exist or hereafter be
executed pursuant to the Senior Credit Agreement, as any of the same may from
time to time be amended, renewed, restated, modified or supplemented, being
referred to herein collectively as the "Senior Guaranties").

     D. In connection with the execution and delivery of the Indenture,
JEDI-II, as agent (the "Agent"), JEDI-II, individually, ECT and B-MO, as agent
for the Senior Lenders (the "Senior Loan Agent"), have executed an
Intercreditor and Subordination Agreement dated as of August 20, 1998 (the
"Subordination Agreement") in order to evidence the relative priorities and
rights of the Senior


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<PAGE>   4

Loan Agent and the Senior Lenders under the Senior Credit Agreement to the
rights and obligations of the Agent and the Noteholders under the Indenture.

     E. The Guarantor will derive substantial benefit, both directly and
indirectly, from the making of the loans under the Indenture and the Notes and
has agreed to execute and deliver this Guaranty Agreement to the Trustee for
the benefit of the Agent and the Noteholders.

     NOW, THEREFORE, (i) in order to comply with the terms and conditions of
the Indenture, (ii) to induce the Noteholders to loan monies, with or without
security to or for the account of Borrower in accordance with the terms of the
Indenture, (iii) at the special insistence and request of the Noteholders, and
(iv) for other good and valuable consideration, the receipt and sufficiency of
which is hereby acknowledged, Guarantor hereby agrees as follows:

                                   ARTICLE 1
                                 GENERAL TERMS

     Section 1.1 Terms Defined Above or in the Indenture. As used in this
Guaranty Agreement, the terms defined above shall have the meanings
respectively assigned to them. Other capitalized terms which are defined in the
Indenture but which are not defined herein shall have the same meanings as
defined in the Indenture.

     Section 1.2 Certain Definitions. As used in this Guaranty Agreement, the
following terms shall have the following meanings, unless the context otherwise
requires:

     "Contribution Obligation" shall mean an amount equal, at any time and from
     time to time and for each respective Subsidiary Guarantor, to the product
     of (a) its Contribution Percentage times (b) the sum of all payments made
     previous to or at the time of calculation by all Subsidiary Guarantors in
     respect of the Liabilities, as a Subsidiary Guarantor (less the amount of
     any such payments previously returned to any Subsidiary Guarantor by
     operation of law or otherwise, but not including payments received by any
     Subsidiary Guarantor by way of its rights of subrogation and contribution
     under Section 2.9 of the other Guaranty Agreements), provided, however,
     such Contribution Obligation for any Subsidiary Guarantor shall in no
     event exceed such Subsidiary Guarantor's Maximum Guaranteed Amount, as
     defined in the respective Guaranty Agreement of such Subsidiary Guarantor.

     "Contribution Percentage" shall mean for any Subsidiary Guarantor for any
     applicable date as of which such percentage is being determined, an amount
     equal to the quotient of (a) the Net Worth of such Subsidiary Guarantor as
     of such date, divided by (b) the sum of the Net Worth of all the
     Subsidiary Guarantors as of such date.

     "Guarantor Claims" shall have the meaning indicated in Section 4.1 hereof.


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<PAGE>   5

     "Guaranty Agreement" shall mean this Guaranty Agreement, and where the
     context indicates, the Guaranty Agreement of any other Subsidiary
     Guarantor, as the same may from time to time be amended or supplemented.

     "Liabilities" shall mean:

          (a) any and all indebtedness, obligations and liabilities of the
     Borrower to the Agent and the Noteholders pursuant to the Indenture,
     including without limitation, the unpaid principal of and interest on the
     Notes;

          (b) any additional Obligations (as defined in the Indenture) owing to
     the Agent and the Noteholders; and

          (c) all renewals, rearrangements, increases, extensions for any
     period, amendments or supplements in whole or in part of the Notes or any
     documents evidencing the above.

     "Maximum Guaranteed Amount" shall mean, for the Guarantor, the greater of
     (a) the "reasonably equivalent value" or "fair consideration" (or
     equivalent concept) received by the Guarantor in exchange for the
     obligation incurred hereunder, within the meaning of any applicable state
     or federal fraudulent conveyance or transfer laws; or (b) the lesser of
     (i) the maximum amount that will not render the Guarantor insolvent, or
     (ii) the maximum amount that will not leave the Guarantor with any
     property deemed an unreasonably small capital. Clauses (i) and (ii) are
     and shall be determined pursuant to and as of the appropriate date
     mandated by such applicable state or federal fraudulent conveyance or
     transfer laws and to the extent allowed by law take into account the
     rights to contribution and subrogation under Section 2.9 in each Guaranty
     Agreement so as to provide for the largest Maximum Guaranteed Amount
     possible.

     "Net Payments" shall mean an amount equal, at any time and from time to
     time and for each respective Subsidiary Guarantor, to the difference of
     (a) the sum of all payments made previous to or at the time of calculation
     by such Subsidiary Guarantor in respect to the Liabilities, as a
     Subsidiary Guarantor, and in respect of its obligations contained in this
     Guaranty Agreement, less (b) the sum of all such payments previously
     returned to such Subsidiary Guarantor by operation of law or otherwise and
     including payments received by such Subsidiary Guarantor by way of its
     rights of subrogation and contribution under Section 2.9 of the other
     Guaranty Agreements.

     "Net Worth" shall mean for any Subsidiary Guarantor, calculated on and as
     of any applicable date on which such amount is being determined, the
     difference between (a) the sum of all such Subsidiary Guarantor's
     property, at a fair valuation and as of


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<PAGE>   6

     such date, minus (b) the sum of all such Subsidiary Guarantor's debts, at
     a fair valuation and as of such date, excluding the Liabilities.

     "Noteholders" shall mean the holders of the Notes from time to time, and
     the holders of any promissory note or notes given in substitution or
     replacement thereof, including, without limitation, pursuant to Section
     2.06 of the Indenture.

     "Subsidiary Guarantors" shall mean the Guarantors as defined in the
     Indenture, including the Guarantor.

                                   ARTICLE 2
                                  THE GUARANTY

     Section 2.1 Liabilities Guaranteed. Guarantor hereby irrevocably and
unconditionally guarantees the prompt payment of the Liabilities when due,
whether at maturity or otherwise, provided, however, that, notwithstanding
anything herein or in any other Basic Document to the contrary, the maximum
liability of Guarantor hereunder shall in no event exceed the Maximum
Guaranteed Amount.

     Section 2.2 Nature of Guaranty. This Guaranty Agreement is an absolute,
irrevocable, completed and continuing guaranty of payment and not a guaranty of
collection, and no notice of the Liabilities or any extension of credit already
or hereafter contracted by or extended to Borrower need be given to Guarantor.
This Guaranty Agreement may not be revoked by Guarantor and shall continue to
be effective with respect to debt under the Liabilities arising or created
after any attempted revocation by Guarantor and shall remain in full force and
effect until the Liabilities are paid in full. Borrower and the Noteholders may
modify, alter, rearrange, extend for any period and/or renew from time to time,
the Liabilities, and the Noteholders may waive any Default or Events of Default
without notice to the Guarantor and in such event Guarantor will remain fully
bound hereunder on the Liabilities. This Guaranty Agreement shall continue to
be effective or be reinstated, as the case may be, if at any time any payment
of the Liabilities is rescinded or must otherwise be returned by any of the
Noteholders upon the insolvency, bankruptcy or reorganization of Borrower or
otherwise, all as though such payment had not been made. This Guaranty
Agreement may be enforced by the Trustee, Agent and any holder of any of the
Liabilities and shall not be discharged by the assignment or negotiation of all
or part of the Liabilities. Guarantor hereby expressly waives presentment,
demand, notice of non-payment, protest and notice of protest and dishonor,
notice of Default or Event of Default, and also notice of acceptance of this
Guaranty Agreement, acceptance on the part of the Noteholders being
conclusively presumed by the Noteholders' request for this Guaranty Agreement
and delivery of the same to the Trustee.

     Section 2.3 Trustee's Rights. Guarantor authorizes the Trustee, without
notice or demand and without affecting Guarantor's liability hereunder, to take
and hold security for the payment of this Guaranty Agreement and/or the
Liabilities, and exchange, enforce, waive and release any such security; and to
apply such security and direct the order or manner of sale thereof as the
Trustee in


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its discretion may determine; and to obtain a guaranty of the Liabilities from
any one or more Persons and at any time or times to enforce, waive, rearrange,
modify, limit or release any of such other Persons from their obligations under
such guaranties.

     Section 2.4 Guarantor's Waivers. Guarantor waives any right to require the
Trustee, Agent or any of the Noteholders to (i) proceed against Borrower or any
other person liable on the Liabilities, (ii) enforce any of their rights
against any other guarantor of the Liabilities (iii) proceed or enforce any of
their rights against or exhaust any security given to secure the Liabilities
(iv) have Borrower joined with Guarantor in any suit arising out of this
Guaranty Agreement and/or the Liabilities, or (v) pursue any other remedy in
the Trustee's, the Agent's or the Noteholders' powers whatsoever. Neither the
Trustee, Agent, nor the Noteholders shall be required to mitigate damages or
take any action to reduce, collect or enforce the Liabilities. Guarantor waives
any defense arising by reason of any disability, lack of corporate authority or
power, or other defense of Borrower or any other guarantor of the Liabilities,
and shall remain liable hereon regardless of whether Borrower or any other
guarantor be found not liable thereon for any reason. Whether and when to
exercise any of the remedies of the Trustee, Agent or the Noteholders under any
of the Basic Documents shall be in the sole and absolute discretion of the
Trustee, acting on behalf of itself, the Agent and the Noteholders, and no
delay by the Trustee in enforcing any remedy, including delay in conducting a
foreclosure sale, shall be a defense to the Guarantor's liability under this
Guaranty Agreement.

     Section 2.5 Maturity of Liabilities; Payment. Guarantor agrees that if the
maturity of any of the Liabilities is accelerated by bankruptcy or otherwise,
such maturity shall also be deemed accelerated for the purpose of this Guaranty
Agreement without demand or notice to Guarantor. Guarantor will, forthwith upon
notice from the Trustee, pay to the Trustee the amount due and unpaid by
Borrower and guaranteed hereby. The failure of the Trustee to give this notice
shall not in any way release Guarantor hereunder.

     Section 2.6 Trustee's, Agent's and Noteholders' Expenses. If Guarantor
fails to pay the Liabilities after notice from Trustee of Borrower's failure to
pay any Liabilities at maturity, and if the Trustee, Agent or any Noteholder
obtains the services of an attorney for collection of amounts owing by
Guarantor hereunder, or obtaining advice of counsel in respect of any of their
rights under this Guaranty Agreement, or if suit is filed to enforce this
Guaranty Agreement, or if proceedings are had in any bankruptcy, probate,
receivership or other judicial proceedings for the establishment or collection
of any amount owing by Guarantor hereunder, or if any amount owing by Guarantor
hereunder is collected through such proceedings, Guarantor agrees to pay to the
Trustee, Agent and Noteholder, the Trustee's, Agent's and Noteholder's
respective reasonable attorneys' fees.

     Section 2.7 Liability. It is expressly agreed that the liability of the
Guarantor for the payment of the Liabilities guaranteed hereby shall be primary
and not secondary.

     Section 2.8 Events and Circumstances Not Reducing or Discharging
Guarantor's Obligations. Guarantor hereby consents and agrees to each of the
following to the fullest extent permitted by law, and agrees that Guarantor's
obligations under this Guaranty Agreement shall not


                                      -5-
<PAGE>   8

be released, diminished, impaired, reduced or adversely affected by any of the
following, and waives any rights (including without limitation rights to
notice) which Guarantor might otherwise have as a result of or in connection
with any of the following:

         (a) Modifications, etc. Any renewal, extension, modification,
increase, decrease, alteration or rearrangement of all or any part of the
Liabilities, the Notes, the Indenture or the Basic Documents or any instrument
executed in connection therewith, or any contract or understanding between
Borrower and the Trustee, the Agent or any of the Noteholders, or any other
Person, pertaining to the Liabilities;

         (b) Adjustment, etc. Any adjustment, indulgence, forbearance or
compromise that might be granted or given by any Trustee, Agent or any
Noteholder to Borrower or Guarantor or any Person liable on the Liabilities;

         (c) Condition of Borrower or Guarantor. The insolvency, bankruptcy
arrangement, adjustment, composition, liquidation, disability, dissolution,
death or lack of power of Borrower or Guarantor or any other Person at any time
liable for the payment of all or part of the Liabilities; or any dissolution of
Borrower or Guarantor, or any sale, lease or transfer of any or all of the
assets of Borrower or Guarantor, or any changes in the shareholders, partners,
or members of Borrower or Guarantor; or any reorganization of Borrower or
Guarantor;

         (d) Invalidity of Liabilities. The invalidity, illegality or
unenforceability of all or any part of the Liabilities, or any document or
agreement executed in connection with the Liabilities, for any reason
whatsoever, including without limitation the fact that the Liabilities, or any
part thereof, exceed the amount permitted by law, the act of creating the
Liabilities or any part thereof is ultra vires, the officers or representatives
executing the documents or otherwise creating the Liabilities acted in excess
of their authority, the Liabilities violate applicable usury laws, the Borrower
has valid defenses, claims or offsets (whether at law, in equity or by
agreement) which render the Liabilities wholly or partially uncollectible from
Borrower, the creation, performance or repayment of the Liabilities (or the
execution, delivery and performance of any document or instrument representing
part of the Liabilities or executed in connection with the Liabilities, or
given to secure the repayment of the Liabilities) is illegal, uncollectible,
legally impossible or unenforceable, or the Indenture, the Basic Documents or
other documents or instruments pertaining to the Liabilities have been forged
or otherwise are irregular or not genuine or authentic;

         (e) Release of Obligors. Any full or partial release of the liability
of Borrower on the Liabilities or any part thereof, of any co-guarantors, or
any other Person now or hereafter liable, whether directly or indirectly,
jointly, severally, or jointly and severally, to pay, perform, guarantee or
assure the payment of the Liabilities or any part thereof, it being recognized,
acknowledged and agreed by Guarantor that Guarantor may be required to pay the
Liabilities in full without assistance or support of any other Person, and
Guarantor has not been induced to enter into this Guaranty Agreement on the
basis of a contemplation, belief, understanding or agreement that other parties


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<PAGE>   9

other than the Borrower will be liable to perform the Liabilities, or the
Trustee, Agent or any of the Noteholders will look to other parties to perform
the Liabilities.

         (f) Other Security. The taking or accepting of any other security,
collateral or guaranty, or other assurance of payment, for all or any part of
the Liabilities;

         (g) Release of Collateral, etc. Any release, surrender, exchange,
subordination, deterioration, waste, loss or impairment (including without
limitation negligent, willful, unreasonable or unjustifiable impairment) of any
collateral, property or security, at any time existing in connection with, or
assuring or securing payment of, all or any part of the Liabilities;

         (h) Care and Diligence. The failure of the Trustee, Agent, Noteholders
or any other Person to exercise diligence or reasonable care in the
preservation, protection, enforcement, sale or other handling or treatment of
all or any part of such collateral, property or security;

         (i) Status of Liens. The fact that any collateral, security, security
interest or lien contemplated or intended to be given, created or granted as
security for the repayment of the Liabilities shall not be properly perfected
or created, or shall prove to be unenforceable or subordinate to any other
security interest or lien, it being recognized and agreed by Guarantor that
Guarantor is not entering into this Guaranty Agreement in reliance on, or in
contemplation of the benefits of, the validity, enforceability, collectibility
or value of any of the collateral for the Liabilities;

         (j) Payments Rescinded. Any payment by Borrower to the Trustee, Agent
or the Noteholders is held to constitute a preference under the bankruptcy
laws, or for any reason the Trustee, Agent or the Noteholders are required to
refund such payment or pay such amount to Borrower or someone else; or

         (k) Other Actions Taken or Omitted. Any other action taken or omitted
to be taken with respect to the Basic Documents, the Liabilities, or the
security and collateral therefor, whether or not such action or omission
prejudices Guarantor or increases the likelihood that Guarantor will be
required to pay the Liabilities pursuant to the terms hereof; it being the
unambiguous and unequivocal intention of Guarantor that Guarantor shall be
obligated to pay the Liabilities when due, notwithstanding any occurrence,
circumstance, event, action, or omission whatsoever, whether contemplated or
uncontemplated, and whether or not otherwise or particularly described herein,
except for the full and final payment and satisfaction of the Liabilities.

     Section 2.9 Right of Subrogation and Contribution. If Guarantor makes a
payment in respect of the Liabilities, it shall be subrogated to the rights of
the Trustee against the Borrower with respect to such payment and shall have
the rights of contribution against the other Subsidiary Guarantors set forth in
Section 2.9 of the Subsidiary Guarantors' Guaranty Agreements; provided that
Guarantor shall not enforce its rights to any payment by way of subrogation or
by exercising its rights of contribution or reimbursement or the right to
participate in any security now or hereafter held by or for the benefit of the
Trustee, Agent or any of the Noteholders until the Liabilities have been paid


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in full. The Guarantor agrees that after all the Liabilities have been paid in
full that if its then current Net Payments are less than the amount of its then
current Contribution Obligation, Guarantor shall pay to the other Subsidiary
Guarantors an amount (together with any payments required of the other
Subsidiary Guarantors by Section 2.9 of each other Guaranty Agreement) such
that the Net Payments made by all Subsidiary Guarantors in respect of the
Liabilities shall be shared among all of the Subsidiary Guarantors in
proportion to their respective Contribution Percentage.

                                   ARTICLE 3
                         REPRESENTATIONS AND WARRANTIES

     Section 3.1 By Guarantor. In order to induce the Trustee, Agent and the
Noteholders to accept this Guaranty Agreement, Guarantor represents and
warrants to the Trustee, Agent and the Noteholders (which representations and
warranties will survive the creation of the Liabilities and any extension of
credit thereunder) that:

         (a) Benefit to Guarantor. Guarantor's guaranty pursuant to this
Guaranty Agreement reasonably may be expected to benefit, directly or
indirectly, Guarantor.

         (b) Existence. Guarantor is duly organized, legally existing and in
good standing under the laws of the state of its formation and is duly
qualified as a foreign entity in all jurisdictions wherein the property owned
or the business transacted by it makes such qualification necessary.

         (c) Power and Authorization. Guarantor is duly authorized and
empowered to execute, deliver and perform this Guaranty Agreement and all
corporate or other organizational action on Guarantor's part requisite for the
due execution, delivery and performance of this Guaranty Agreement has been
duly and effectively taken.

         (d) Binding Obligations. This Guaranty Agreement constitutes valid and
binding obligations of Guarantor, enforceable in accordance with its terms
(except that enforcement may be subject to any applicable bankruptcy,
insolvency or similar laws generally affecting the enforcement of creditors'
rights or by general principles of equity).

         (e) No Consent. Guarantor's execution, delivery and performance of
this Guaranty Agreement does not require the consent or approval of any other
Person, including without limitation any regulatory authority or governmental
body of the United States or any state thereof or any political subdivision of
the United States or any state thereof.

         (f) Solvency. The Guarantor hereby represents that (i) it is not
insolvent as of the date hereof and will not be rendered insolvent as a result
of this Guaranty Agreement, (ii) it is not engaged in business or a
transaction, or about to engage in a business or a transaction, for which any
property or assets remaining with such Guarantor is unreasonably small capital,
and (iii) it does not intend to incur, or believe it will incur, debts that
will be beyond its ability to pay as such debts mature.


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<PAGE>   11

         (g) Litigation. Except as disclosed to the Noteholders in Schedule
4.03 of the Securities Purchase Agreement, 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 Guarantor
threatened against the Guarantor or any of its Subsidiaries which involves the
possibility of any judgment or liability against the Guarantor or any of its
Subsidiaries not fully covered by insurance (except for normal deductibles),
and which would be more likely than not to have a Material Adverse Effect.

         (h) No Breach. Neither the execution and delivery of this Guaranty
Agreement, nor compliance with the terms and provisions hereof will conflict
with or result in a breach of, or require any consent which has not been
obtained as of the Closing Date under, the respective charter or by-laws or
other constituent documents of the Guarantor or any of its Subsidiaries or any
Governmental Requirement or any material agreement or instrument to which the
Guarantor or any of its Subsidiaries is a party or by which it is bound or to
which it or its Properties are subject, or constitute a default under any such
agreement or instrument, or result in the creation or imposition of any Lien
upon any of the material revenues or assets of the Guarantor or any of its
Subsidiaries pursuant to the terms of any such agreement or instrument other
than the Liens created by the Basic Documents.

     Section 3.2 No Representation by Noteholders. Neither the Trustee, the
Agent or the Noteholders nor any other Person has made any representation,
warranty or statement to the Guarantor in order to induce the Guarantor to
execute this Guaranty Agreement.

                                   ARTICLE 4
                         SUBORDINATION OF INDEBTEDNESS

     Section 4.1 Subordination of All Guarantor Claims. As used herein, the
term "Guarantor Claims" shall mean all debts and liabilities of Borrower to
Guarantor, whether such debts and liabilities now exist or are hereafter
incurred or arise, or whether the obligation of Borrower thereon be direct,
contingent, primary, secondary, several, joint and several, or otherwise, and
irrespective of whether such debts or liabilities be evidenced by note,
contract, open account, or otherwise, and irrespective of the person or persons
in whose favor such debts or liabilities may, at their inception, have been, or
may hereafter be created, or the manner in which they have been or may
hereafter be acquired by Guarantor. The Guarantor Claims shall include without
limitation all rights and claims of Guarantor against Borrower arising as a
result of subrogation or otherwise as a result of Guarantor's payment of all or
a portion of the Liabilities. If any Default exists and is continuing, and if
the Trustee gives notice thereof to the Guarantor requiring the Guarantor
Claims not be paid, then, for so long as any Default continues to exist,
Guarantor shall not receive or collect, directly or indirectly, from Borrower
or any other party any amount upon the Guarantor Claims.

     Section 4.2 Claims in Bankruptcy. In the event of receivership,
bankruptcy, reorganization, arrangement, debtor's relief, or other insolvency
proceedings involving Borrower as debtor, the Trustee, Agent and/or the
Noteholders shall have the right to prove their claim in any


                                      -9-
<PAGE>   12

proceeding, so as to establish its rights hereunder and receive directly from
the receiver, trustee or other court custodian, dividends and payments which
would otherwise be payable upon Guarantor Claims. Guarantor hereby assigns such
dividends and payments to the Trustee, as trustee under the Indenture. Should
the Trustee, Agent or any Noteholder receive, for application upon the
Liabilities, any such dividend or payment which is otherwise payable to
Guarantor, and which, as between Borrower and Guarantor, shall constitute a
credit upon the Guarantor Claims, then upon payment in full of the Liabilities,
Guarantor shall become subrogated to the rights of the Trustee, Agent or the
Noteholders, as applicable, to the extent that such payments to the Trustee,
Agent or the Noteholders, as applicable, on the Guarantor Claims have
contributed toward the liquidation of the Liabilities, and such subrogation
shall be with respect to that proportion of the Liabilities which would have
been unpaid if the Trustee, Agent or Noteholders, as applicable, had not
received dividends or payments upon the Guarantor Claims.

     Section 4.3 Payments Held in Trust. In the event that notwithstanding
Sections 4.1 and 4.2 above, Guarantor should receive any funds, payments,
claims or distributions which are prohibited by such Sections, Guarantor agrees
to hold in trust for the Trustee, as trustee under the Indenture, an amount
equal to the amount of all funds, payments, claims or distributions so
received, and agrees that it shall have absolutely no dominion over the amount
of such funds, payments, claims or distributions except to pay them promptly to
the Trustee, and Guarantor covenants promptly to pay the same to the Trustee.

     Section 4.4 Liens Subordinate. Guarantor agrees that any liens, security
interests, judgment liens, charges or other encumbrances upon Borrower's assets
securing payment of the Guarantor Claims shall be and remain inferior and
subordinate to any liens, security interests, judgment liens, charges or other
encumbrances upon Borrower's assets securing payment of the Liabilities,
regardless of whether such encumbrances in favor of Guarantor, the Trustee,
Agent or the Noteholders presently exist or are hereafter created or attach.
Without the prior written consent of the Trustee, Guarantor shall not (a)
exercise or enforce any creditor's right it may have against the Borrower, or
(b) foreclose, repossess, sequester or otherwise take steps or institute any
action or proceeding (judicial or otherwise, including without limitation the
commencement of or joinder in any liquidation, bankruptcy, rearrangement,
debtor's relief or insolvency proceeding) to enforce any lien, mortgages, deeds
of trust, security interest, collateral rights, judgments or other encumbrances
on assets of Borrower held by Guarantor.

                                   ARTICLE 5
                                 MISCELLANEOUS

     Section 5.1 Successors and Assigns. This Guaranty Agreement is and shall
be in every particular available to the successors and assigns of Trustee,
Agent and the Noteholders and is and shall always be fully binding upon the
legal representatives, heirs, successors and assigns of Guarantor,
notwithstanding that some or all of the monies, the repayment of which this
Guaranty Agreement applies, may be actually advanced after any bankruptcy,
receivership, reorganization, death, disability or other event affecting
Guarantor. The Trustee may resign, withdraw or be replaced


                                     -10-
<PAGE>   13

as trustee under the Indenture, and upon any such event a new trustee may be
appointed under the Indenture. In such event, Trustee shall be fully discharged
thereafter from all liability therefor, and any new trustee under the Indenture
shall be vested with all rights, powers and remedies of Trustee hereunder. In
connection therewith, Guarantor will take whatever action is reasonably
required in order to reaffirm its obligations under this Guaranty Agreement

     Section 5.2 Notices. Any notice or demand to Guarantor under or in
connection with this Guaranty Agreement may be given and shall conclusively be
deemed and considered to have been given and received in accordance with
Section 13.05 of the Indenture, addressed to Guarantor at the address on the
signature page hereof or at such other address provided to Trustee and Agent in
writing.

     Section 5.3 Business and Financial Information. Subject to any applicable
confidentiality agreements, the Guarantor will promptly furnish to Trustee,
Agent and the Noteholders from time to time upon request such information
regarding the business and affairs and financial condition of the Guarantor and
its subsidiaries as the Trustee, Agent or the Noteholders may reasonably
request.

     Section 5.4 Construction. This Guaranty Agreement is a contract made under
and shall be construed in accordance with and governed by the laws of the State
of Texas.

     Section 5.5 Invalidity. In the event that any one or more of the
provisions contained in this Guaranty Agreement shall, for any reason, be held
invalid, illegal or unenforceable in any respect, such invalidity, illegality
or unenforceability shall not affect any other provision of this Guaranty
Agreement.

     Section 5.6 Subordination Agreement. This Guaranty Agreement and the
rights and remedies of Agent and the Noteholders under this Guaranty Agreement
are subject to the terms and conditions of the Subordination Agreement.

     Section 5.7 ENTIRE AGREEMENT. THIS WRITTEN GUARANTY AGREEMENT EMBODIES THE
ENTIRE AGREEMENT AND UNDERSTANDING AMONG THE AGENT, THE NOTEHOLDERS AND THE
GUARANTOR AND SUPERSEDES ALL OTHER AGREEMENTS AND UNDERSTANDINGS BETWEEN SUCH
PARTIES RELATING TO THE SUBJECT MATTER HEREOF AND THEREOF. THIS WRITTEN
GUARANTY AGREEMENT REPRESENTS THE FINAL AGREEMENT BETWEEN THE PARTIES AND MAY
NOT BE CONTRADICTED BY EVIDENCE OF PRIOR, CONTEMPORANEOUS, OR SUBSEQUENT ORAL
AGREEMENTS OF THE PARTIES. THERE ARE NO UNWRITTEN ORAL AGREEMENTS BETWEEN THE
PARTIES.


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<PAGE>   14

     WITNESS THE EXECUTION HEREOF, as of this the 20th day of August, 1998.

                                        [See Schedule I hereto]



                                        By:
                                           ------------------------------------
                                        Name:
                                        Title:

                                        Address:
                                                -------------------------------

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

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

                                        Telecopier No.:
                                                       ------------------------
                                        Telephone No.:
                                                      -------------------------
                                        Attention:
                                                  -----------------------------


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<PAGE>   15

                                   Schedule I

Subsidiary Guarantors

Brigham Oil & Gas, L.P.
Brigham, Inc.
Brigham Holdings I, LLC
Brigham Holdings II, LLC
Sooner Production, LLC
DND Oil & Gas, L.P.



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