SECURITIES AND NOTE ACQUISITION AGREEMENT
                    -----------------------------------------

                                    RECITALS:

         (a) Brigham Exploration Company ("BEC") and Chase Bank of Texas,
National Association, now The Chase Manhattan Bank, as Trustee (in such
capacity, herein called "Trustee"), have entered into that certain Indenture
dated as of August 20, 1998, as amended under that certain First Amendment to
Indenture dated as of March 26, 1999, and that Second Amendment to Indenture
dated as of February 17, 2000 (as so amended, and as otherwise heretofore
amended, herein called the "Indenture"); all capitalized terms used but not
defined herein shall have the meanings assigned to them in the Indenture or, if
not defined in the Indenture but defined in the form of Term ORRI Conveyance,
they shall have the meanings assigned to them in the form of Term ORRI
Conveyance.

         (b) Enron Capital & Trade Resources Corp. ("Enron Capital"),
predecessor in interest to ECT Merchant Investments Corp. ("ECT"), and Joint
Energy Development Investments II Limited Partnership ("JEDI II") (ECT and JEDI
II are herein collectively called "Noteholders") and BEC have entered into that
certain Securities Purchase Agreement dated as of August 20, 1998 (as heretofore
amended, the "SPA").

         (c) Pursuant to the terms of the SPA and the Indenture, BEC (i) issued
in favor of Enron Capital a Senior Subordinated Secured Note, in the original
principal amount of $12,500,000, which Senior Subordinated Secured Note was
replaced by a Senior Subordinated Secured Note issued to ECT (as same may have
been supplemented, amended or modified, and any other notes given in
substitution therefor or in renewal or extension thereof, herein called the "ECT
Note"), in the original principal amount of $12,500,000, and (ii) issued in
favor of JEDI II a Senior Subordinated Secured Note, in the original principal
amount of $37,500,000 (as same may have been supplemented, amended or modified,
and any other notes given in substitution therefor or in renewal or extension
thereof, herein called the "JEDI II Note") (the JEDI II Note and the ECT Note
are herein collectively called the "Notes").

         (d) Pursuant to the SPA, (i) BEC issued to Enron Capital 263,158 shares
of BEC's common stock, as evidenced by certificate number 0089, as replaced by
certificate number 0131, issued in favor of ECT, evidencing the change in
ownership of said 263,158 shares (the "ECT shares") from Enron Capital to ECT,
and (ii) BEC issued to JEDI II 789,474 shares of BEC's common stock, as
evidenced by certificate number 0131 (the "JEDI II Shares); the ECT Shares and
the JEDI II Shares are herein collectively called the "Shares".

         (e) Pursuant to the SPA and the Indenture, (i) BEC issued to ECT
250,000 warrants (the "ECT Warrants") to purchase common stock of BEC, as
evidenced by Warrant No. A-5 (the "ECT Warrant Certificate"), and (ii) BEC
issued to JEDI II 750,000 warrants to purchase common stock of BEC (the "JEDI II
Warrants"), as evidenced by Warrant No. A-6 (the JEDI II "Warrant
Certificates"); the ECT Warrants and the JEDI II Warrants are herein
collectively called the Warrants, the ECT Warrant Certificate and the JEDI II
Warrant Certificate are herein collectively called the "Warrant Certificates",


                                       1


the shares of common stock and other securities, if any, receivable upon
exercise of the ECT Warrants are herein called the ECT Warrant Shares and the
shares of common stock and other securities, if any, receivable upon exercise of
the JEDI II Warrants are herein called the JEDI II Warrant Shares, and the ECT
Warrant Shares and the JEDI II Warrant Shares are herein collectively called the
"Warrant Shares".

         (f) Pursuant to the Indenture, Brigham Oil & Gas, L.P. ("BOG") has, at
the direction of BEC, executed in favor of Noteholders a series of instruments,
each entitled Conveyance of Adjustable Term Overriding Royalty Interest,
recorded as set forth in Schedule I hereto (such instruments, as well as any
other "Term ORRI Conveyance" executed pursuant to the Indenture, are herein
collectively called the "Conveyances").

         (g) BEC desires to (i) reacquire the Shares, (ii) except as expressly
provided otherwise herein below, acquire the Notes, and all other Obligations,
including without limitation the Accrued PIK Amount (the Notes, together with
such other Obligations being herein collectively called the "Enron
Indebtedness"), together with any and all rights and interests (the "Collateral
Interests") under any Mortgage or other Collateral Documents securing same,
including without limitation under any Collateral Document described in Schedule
1 to the "Full Release", hereafter defined, (iii) acquire, terminate and cancel
the Warrants and extinguish all rights of Noteholders under the Warrant
Certificates and in relation to the Warrant Shares, and (iv) extinguish all
rights and interests, whether vested or contingent, accrued or unaccrued, under
the Indenture, the SPA and any other Equity Documents or Loan Documents,
including without limitation under any Guaranty Agreement (all of items (i)
through and including (iv), above, are herein collectively called the "Acquired
Interests"), all upon and subject to the terms and conditions hereof.

                                   AGREEMENT:

1. PURCHASE PRICE. The aggregate purchase price (the "Purchase Price") to be
paid by BEC for the Acquired Interests is Twenty Million Dollars ($20,000,000).
The Purchase Price shall be paid, in immediately available funds, in the
relative percentage shares of 25% to ECT and 75% to JEDI II, upon performance by
Noteholders and Trustee of their respective obligations hereunder. As conditions
precedent to the Noteholder's obligations hereunder, BEC shall (i) pay all
outstanding fees and expenses of the Noteholder's counsel incurred in connection
with the Acquired Interests and (ii) deliver to the Noteholders, a consent and
release from the Senior Lenders, in form and substance identical to that
attached hereto as Schedule III.

2. ACQUISITION. Except as expressly provided otherwise in subsection (a) below,
Noteholders hereby severally and not jointly, generally assign, transfer,
release, surrender and deliver unto BEC all of their collective right, title and
interest in respect of the Acquired Interests, and Trustee hereby, at the
direction of Noteholders, hereby generally assigns, transfers, releases,
surrenders and delivers unto BEC all of its right, title and interest, of any
kind or character, in, to and under the Collateral Documents and the Collateral
Interests; in order to give further effect to the foregoing, the parties
covenant and agree as follows:


                                       2


         (a)      THE TERM ORRI.
                  -------------

                  (1) At the direction of BEC, Noteholders shall, on even date
                  herewith, reassign, grant and convey to BOG, its successors
                  and assigns, under a form of reassignment substantially
                  identical to that attached hereto as Schedule I (the
                  "Reassignment"), the Term ORRI and any other rights titles and
                  interests created under a Conveyance or otherwise under or
                  pursuant to Section 7.12 of the Indenture (collectively, the
                  "Reassigned Interests"). The Reassignment shall be duly
                  executed by Noteholders, in a sufficient number of
                  counterparts as BEC shall reasonably request.

                  (2) Noteholders agree that all proceeds from or attributable
                  to the Reassigned Interests (regardless of when the severance
                  of the production to which such proceeds relates occurred),
                  other than only those proceeds that are attributable to
                  periods prior to the "Effective Date" of the Reassignment and
                  that are actually received by Noteholders on or before the
                  date hereof, shall be the property of and should be paid to
                  BOG.

                  (3) Brigham Exploration Company is an intended third party
                  beneficiary of the Reassignment.

         (b)      THE SHARES. On even date herewith, the originals of the stock
                  certificates representing the Shares, duly endorsed in blank,
                  or accompanied by stock powers duly executed in blank, and
                  otherwise in form acceptable to BEC for transfer on the books
                  of BEC, shall be delivered to BEC, and BEC shall receive from
                  Noteholders the written resignation of Jempy Neyman, a
                  representative of Noteholders as an observer on the Board of
                  Directors of BEC, such resignation to be effective as of
                  October 31, 2000.

         (c)      THE WARRANTS. On even date herewith, the original Warrant
                  Certificates, together with the associated Transfer Forms,
                  duly endorsed in blank, shall be surrendered to BEC.

         (d)      THE NOTES. On even date herewith, the Original Notes shall be
                  endorsed "pay to the order of Brigham Exploration Company,
                  without recourse or warranty" and delivered to BEC (or an
                  allonge will be attached to the same effect).

         (e)      RELEASE OF LIENS. On even date herewith, Trustee shall, at the
                  direction of Noteholders, execute a Full Release, in a form
                  substantially identical to that attached hereto as Schedule II
                  (the "Full Release"), in a sufficient number of counterparts
                  as BEC shall reasonably request.

                                    RELEASE:

(a)      DEFINED TERMS. As used in this section, the following terms shall have
         the following meanings:


                                       3


         "RELEASED CLAIMS" SHALL MEAN ANY AND ALL CLAIMS (INCLUDING WITHOUT
LIMITATION ANY LIABILITIES, DAMAGES, DEMANDS AND CAUSES OF ACTION ARISING
THEREFROM), WHETHER (A) AT LAW OR IN EQUITY, (B) ON THE ALLEGED COMMISSION OF A
TORT, (C) ON THE ALLEGED BREACH (OR ANTICIPATORY BREACH OR REPUDIATION) OF ANY
CONTRACT, DUTY, OR WARRANTY (WHETHER ORAL OR WRITTEN, EXPRESS OR IMPLIED), (D)
ON THE ALLEGED VIOLATION OF ANY STATUTE, TARIFF, OR REGULATION (WHETHER
PROMULGATED BY THE UNITED STATES, ANY STATE THEREOF, ANY FOREIGN STATE OR
COUNTRY, OR ANY OTHER GOVERNMENTAL AGENCY OR ENTITY, WHEREVER LOCATED, OR (E) ON
ANY OTHER FACTUAL, LEGAL OR EQUITABLE THEORY, INCLUDING WITHOUT LIMITATION, ANY
CLAIM FOR DAMAGES OF ANY TYPE OR NATURE FOR INJUNCTIVE OR OTHER RELIEF, FOR
ATTORNEY'S FEES, INTEREST OR ANY OTHER LIABILITY WHATSOEVER ON ANY THEORY,
INCLUDING WITHOUT LIMITATION ANY LOSS COST OR DAMAGE IN CONNECTION WITH OR BASED
UPON "LENDER LIABILITY", UNFAIR DEALING, DURESS, COERCION, CONTROL OR UNDUE
INFLUENCE, EXTORTION OR COMMERCIAL BRIBERY, BREACH OF AN IMPLIED COVENANT OR
DUTY OF GOOD FAITH AND FAIR DEALING, MATERIAL MISREPRESENTATION OR OMISSION,
OVERREACHING, UNCONSCIONABILITY, CONFLICT OF INTEREST, BAD FAITH, MALPRACTICE,
DISPARATE BARGAINING POSITION, DETRIMENTAL RELIANCE, PROMISSORY ESTOPPEL,
ESTOPPEL BY DEED, WAIVER, LACHES, OR ANY OTHER EQUITABLE THEORY, EQUITABLE
SUBORDINATION, BREACH OF FIDUCIARY DUTY OR ANY OTHER DUTY, OR TORTIOUS
INDUCEMENT TO COMMIT SUCH BREACH, TORTIOUS INTERFERENCE WITH CONTRACT OR
PROSPECTIVE BUSINESS RELATIONS, NEGLIGENT PERFORMANCE OF CONTRACTUAL
OBLIGATIONS, OR OTHER THEORIES OF NEGLIGENCE, NEGLIGENT OR INTENTIONAL
INFLICTION OF EMOTIONAL DISTRESS, SLANDER, LIBEL, OTHER DEFAMATION, FRAUDULENT
TRANSFER, CONVERSION, TRESPASS TO (OR CLOUDING THE TITLE OF) PROPERTY, USURY,
VIOLATIONS OF THE RACKETEER INFLUENCED AND CORRUPT ORGANIZATIONS ACT, DECEPTIVE
TRADE PRACTICES, CONSPIRACY, OR ANY THEORY OF LIABILITY AS PARTNERS OR JOINT
VENTURERS, THAT ANY RELEASING PARTY MAY HAVE AS OF THE DATE HEREOF AGAINST ANY
RELEASED PARTY WITH RESPECT OR RELATED TO THE ACQUIRED INTERESTS, THE
TRANSACTIONS EVIDENCED THEREBY AND THE ACTIONS AND RELATIONSHIP ARISING OUT OF
OR RELATED THERETO, OTHER THAN CLAIMS ARISING OUT OF A BREACH OF ANY
REPRESENTATION, WARRANTY OR COVENANT MADE OR UNDERTAKEN BY ANY NOTEHOLDER OR
TRUSTEE UNDER THIS AGREEMENT, THE FULL RELEASE AND/OR THE REASSIGNMENT.

         "RELEASED PARTY" shall mean each of the Trustee, the Noteholders and
their representative predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals and Affiliates and all other
Persons liable or who might be claimed to be liable on their behalf
(collectively, the "Released Parties").


                                       4


         "RELEASING PARTY" shall mean each of BEC, BOG and the Guarantors and
their respective predecessors, successors, assigns, directors, officers,
partners, employees, agents, attorneys, principals, Affiliates and all other
Persons who might have a claim against any Released Party (collectively, the
"Releasing Parties").

(b) RELEASE. EACH OF THE RELEASING PARTIES DESIRES AND INTENDS FULLY TO
COMPROMISE, RELEASE AND SETTLE ANY AND ALL OF THE RELEASED CLAIMS; AND EACH OF
THE RELEASING PARTIES HEREBY COVENANTS, WARRANTS AND REPRESENTS UNTO EACH OF THE
RELEASED PARTIES THAT SUCH RELEASING PARTY DOES HEREBY FOREVER RELEASE, ACQUIT,
WAIVE AND DISCHARGE EACH OF THE RELEASED PARTIES OF AND FROM THE RELEASED CLAIMS
AND EACH OF THE RELEASING PARTIES HEREBY DECLARES THE SAME FOREVER RELEASED,
ACQUITTED, WAIVED, SETTLED AND DISCHARGED. THIS RELEASE IS EFFECTIVE WITHOUT
REGARD TO WHETHER (I) SUCH RELEASED CLAIMS ARE KNOWN OR UNKNOWN, (II) DAMAGES
ARISING OUT OF SUCH RELEASED CLAIMS HAVE YET ACCRUED, (III) SUCH RELEASED CLAIMS
AROSE COLLATERALLY, DIRECTLY, DERIVATIVELY, OR OTHERWISE BETWEEN THE PARTIES
HERETO OR (IV) AN ORDINARY PERSON IN THE SAME OR SIMILAR CIRCUMSTANCES WOULD OR
WOULD NOT, THROUGH THE EXERCISE OF DUE CARE, HAVE DISCOVERED SUCH CLAIMS BY THE
DATE OF THIS AMENDMENT. IN CONNECTION WITH THE FOREGOING RELEASE:

                  (i) BEC, BOG and each of the Guarantors, represents and
                  warrants that it has the full power and authority to perform
                  the release granted in this section and that it has not in any
                  manner made any assignment of any Released Claim to any third
                  party.

                  (ii) The release granted in this section will be effective
                  upon execution of this Agreement by all of the parties hereto.

                  (iii) Each party executing this Agreement understands and
                  agrees that the release granted in this section is a full,
                  final and complete release of the Released Claims and that
                  such release may be pleaded as an absolute and final bar to
                  any or all suits which may hereafter be filed or prosecuted by
                  any one or more of the Releasing Parties or anyone claiming
                  by, through or under any one or more of the Releasing Parties
                  in respect of any of the matters released hereby, and that no
                  recovery on account of the Released Claims may hereafter be
                  had from any of the Released Parties; and that the
                  consideration given for such release is not an admission of
                  liability or fault on the part of any of the Released Parties
                  (it being the express intent of the parties hereto to obtain
                  peace of mind and avoid the expense and uncertainty of
                  potential litigation), and that none of the Releasing Parties
                  or those claiming by, through or under any of them will ever
                  claim that it is.


                                       5


                             ADDITIONAL PROVISIONS:

1.       REPRESENTATIONS AND WARRANTIES:

         (a)    REPRESENTATIONS AND WARRANTIES OF NOTEHOLDERS. Each Noteholder
severally and not jointly represents and warrants that:

                  (i) it owns its respective Acquired Interests, free and clear
                  of any liens, encumbrances, security agreements, equities,
                  options, claims or charges created by, through or under such
                  Noteholder.

                  (ii) in connection with the sale of the Acquired Interests to
                  BEC, each Noteholder has (A) had available such information
                  concerning BEC and the Acquired Interests as it has deemed
                  necessary in order to make an informed investment decision
                  with respect such Noteholder's disposition of the Acquired
                  Interests; (B) completed its own independent investigation,
                  analysis and evaluation of BEC; (C) made all such reviews and
                  inspections of the business, assets, results of operations,
                  condition (financial or otherwise) and prospects of BEC as it
                  has deemed necessary or appropriate; and (D) has such
                  knowledge and experience in financial and business matters
                  that it is capable of, and has relied solely upon the
                  information described above in evaluating the risks relating
                  to its disposition of the Acquired Interests.

                  (iii) In connection with the transactions contemplated hereby,
                  such Noteholder has full legal right, power and authority to
                  execute and deliver this Agreement and that this Agreement is
                  a valid and binding agreement of such Noteholder, enforceable
                  in accordance with its terms, and other than consents already
                  obtained, no consents, notices, filings or approvals are
                  required to be made or received from any person in connection
                  with BEC's and the Noteholders' execution of this agreement
                  and the transactions contemplated hereby.

                           (iv) Except for the representations and warranties
                  contained in this Section 1, neither of the Noteholders makes
                  any representation or warranty regarding the Acquired
                  Interests (including the amount or enforceability thereof).

                           (v) There are no suits, actions, claims,
                  investigations, inquiries, proceedings or demands pending (or
                  to the best of such Noteholder's knowledge, threatened) which
                  affect Noteholder's title to any of the Acquired Interests, or
                  the execution and delivery of this Securities and Note
                  Acquisition Agreement (this "Agreement") or the consummation
                  of transactions contemplated hereby.

         (b) REPRESENTATIONS AND WARRANTIES OF BEC. In connection with the
transactions contemplated hereby, BEC hereby represents and warrants to
Noteholders that (i) BEC has full legal right, power and authority to execute
and deliver this Agreement and that this Agreement is a valid and binding
agreement of BEC, enforceable in accordance with its terms, (ii) there are no
suits, actions, claims, investigations, inquiries, proceedings or demands


                                       6


pending (or to the best of BEC's knowledge, threatened) which affect any of the
Acquired Interests, or the execution and delivery of this Agreement or the
consummation of transactions contemplated hereby, and (iii) other than consents
already obtained, no consents, notices, filings or approvals are required to be
made or received from any person in connection with BEC's or the Guarantor's
execution of this agreement and the transactions contemplated hereby.

         (c) SURVIVAL OF COVENANTS, REPRESENTATIONS AND WARRANTIES. All
representations, warranties, covenants and agreements contained herein shall not
be discharged or dissolved upon, but shall survive, the Closing.

2. COUNTERPARTS: This Agreement is being executed in several counterparts, all
of which are identical; all such counterparts together shall constitute one and
the same instrument.

3. CHOICE OF LAW: THIS AGREEMENT SHALL, WITHOUT REGARD TO PRINCIPLES OF
CONFLICTS OF LAW, BE GOVERNED AND CONSTRUED UNDER AND IN ACCORDANCE WITH THE
LAWS OF THE STATE OF TEXAS.

4. FURTHER ASSURANCES: After the date hereof, Noteholders shall execute and
deliver, and shall otherwise cause to be executed and delivered, from time to
time, such further instruments, notices, division orders, transfer orders, lien
releases, financing statement releases and other documents, and do such other
and further acts and things, as may be reasonably necessary to more fully and
effectively assign or release to BOG the Acquired Interests provided that BEC
shall pay all reasonable costs and expenses incurred by the Noteholders in
connection therewith (including reasonable attorney's fees).

5. SUCCESSORS: This Agreement shall be binding upon and shall enure to the
benefit of Noteholders and BEC and their respective permitted successors and
assigns.

6. ENTIRETY AND MODIFICATION. This Agreement constitutes the entire agreement
between the parties hereto with respect to the subject matter hereof and
supercedes any and all prior agreements and understandings, whether oral or
written, between the parties hereto relating to such subject matter. No
modification, alteration, amendment or supplement to this Agreement shall be
valid or effective unless the same is in writing and signed by all parties
hereto.


         This Agreement is executed and delivered on this 31st day of October,
2000.

                                         ECT Merchant Investment Corp.
                                         By:    /s/ JESSE E. NEYMAN
                                                ----------------------------
                                         Name:  JESSE E. NEYMAN
                                                ----------------------------
                                         Title: VICE PRESIDENT
                                                ----------------------------


Brigham Oil & Gas, L.P.              Joint Energy Development Investments II
By:    Brigham, Inc.                     Limited Partnership
       Managing General Partner    By:   Enron Capital Management II
                                         Limited Partnership, General Partner
By:    /s/ KAREN E. LYNCH                By:    Enron Capital II Corp.,
       --------------------------               General Partner
Name:  KAREN E. LYNCH                    By:    /s/ JESSE E. NEYMAN
       --------------------------               ----------------------------
Title: VICE PRESIDENT                    Name:  JESSE E. NEYMAN
       --------------------------               ----------------------------
                                         Title: AGENT AND ATTORNEY-IN-FACT
                                                ----------------------------


                                        7


Brigham, Inc.                            Brigham Exploration Company
By:    /s/ KAREN E. LYNCH                By:    /s/ KAREN E. LYNCH
       --------------------------               ----------------------------
Name:  KAREN E. LYNCH                    Name:  KAREN E. LYNCH
       --------------------------               ----------------------------
Title: VICE PRESIDENT                    Title: VICE PRESIDENT
       --------------------------               ----------------------------


Brigham Holdings I, LLC                  Brigham Holdings II, LLC
a Nevada Limited Liability Company       a Nevada Limited Liability Company
By:    /s/ BEN M. BRIGHAM                By:    /s/ BEN M. BRIGHAM
       --------------------------               ----------------------------
Name:  BEN M. BRIGHAM                    Name:  BEN M. BRIGHAM
       --------------------------               ----------------------------
Title: PRESIDENT                         Title: PRESIDENT
       --------------------------               ----------------------------


                                        8