Exhibit 10.50

REGISTRATION RIGHTS AGREEMENT

THIS REGISTRATION RIGHTS AGREEMENT (this"Agreement") is entered into as of December 20, 2002, by and among
Brigham Exploration Company, a Delaware corporation (the"Company"), and Shell Capital Inc. ("SCI").

RECITALS

WHEREAS, pursuant to that certain Exchange Agreement (the"Exchange Agreement") dated as of November 21,
2002 between the Company and SCI, the Company has agreed to issue SCI 550,000 shares of the Company's common stock, par value $.01 per share (the"Common
Stock");

WHEREAS,
in connection with such issuance, the Company and SCI desire to enter into this Agreement in order to grant the registration rights as set forth below.

AGREEMENT

1.Definitions

For
purposes of this Agreement, the following terms have the following meanings:



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2.Request for Registration



3.Company Registration

If
the Company proposes to register (including for this purpose a registration effected by the Company for stockholders ("Requesting
Holders") other than the Holders) any of its stock or other securities under the Act in connection with the public offering of such securities solely for cash (other than a
registration relating solely to the sale of securities to participants in a Company stock plan, or a registration on any form that does not include substantially the same information as would be
required to be included in a registration statement covering the sale of Registrable Securities), the Company shall, at each such time, promptly give each Holder written notice of such registration.
Upon the written request of each such Holder given within 20 days after receipt of such notice by such Holder from the Company, the Company shall, subject to the provisions of the following
sentence, use its reasonable best efforts to cause to be registered under the Act all of the Registrable Securities that each such Holder has requested to be registered. If the managing underwriter of
a proposed public offering shall advise the Company in writing that, in its opinion, the distribution of the Registrable Securities requested to be included in the registration concurrently with the
securities being registered
by the Company or any Requesting Holder would materially and adversely affect the distribution of such securities by the Company or such Requesting Holders, then all selling security holders (but not
the Company or the Requesting Holders) shall reduce the amount of Registrable Securities of each intended to be distributed through such offering on a pro rata basis to the greatest aggregate amount
which, in the opinion of such managing underwriter, would not materially and adversely affect the distribution of such securities.

In
the event that the Company decides for any reason not to complete the registration of shares of Common Stock other than Registrable Securities, the Company shall have no obligation
under this Section 3 to continue with the registration of Registrable Securities. Any request pursuant to this

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Section 3 to register Registrable Securities as part of an underwritten public offering of Common Stock shall specify that such Registrable Securities are to be included in the underwriting on
the same terms and conditions as the shares of Common Stock otherwise being sold through underwriters under such registration. Notwithstanding any provision herein, the rights of all Holders under
this Section 3 are subject to the express limitations contained in the registration rights agreements in effect on the date hereof between the Company and other parties, all of which are on
file with the SEC on the date hereof.

4.Obligations of the Company

Whenever
required under this Agreement to effect the registration of any Registrable Securities, the Company shall, as expeditiously as reasonably possible:



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5.Furnish Information

It
shall be a condition precedent to the obligations of the Company to take any action pursuant to this Agreement that the selling Holders shall furnish to the Company such information
regarding themselves, the Registrable Securities held by them and the intended method of disposition of such securities as shall be reasonably required to effect the registration of their Registrable
Securities and shall execute such documents in connection with such registration as the Company may reasonably request.

6.Expenses of Registration

In
connection with any registration pursuant to this Agreement, the Company shall be responsible for the payment of all reasonable expenses of the registration, with the exception of
(i) underwriting discounts and commissions, which shall be paid by the Company, the Holders and any other selling ho lders of the Company's securities in proportion to the aggregate value of
the securities offered for sale by each of them, (ii) the fees and expenses of counsel to the selling Holders The expenses to be paid by the Company shall include, without limitatio n, all
registration, filing and qualification fees, printing and accounting fees, and the fees and disbursements of counsel for the Company; provided, however, that the Company shall not be required to pay
for any expenses of any registration proceeding begun pursuant to Section 2 if the registration request is subsequently withdrawn (other than a withdrawal due to a material adverse change in
the Company's business or financial condition or pursuant to the last sentence of Section 2(c)), unless, in the eve nt of a registration initiated pursuant to the provisions of
Section 2, the Holders of all of the Registrable Securities agree to forfeit the right to one demand registration.

7.Delay of Registration

No
Holder shall have any right to obtain or seek an injunction restraining or otherwise delaying any registration of the Company as the result of any controversy that might arise with
respect to the interpretation or implementation of this Agreement.

8.Indemnification

In
the event any Registrable Securities are included in a registration statement under this Agreement:



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9.Reports Under the Act

With
a view to making available to the Holders the benefits of SEC Rule 144 promulgated under the Act and any other rule or regulation of the SEC that may at an time permit a
Holder to sell securities of the Company to the public without registration or pursuant to a registration on Form S-3, the Company agrees to use commercially reasonable efforts to:



10.Assignment of Registration Rights

The
rights to cause the Company to register Registrable Securities pursuant to this Agreement may be assigned by a Holder to a transferee or assignee of such securities who shall, upon
such transfer or assignment, be deemed a "Holder" under this Agreement; provided that the Company is, within a reasonable period of time after such transfer, furnished with written notice of the name
and address of such transferee or assignee and the securities with respect to which such registration rights are being assigned; provided, further, that such assignment shall be effective only if
immediately following such transfer the further disposition of such securities by the transferee or assignee is restricted under the Act and that such transferee or assignee is (a) an entity
controlling, controlled by or under common control with any Holder that is not an individual or (b) a transferee or assignee that after the transfer or assignment holds at least
one-third of the Registrable Securities or 175,000 of the Registrable Securities, whichever is greater.

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11."Market Standoff" Agreement

The
Holders hereby agree that they shall not, to the extent requested by the Company and an underwriter of Common Stock (or other securities) of the Company, sell or otherwise transfer
or dispose (other than to transferees who agree to be similarly bound) of any Registrable Securities for 180 days following the effective date of a registration statement of the Company filed
under the Act; provided, however, that the foregoing shall not be effective unless all officers and directors of the Company (whether or not pursuant to this Agreement) enter into similar agreements
and the Company has used all reasonable efforts to obtain similar agreements from all holders of at least 1% of the Company's then outstanding Common Stock.

To
enforce the foregoing covenant, the Company may impose stop-transfer instructions with respect to the Registrable Securities of the Holders (and the shares or securities
of every other person subject to the foregoing restriction) until the end of such period.

12.Termination of Registration Rights

The
registration rights granted under Sections 2, 3 and 4 of this Agreement shall terminate as to each Holder on the third (3rd) anniversary of the date of this Agreement.

13.Miscellaneous



Any
notice required or permitted under this Agreement shall be given in writing and shall be deemed effectively given (a) upon personal delivery to the party to be notified,
(b) upon confirmation of receipt by fax by the party to be notified, (c) one business day after deposit with a reputable overnight courier, prepaid for overnight delivery and addressed
as set forth in (d), or (d) three days after deposit with the United States Post Office, postage prepaid, registered or certified with return receipt requested and addressed to the party to be
notified at the address indicated for such party on the signature page, or at such other address as such party may designate by 10 days' advance written notice to the other parties given in the
foregoing manner.

13.2Amendments and Waivers

Any
term of this Agreement may be amended and the observance of any term may be waived (either generally or in a particular instance and either retroactively or prospectively) only with
the written consent of the Company and the holders of a majority of the Registrable Securities then outstanding; provided that no amendment may have the effect of excluding any Holder from
participating in any registratio n covered hereby or grant additional rights to any Holder that are not granted to all Holders, unless the Holder adversely affected has executed the amendment.
Additional Holders may be added to this Agreement with such consent by amendingSchedule Aand adding a signature page executed by such
additional Holder.

13.3Governing Law; Jurisdiction; Venue

This
Agreement shall be governed by and construed under the laws of the State of New York without regard to principles of conflict of laws. The parties irrevocably consent to the
jurisdiction and venue of the state and federal courts located in New York City in connection with any action relating to this Agreement.

13.4Successors and Assigns

The
terms and conditions of this Agreement shall inure to the benefit of and be binding on the respective successors and assigns of the parties as provided herein.

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13.5.Severability

If
one or more provisions of this Agreement are held to be-unenforceable under applicable law, such provision shall be excluded from this Agreement, and the balance of this
Agreement shall be interpreted as if such provision were so excluded and shall be enforceable in accordance with its terms.

13.6Entire Agreement; Counterparts

This
Agreement constitutes the entire agreement between the parties about its subject and supersedes all prior agreements. This Agreement may be executed in two or more counterparts,
which together shall constitute one instrument.

[Signature
page follows]

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

| |  | BRIGHAM EXPLORATION COMPANY                                                                                                                      
| |  | -------------------------------------------------------------------------------------------------------------------------------------------------
| |  | By:                                                                                                                                              
| |  |                                                                                                                                                  
| |  | Address:                                                                                                                                         
| |  | Brigham Exploration Company
6300 Bridge Point Parkway
Building 2, Suite 500
Austin, TX 78730
Attention: Chief Financial Officer
Fax: 512-427-3400
| |  | SHELL CAPITAL INC.                                                                                                                               
| |  | By:                                                                                                                                              
| |  |                                                                                                                                                  
| |  | Address:                                                                                                                                         
| |  |                                                                                                                                                  
| |  |                                                                                                                                                  
| |  | with a copy to:                                                                                                                                  
| |  |                                                                                                                                                  
| |  |                                                                                                                                                  

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| |  | and a copy to:
| |  | --------------
| |  |               
| |  |               
| |  |               

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Schedule A  to Registration Rights Agreement

|Holder Name                                |  | Number of Shares
|------------------------------------------ |  | ----------------
|Shell Capital Inc.,
a Delaware corporation |  | 550,000         

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