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                                                                   EXHIBIT 10.13


                      ASSIGNMENT OF STOCK WARRANT RIGHTS

     This Assignment of Stock Warrant Rights (this "Assignment") is made
effective as of May 31, 2000, by and among Crosby Capital LLC, a Texas limited
liability company ("Warrant Rights Holder"), and Aviva Petroleum Inc., a Texas
corporation ("Parent").

                                 R E C I T A L

     WHEREAS, pursuant to Sections 1.03 and 5.03 of that certain Loan,
Settlement and Acquisition Agreement dated as of May 31, 2000 (the "Purchase
Agreement"), by and among Warrant Rights Holder, and Parent, Aviva America,
Inc., a Delaware corporation ("Aviva America"), Aviva Operating, Inc., a
Delaware corporation ("Aviva Operating"), Aviva Overseas, Inc., a Delaware
corporation ("Aviva Overseas"), Neo Energy Inc., a Texas corporation ("Neo"),
Garnet Resources Corp., a Delaware corporation ("Garnet"), Argosy Energy, Inc.,
a Delaware corporation ("Argosy Energy"), and Argosy Energy International, a
Utah limited partnership ("Argosy International"), Warrant Rights Holder agreed
to transfer and deliver to Parent Warrant Rights Holder's right to purchase
1,500,000 shares of Parent's common stock (the "Warrant Rights").

                               A G R E E M E N T

     NOW, THEREFORE, in consideration of the promises herein and in the Purchase
Agreement, and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Warrant Rights Holder and
Parent hereby agree as follows:

     1.   Transfer of Warrant Rights. Warrant Rights Holder hereby conveys,
          --------------------------
transfers, assigns, grants, sells and delivers, to Parent, and Parent acquires,
accepts and purchases, all of Warrant Rights Holder's right, title and interest
in and to the Warrant Rights.

     2.   Assumption. Parent hereby assumes and accepts the Warrant Rights.
          ----------

     3.   Delivery. Warrant Rights Holder is delivering to Parent simultaneously
          --------
herewith that certain Affidavit of Lost Stock Warrants executed by ING (U.S.)
Capital LLC on April 27, 2000, and Parent hereby acknowledges receipt of same.

     4.   Further Assurances. Warrant Rights Holder shall execute and deliver to
          ------------------
Parent such further documents and instruments, and take such other action, that
may be reasonably requested by Parent to evidence this conveyance, transfer and
assignment of the Warrant Rights.

     5.   Definitions. All capitalized terms not otherwise defined herein shall
          -----------
have the meaning ascribed to them in the Purchase Agreement.

     6.   Inurement. The conveyance, assignment and transfer herein shall be
          ---------
effective as of the date hereof, and shall inure to the benefit of and be
binding upon the parties hereto and their successors or permitted assigns.
However, nothing in this Assignment, express or implied, shall give any other
person any benefit or any legal or equitable right or remedy with respect
hereto.
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     7.   Conveyance Subject to the Purchase Agreement. This conveyance is made
          --------------------------------------------
pursuant to the Purchase Agreement and is subject to the terms thereof.

     8.   Counterparts. This Assignment may be separately executed in
          ------------
counterparts, each of which when so executed shall be deemed to constitute one
and the same agreement. Such execution and delivery may be accomplished by
facsimile transmission.

     9.   Governing Law. This Assignment shall be governed by and construed in
          -------------
accordance with the laws of the State of Texas, without regard to principles of
conflicts of law thereof.


                           [SIGNATURES ON NEXT PAGE]

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     IN WITNESS WHEREOF, each of the undersigned has caused this Assignment to
be executed as of the day and year first written above.



                                        AVIVA PETROLEUM, INC.





                                        By: /s/ R. Suttill
                                            --------------
                                            President

                                        CROSBY CAPITAL, LLC



                                        By: /s/ Jay A. Chaffee
                                            ------------------
                                            Jay A. Chaffee
                                            President

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