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                                                                   EXHIBIT 10(b)


                              SECOND AMENDMENT TO
                             PLAINS RESOURCES INC.
                           1992 STOCK INCENTIVE PLAN

     Plains Resources Inc., having heretofore adopted the Plains Resources Inc.
1992 Stock Incentive Plan (the "Plan"), as amended by that certain First
Amendment to the Plan dated February 6, 1997, and having reserved the right
under Section 9 thereof to amend the Plan, does hereby amend the Plan, effective
as of May 22, 1997, as follows:

1.   Article 8 of the Plan is hereby amended and restated in its entirety 
     to read as follows:

     8.  Awards to Non-employee Directors.

              8.1  Awards in Lieu of Regular Meeting Attendance Fees. Each Non-
     employee Director shall have the right to make an annual election to
     receive Shares (a "Shares Election") in lieu of regular meeting attendance
     fees (excluding attendance fees for special meetings, committee meetings
     and telephonic meetings) earned for service on the Board in the year
     following receipt by the Company of a Shares Election.

              (a)  Shares Election.  A Non-employee Director may make a Shares
     Election by written notice to the Secretary of the Company on or before
     each annual stockholders' meeting and such election shall remain in effect
     for a one-year period which shall begin on the day of the annual
     stockholders' meeting and end on the day before the succeeding annual
     stockholders' meeting (the "Election Year").  Provided, however, a Non-
     employee Director who is elected or appointed to the Board at a time other
     than the annual stockholders' meeting, may make a Shares Election by
     written notice to the Secretary of the Company within 10 days after the
     date his term begins and such election shall remain in effect for the
     remainder of the Election Year.

              (b)  Issuance of Shares. After each regular meeting of the Board,
     the Company shall award to each Non-employee Director who made a Shares
     Election and attended such meeting, a number of Shares (rounded to the
     nearest whole Share) determined by dividing the amount of the fee to which
     he would have otherwise been entitled for attendance at such meeting by the
     Fair Market Value of a Share on the date of such meeting. Certificates for
     the Shares awarded shall be issued to the recipient as soon as practicable
     and thereupon the recipient shall have full voting, dividend and other
     ownership rights with respect to such Shares.
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              8.2  Awards in Lieu of Committee Chairmen Fees. Each Non-employee
     Director who is appointed to serve as a Chairman of a committee (a
     "Committee Chairman") of the Board shall have the right to make an annual
     election to receive Shares (a "Chairman's Election") in lieu of the annual
     fee earned for service as a Committee Chairman.

              (a)  Chairman's Election. A Committee Chairman may make a
     Chairman's Election by written notice to the Secretary of the Company on or
     before the tenth (10/th/) day following the Board meeting at which he or
     she is appointed (or re-appointed) to serve as a Committee Chairman.

              (b)  Issuance of Shares. Upon receipt of a Chairman's Election,
     the Company shall award to each Committee Chairman who made such an
     election, a number of Shares (rounded to the nearest whole share)
     determined by dividing the amount of the annual fee to which he or she
     would otherwise be entitled to receive for his service as a Committee
     Chairman by the Fair Market Value of a Share on the date of the meeting at
     which he was appointed as a Committee Chairman. Following the receipt of a
     Chairman's Election, a certificate for the Shares awarded shall be issued
     the recipient as soon as practicable and thereupon the recipient shall have
     full voting, dividend and other ownership rights with the respect to such
     Shares.

     Adopted by the Board of Directors of Plains Resources Inc. on May 22, 1997.