EXECUTION COPY

EXHIBIT 10(p)

EXECUTION COPY

AMENDMENT NO. 1, dated as of December 31, 1998 (this “Amendment”) to the PUT/CALL, REGISTRATION RIGHTS AND STANDSTILL AGREEMENT dated as of January 1, 1998 (the “Agreement”) among MARATHON OIL COMPANY, an Ohio corporation, USX CORPORATION, a Delaware corporation, ASHLAND INC., a Kentucky corporation and MARATHON ASHLAND PETROLEUM LLC, a Delaware limited liability company (collectively, the “Parties”).

WHEREAS, the Parties have heretofore entered into the Agreement (capitalized terms used in this Amendment and not defined herein shall have the meanings given such terms in the Agreement); and

WHEREAS, the Parties wish to amend the Agreement to reflect certain changes to the prices set forth therein.

NOW, THEREFORE, in consideration of the mutual agreements herein contained and other good and valuable consideration, the sufficiency and receipt of which are hereby acknowledged, the Parties agree as follows:

Section 1. Amendments:

(a) Section 1.01 of the Agreement is amended to insert the following definition after the definition of “Price Index” and prior to the definition of “Private Label Packaged Motor Oil Business”:

“‘Price Reduction’ shall have the meaning set forth in Section 2.02(b) of the Put/Call, Registration Rights and Standstill Agreement.”

(b) Section 2.02(a) of the Agreement is amended to read in its entirety as follows:

“(a) Amount. The Special Termination Price shall be an amount equal to (i) the product of (x) 100% of the Appraised Value of the Company multiplied by (y) the Terminating Member’s Percentage Interest, less (ii) if the Terminating Member is Ashland, the Price Reduction.”

(c) Sections 2.02(b) and 2.02(c) as numbered in the Agreement are numbered Sections 2.02(c) and 2.02(d) respectively and a new Section 2.02(b) of the Agreement is added to read in its entirety as follows:

“(b) Price Reduction. Price Reduction means an amount equal to the excess of (i) $14,139,519, which is the agreed present value at January 1, 1998, of the tax cost to Ashland (“Present Value Tax Cost”) of allocating to it depreciation deductions as shown in Chart A in Schedule 2.02(b)(1) (“Chart A Depreciation”), as compared to allocating to Ashland depreciation deductions as shown in Chart B in Schedule 2.02(b)(1) (“Chart B Depreciation”), over (ii) the present value at January 1, 1998, of the tax cost to Ashland of allocating to it Chart A Depreciation as compared to Chart B Depreciation, taking into account Ashland’s decreased taxable gain or increased taxable loss on the sale of all of its Membership Interest in the Company when Chart A Depreciation as compared to Chart B Depreciation is allocated to it (“Present Value Tax Cost on Sale”).

“Chart A Depreciation represents the agreed depreciation deductions with respect to property contributed by Ashland on the Closing of the Asset Transfer and Contribution Agreement allocated to it through the depreciable life of such property as set forth in Section 6.03 of the LLC Agreement as amended and restated as of December 31, 1998. Chart B Depreciation represents the agreed depreciation deductions with respect to property contributed by Ashland on the Closing of the Asset Transfer and Contribution Agreement allocated to it through the depreciable life of such property as set forth in Sections 6.03, 6.12 and 4.01(c) of such agreement as in effect prior to such restatement as if it were in effect through such depreciable life, but treating the assets comprising the Merrill Lynch Master Lease Program as Subleased Property listed on Schedule 4.01(c) for purposes of Sections 4.01(c) and 6.12. Chart A Depreciation and Chart B Depreciation shall not be

revised to reflect the actual amount of depreciation deductions with respect to property contributed by Ashland on the Closing of the Asset Transfer and Contribution Agreement allocated to Ashland, or to take into account the sale or other disposition by the Company of any of the property contributed by Ashland on the Closing of the Asset Transfer and Contribution Agreement.

“Solely for purposes of determining the Present Value Tax Cost and the Present Value Tax Cost on Sale, the following factors and assumptions have been and will be used: (i) discount rate of 9% per annum, (ii) combined Federal/State income tax rate of 39%, (iii) the cash flow impact of a reduction in Ashland’s income taxes for a year as the result of Chart A or Chart B Depreciation is realized on the last day of that year and (iv) the cash flow impact of Ashland’s income tax expense or benefit arising from a sale of all of its membership interest in the Company is incurred or realized on the last day of the year of sale.

“Schedule 2.02(b)(2) reflects, for purposes of illustration, the Present Value Tax Cost on Sale if Ashland sells all of its 38% membership interest in the Company on January 1, 2005. The Present Value Tax Cost on Sale with respect to Ashland’s sale of all of its interest in the Company at a date different than January 1, 2005, shall be computed in the same manner as the Present Value Tax Cost on Sale illustrated in Schedule 2.02(b)(2).

“Consistent with the foregoing principle, if Ashland sells all or part of its Membership Interest to Marathon in a transaction not otherwise described in this Agreement, the price paid by or on behalf of Marathon for such interest shall be appropriately reduced.”

(d) Attached new Schedules 2.02(b)(1) and 2.02(b)(2) are inserted between Schedule 1.03(d) and Schedule 14.01(a).

(e) Section 3.02(a) of the Agreement is amended to read in its entirety as follows:

“(a) Amount. The Marathon Call Price shall be an amount equal to (i) the product of (x) 115% of the Appraised Value of the Company multiplied by (y) Ashland’s Percentage Interest, less (ii) the Price Reduction.”

(f) Section 4.02(a) of the Agreement is amended to read in its entirety as follows:

“(a) Amount. The Ashland Put Price shall be an amount equal to the sum of (i) for that portion of the Ashland Put Price to be paid to Ashland in Cash or in Marathon Debt Securities, an amount equal to the product of (1) the excess of (x) the product of (A) 85% of the Appraised Value of the Company multiplied by (B) Ashland’s Percentage Interest over (y) the Price Reduction, multiplied by (2) the percentage of the Ashland Put Price to be paid to Ashland in Cash and/or in Marathon Debt Securities, plus (ii) for that portion of the Ashland Put Price to be paid to Ashland in Marathon Equity Securities the same as above but substituting 90% for 85% in Clause (A) and substituting Marathon Equity Securities for Cash and/or Marathon Debt Securities in clause (2).”

Section 2. Parties in Interest. This Amendment shall inure to the benefit of, and be binding upon, the Parties hereto and their respective successors, legal representatives and permitted assigns.

Section 3. Counterparts. This Amendment may be executed in counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

Section 4. Governing Law. THIS AMENDMENT SHALL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, WITHOUT GIVING EFFECT TO THE PRINCIPLES OF CONFLICTS OF LAW THEREOF. ANY RIGHT TO TRIAL BY JURY WITH RESPECT TO ANY CLAIM OR PROCEEDING RELATED TO OR ARISING OUT OF THIS AMENDMENT, OR ANY TRANSACTION OR CONDUCT IN CONNECTION HEREWITH, IS WAIVED.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the day and year first above written.

Put/Call, Registration Rights and Standstill Agreement Schedule 2.02(b)(1) Chart A and Chart B Depreciation

Chart A

Chart B

Put/Call, Registration Rights and Standstill Agreement

Schedule 2.02(b)(2)

Present Value Tax Cost on Sale Illustration

Sale of 100% Interest 1/1/2005