DEMAND PROMISSORY NOTE

Exhibit 10.1

DEMAND PROMISSORY NOTE

FOR VALUE RECEIVED, JPMORGAN CHASE BANK, N.A., solely in its capacity as trustee for MESA OFFSHORE TRUST, a trust formed under the laws of the State of Texas, having an address at 919 Congress Avenue, Austin, Texas 78701 (“Borrower”), promises to pay ON DEMAND to the order of JPMORGAN CHASE BANK, N.A. (“Lender”), whose address is 1111 Polaris Parkway, Columbus, Ohio 43240, at said address or such other address as may be designated in writing by the holder hereof from time to time, the principal sum of  THREE MILLION AND No/100 Dollars ($3,000,000.00), or, if less, the aggregate unpaid principal amount of all loans (collectively, the “Demand Loans”, and each a “Demand Loan”) made by the Lender to the Borrower, together with interest on said principal, at a rate equal to prime rate plus TWO percent (2%); provided, however, that in no event shall such rate exceed the maximum legal rate of interest permitted by applicable law.

This Demand Note evidences an extension of credit for borrowed money authorized under Section 3.07 of the Royalty Trust Indenture, dated as of December 1, 1982, by and between Mesa Petroleum Co., as Trustor, and Texas Commerce Bank National Association, as Trustee (the “Trust Indenture”).  This Demand Note shall have the priority with regard to payments set forth in Section 3.07 of the Trust Indenture, and the Borrower agrees to comply with Section 3.07 of the Trust Indenture with regards to distributions to its unitholders.

Prior to any demand for the repayment hereof, Borrower promises to pay interest on the unpaid principal amount of each Demand Loan from the date of such Demand Loan until such principal amount is paid in full, annually, in arrears, at such interest rates as are specified herein.  The date, amount, and payment(s) (if any) of principal, the Demand Loan(s) to which such payment(s) will be applied (which shall be at the discretion of the Lender) and the outstanding principal balance of Demand Loans shall be recorded by the Lender on its books and records (which may be electronic in nature) and at any time and from time to time may be, and shall be prior to any transfer and delivery of this Note, entered by the Lender on the schedule attached or any continuation of the schedule attached hereto by the Lender (at the discretion of the Lender, any such entries may aggregate Demand Loans (and payments thereon) with the same interest rate and tenor and, if made on a given date, may show only the Demand Loans outstanding on such date).

Borrower may prepay any outstanding principal and accrued and unpaid interest under this Demand Note, in whole or in part, at any time without penalty.

The Lender has approved an uncommitted line of credit to the Borrower in a principal amount not to exceed the face amount of this Note.  The execution and delivery of this Note and the acceptance by the Lender of this Note shall not be deemed or construed to create any contractual commitment to lend by the Lender to the Borrower. The line of credit is in the form of advances made from time to time by the Lender in its sole and absolute discretion to the Borrower. Borrower may borrow sums under this Note, up to the principal amount of this Note, until such time as Lender makes demand for payment in full

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of this Note or until December 31, 2008, whichever is earlier, and may repay those sums at any time, at its option; provided, however, that if any sums are so repaid they may not later be reborrowed.

The Lender may decline to fund any request by Borrower for borrowings under this Demand Note at any time in its sole discretion, for any reason whatsoever, including without limitation in the event that Lender has reason to believe that Borrower will not be able to satisfy its obligations to repay Demand Loans under this Demand Note as required under the terms of this Demand Note.  Lender further reserves the right at any time to demand a mortgage, pledge, grant of security interests in or other encumbrance on assets of Borrower prior to making any additional Demand Loans under this Demand Note to the extent permitted under Section 3.07 of the Trust Indenture.  The failure of Lender to make Demand Loans hereunder for any reason whatsoever shall not constitute a breach of this Demand Note.

In the event of default in the payment of any installment of principal or interest when due hereunder, or upon failure in performance of any covenant, agreement, or obligation to be performed under any documents executed in connection with this Demand Note, Lender may declare the entirety of this Demand Note, principal and interest, immediately due and payable without further notice, but failure to exercise said option shall not constitute a waiver on the part of Lender of the right to exercise the same at any other time.

In the event default is made in the payment of this Demand Note in whatever manner its maturity may be brought about, and it is placed in the hands of an attorney for collection, or is collected through probate, bankruptcy or other proceedings, Borrower promises to pay all reasonable amounts actually incurred by Lender for court costs and attorneys’ fees in connection therewith.

Borrower waives grace, notice, demand, presentment for payment, notice of non-payment, protest, notice of protest, notice of intention to accelerate, notice of acceleration of the indebtedness due hereunder and all other notice, filing of suit and diligence in collecting this Demand Note, and the enforcing of any of the security rights of Lender, and consent and agree that the time of payment hereof may be extended without notice at any time and from time to time, and for periods of time, whether or not for a term or terms in excess of the original term hereof, without notice or consideration to, or consent from, any of them.  Time is of the essence hereof.

This note is secured by a pledge of the Trust Estate, as that term is defined in the Trust Indenture, including without limitation the 99.99% general partnership interest in the Mesa Offshore Royalty Partnership owned by the Mesa Offshore Trust, pursuant to that one certain pledge agreement of even date herewith executed by Borrower for the benefit of Lender .

THIS DEMAND NOTE SHALL BE GOVERNED BY, AND SHALL BE CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF TEXAS WITHOUT REFERENCE TO PRINCIPLES OF CONFLICT OF LAWS.

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EXECUTED to be effective the day and year first written above.

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DEMAND LOANS AND PAYMENTS OF PRINCIPAL

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