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                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                   FORM 10-K

[X] ANNUAL REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE ACT
    OF 1934 FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998

[ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
    ACT OF 1934 FOR THE TRANSITION PERIOD FROM ________________ TO _____________

                         COMMISSION FILE NUMBER 1-8432

                              MESA OFFSHORE TRUST
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

                  TEXAS                                      76-6004065
     (STATE OR OTHER JURISDICTION OF                      (I.R.S. EMPLOYER
     INCORPORATION OR ORGANIZATION)                      IDENTIFICATION NO.)

          CHASE BANK OF TEXAS,
          NATIONAL ASSOCIATION
        CORPORATE TRUST DIVISION
             712 MAIN STREET
             HOUSTON, TEXAS                                     77002
(ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                     (ZIP CODE)

       REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE: (713) 216-6369

           SECURITIES REGISTERED PURSUANT TO SECTION 12(b) OF THE ACT:

                                                 NAME OF EACH EXCHANGE ON
     TITLE OF EACH CLASS                             WHICH REGISTERED
     -------------------                             ----------------
UNITS OF BENEFICIAL INTEREST                         PACIFIC EXCHANGE

          SECURITIES REGISTERED PURSUANT TO SECTION 12(g) OF THE ACT:

                                      NONE

     Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes [X]  No [ ]

     Indicate by check mark if disclosure of delinquent filers pursuant to Item
405 of Regulation S-K is not contained herein, and will not be contained, to the
best of registrant's knowledge, in definitive proxy or information statements
incorporated by reference in Part III of this Form 10-K or any amendment to this
Form 10-K. [X]

     The aggregate market value of 71,980,216 Units of Beneficial Interest in
Mesa Offshore Trust held by non-affiliates of the registrant at the closing
sales price on March 26, 1999, of $.0516 was approximately $1,122.891.37.

     Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.

     As of March 26, 1999, 71,980,216 Units of Beneficial Interest in Mesa
Offshore Trust.

     Documents Incorporated By Reference: None.

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<PAGE>
                               TABLE OF CONTENTS
                                     PART I
<TABLE>
<CAPTION>
                                                                                                             PAGE
                                                                                                             ----
<S>        <C>                                                                                                <C>
Item  1.   Business........................................................................................     1
           Description of the Trust........................................................................     1 
           Description of the Units........................................................................     2 
           Termination of the Trust........................................................................     5 
           Description of Royalty Properties...............................................................     6 
           Contracts.......................................................................................    13 
           Regulation and Prices...........................................................................    15 
Item  2.   Properties......................................................................................    16
Item  3.   Legal Proceedings...............................................................................    16
Item  4.   Submission of Matters to a Vote of Security Holders.............................................    16
</TABLE>
                                    PART II
<TABLE>
<S>        <C>                                                                                                <C>
Item  5.   Market for the Registrant's Common Equity and Related Unitholder Matters........................    17
Item  6.   Selected Financial Data.........................................................................    17
Item  7.   Management's Discussion and Analysis of Financial Condition and Results of                  
             Operations....................................................................................    17
           Net Proceeds, Production and Average Prices (Unaudited).........................................    22
Item  8.   Financial Statements and Supplementary Data.....................................................    23
Item  9.   Changes in and Disagreements with Accountants on Accounting and Financial        
             Disclosure....................................................................................    31
</TABLE>
                                    PART III
<TABLE>
<S>        <C>                                                                                                <C>
Item 10.   Directors and Executive Officers of the Registrant..............................................    31
Item 11.   Executive Compensation..........................................................................    31
Item 12.   Security Ownership of Certain Beneficial Owners and Management..................................    31
Item 13.   Certain Relationships and Related Transactions..................................................    31
</TABLE>
                                    PART IV
<TABLE>
<S>        <C>                                                                                                <C>
Item 14.   Exhibits, Financial Statement Schedules, and Reports on Form 8-K................................    31
SIGNATURES.................................................................................................    33
</TABLE>

NOTE REGARDING FORWARD-LOOKING STATEMENTS

     This Form 10-K includes "forward-looking statements" within the meaning
of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the
Securities Exchange Act of 1934, as amended. All statements other than
statements of historical facts included in this Form 10-K, including without
limitation the statements under "Business -- Termination of the Trust,"
"Management's Discussion and Analysis of Financial Condition and Results of
Operations" and Note 1 to the financial statements of the Trust regarding the
future net revenues of the Trust, are forward-looking statements. Although
Pioneer Natural Resources Company ("Pioneer") has advised the Trust that it
believes that the expectations reflected in such forward-looking statements are
reasonable, no assurance can be given that such expectations will prove to have
been correct. Important factors that could cause actual results to differ
materially from expectations ("Cautionary Statements") are disclosed in this
Form 10-K, including, without limitation in conjunction with the forward-looking
statements included in this Form 10-K. All subsequent written and oral
forward-looking statements attributable to the Trust or persons acting on its
behalf are expressly qualified in their entirety by the Cautionary Statements.

<PAGE>
                                     PART I
ITEM 1.  BUSINESS.
                            DESCRIPTION OF THE TRUST

     The Mesa Offshore Trust (the "Trust"), created under the laws of the
State of Texas, maintains its offices at the office of the Trustee, Chase Bank
of Texas National Association (the "Trustee"), 712 Main Street, Houston, Texas
77002. The telephone number of the Trust is (713) 216-6369.

     The principal asset of the Trust consists of a 99.99% interest in the Mesa
Offshore Royalty Partnership (the "Partnership"). The Trust was created on
December 28, 1982, effective December 1, 1982, when Mesa Petroleum Co. conveyed
to the Partnership certain overriding royalty interests (collectively, the
"Royalty") carved out of Mesa Petroleum Co.'s existing working interests in
ten producing and non-producing oil and gas leases offshore Louisiana and Texas
(the "Royalty Properties"). The Partnership was formed for the purpose of
receiving and holding the Royalty, receiving the proceeds from the Royalty,
paying the liabilities and expenses of the Partnership and disbursing remaining
revenues to the Trustee and Mesa Offshore Management Co., the managing general
partner of the Partnership at that time, in accordance with their interests.
Until August 7, 1997, MESA Inc. owned and operated its assets through Mesa
Operating Co. ("Mesa"), the operator and the managing general partner of the
Royalty Properties. On August 7, 1997, MESA Inc. merged with and into Pioneer,
formerly a wholly owned subsidiary of MESA Inc., and Parker & Parsley Petroleum
Company merged with and into Pioneer Natural Resources USA, Inc. (successor to
Mesa Operating Co.), a wholly owned subsidiary of Pioneer ("PNR")
(collectively, the mergers are referred to herein as the "Merger"). Subsequent
to the Merger, Pioneer owns and operates its assets through PNR and is also the
managing general partner of the Partnership. As hereinafter used in this report,
the term PNR generally refers to the operator of the Royalty Properties, unless
otherwise indicated. See "Termination of the Trust" on page 5 of this Form
10-K for additional information regarding PNR and the Trust.

     Units of beneficial interest ("units") in the Trust were issued on
December 28, 1982 to Mesa Petroleum Co. shareholders, who received one unit for
each share of Mesa Petroleum Co. common stock held. The units are listed on the
Pacific Exchange under the symbol "MOS".

     The terms of the Mesa Offshore Trust Indenture (the "Trust Indenture")
provide, among other things, that: (1) the Trust cannot acquire any asset other
than its interest in the Partnership and cannot engage in any business or
investment activity; (2) the Royalty can be sold in part or in total for cash
upon approval of the unitholders or upon termination of the Trust; (3) the
Trustee can establish cash reserves and borrow funds to pay liabilities of the
Trust and can pledge the assets of the Trust to secure payment of the borrowing;
(4) the Trustee will make quarterly distributions of cash available for
distribution to the unitholders in January, April, July and October of each
year; and (5) the Trust will terminate upon the first to occur of the following
events: (i) the total amount of cash received per year by the Trust for each of
three successive years commencing after December 31, 1987 is less than ten times
one-third of the total amount payable to the Trustee as compensation for such
three-year period or (ii) a vote by holders of a majority of the outstanding
units in favor of termination. Amounts paid to the Trustee as compensation were
$128,000, $173,000 and $123,000, for the years 1998, 1997 and 1996,
respectively. Upon termination of the Trust, the Trustee will sell for cash all
the assets held in the Trust estate and make a final distribution to unitholders
of any funds remaining after all Trust liabilities have been satisfied.

     The terms of the First Amended and Restated Articles of General Partnership
of the Partnership (the "Partnership Agreement") provide that the Partnership
shall dissolve upon the occurrence of any of the following: (1) December 31,
2030; (2) the election of the Trustee to dissolve the Partnership; (3) the
termination of the Trust; (4) the bankruptcy of the Managing General Partner; or
(5) the dissolution of the Managing General Partner or its election to dissolve
the Partnership; provided that the Managing General Partner shall not elect to
dissolve the Partnership so long as the Trustee remains the only other partner
of the Partnership.

                                       1
<PAGE>
     The discussions of terms of the Trust Indenture and the Partnership
Agreement contained herein are qualified in their entirety by reference to the
Trust Indenture and the Partnership Agreement themselves, which are exhibits to
this Form 10-K and are available upon request from the Trustee.

     Under the instrument conveying the Royalty to the Partnership, the Trust is
entitled to its share (99.99%) of 90% of the Net Proceeds, as hereinafter
defined, realized from the sale of the minerals as, if and when produced from
the Royalty Properties. See "Description of Royalty Properties" on page 6 of
this Form 10-K. The instrument of conveyance provides for a monthly computation
of Net Proceeds. "Net Proceeds" means the excess of Gross Proceeds, as
hereinafter defined, received by PNR during a particular period over operating
and capital costs and an amount to be recovered for future abandonment costs
during such period. "Gross Proceeds" means generally the amount received by
PNR from the sale of its share of minerals covered by the Royalty, subject to
certain adjustments. Operating costs means, generally, costs incurred by PNR in
operating the Royalty Properties, including capital costs. If operating and
capital costs exceed the Gross Proceeds for any month, the excess plus interest
thereon at the prime rate of the Bank of America plus one-half percent is
recovered out of future Gross Proceeds prior to the making of further payment to
the Trust. The Trust is not liable for any operating costs or other costs or
liabilities attributable to the Royalty Properties or minerals produced
therefrom. PNR, as owner of the working interest in the Royalty Properties, is
required to maintain books and records sufficient to determine the amounts
payable under the Royalty. Additionally, in the event of a controversy between
PNR and any purchaser as to the correct sale price for any production, amounts
received by PNR and promptly deposited by it with an escrow agent are not
considered as having been received by PNR and therefore are not subject to being
payable with respect to the Royalty until the controversy is resolved; but all
amounts thereafter paid to PNR by the escrow agent will be considered amounts
received from the sale of production. Similarly, operating costs include any
amounts PNR is required to pay whether as a refund, interest or penalty to any
purchaser because the amount initially received by PNR as the sales price was in
excess of that permitted by the terms of any applicable contract, statute,
regulation, order, decree or other obligation. Within 30 days following the
close of each calendar quarter, PNR is required to deliver to the Trustee a
statement of the computation of Net Proceeds attributable to such quarter.

     The Royalty Properties are required to be operated by PNR in accordance
with reasonable and prudent business judgment and good oil and gas field
practices. PNR has the right to abandon any well or lease if, in its opinion,
such well or lease ceases to produce or is not capable of producing oil, gas or
other minerals in commercial quantities. PNR markets the production on terms
deemed by it to be the best reasonably obtainable in the circumstances. See
"Contracts" on page 13 of this Form 10-K. The Trustee has no power or
authority to exercise any control over the operation of the Royalty Properties
or the marketing of production therefrom.

     The Trust has no employees. Administrative functions of the Trust are
performed by the Trustee.

                            DESCRIPTION OF THE UNITS

     Each unit is evidenced by a transferable certificate issued by the Trustee,
which ranks equally as to distributions and has one vote on any matter submitted
to unitholders. Each unit evidences an undivided interest in the Trust, which in
turn owns a 99.99% interest in the Partnership.

DISTRIBUTIONS

     The Trustee determines for each month the amount of cash available for
distribution for such month. Such amount (the "Monthly Distribution Amount")
is equal to the excess, if any, of the cash distributed by the Partnership to
the Trust during such month, plus any other cash receipts of the Trust during
such month (other than interest earned on the Monthly Distribution Amount for
any other month), over the liabilities of the Trust paid during such month, and
adjusted for changes made by the Trustee during such month in any cash reserves
established for the payment of contingent or future obligations of the Trust.
The Monthly Distribution Amount for each month is payable to unitholders of
record on the monthly record date (the "Monthly Record Date"), which is the
close of business on the last business day of such month, or such later date as
the Trustee determines is required to comply with legal or stock exchange
requirements. However, to reduce the administrative expenses of the Trust, the

                                       2
<PAGE>
Trust Indenture provides that the Trustee does not distribute cash monthly, but
rather, during January, April, July and October of each year, distributes to
each person who was a unitholder of record on a Monthly Record Date during one
or more of the immediately preceding three months, the Monthly Distribution
Amount for the month or months that he was a unitholder of record, together with
interest earned on such Monthly Distribution Amount from the Monthly Record Date
to the payment date.

LIABILITY OF UNITHOLDERS

     As regards the unitholders, the Trustee is fully liable if the Trustee
incurs any liability without ensuring that such liability will be satisfiable
only out of the Trust assets (regardless of whether the assets are adequate to
satisfy the liability) and in no event out of amounts distributed to, or other
assets owned by unitholders. However, under Texas law, it is unclear whether a
unitholder would be jointly and severally liable for any liability of the Trust
in the event that all of the following conditions were to occur: (1) the
satisfaction of such liability was not by contract limited to the assets of the
Trust; (2) the assets of the Trust were insufficient to discharge such
liability; and (3) the assets of the Trustee were insufficient to discharge such
liability. Although each unitholder should weigh this potential exposure in
deciding whether to retain or transfer his units, the Trustee is of the opinion
that because of the passive nature of the Trust assets, the restrictions on the
power of the Trustee to incur liabilities and the required financial net worth
of any trustee, the imposition of any liability on a unitholder is extremely
unlikely.

FEDERAL INCOME TAX MATTERS

  OWNERSHIP OF UNITS

     The federal income tax consequences to the unitholders of owning units
depend on whether the Trust is classifiable as a grantor trust, a non-grantor
trust, or a corporation. The Trustee reports on the basis that the Trust is a
grantor trust. Based on its recent audit policy, the Internal Revenue Service
(the "IRS") is expected to concur with such action. No IRS ruling has been
received with respect to the Trust, however, and no court case has been decided
involving identical facts and circumstances. It is possible, therefore, that the
IRS will assert on audit that the Trust is taxable as a corporation and that a
court might agree with such assertion.

  INCOME AND DEPLETION

     Royalty income, net of depletion and severance taxes, is treated as
portfolio income, and, subject to certain exceptions and transitional rules,
Royalty income cannot be offset by losses from passive businesses. Additionally,
interest income is portfolio income. Administrative expense is an investment
expense.

     Generally, prior to the Revenue Reconciliation Act of 1990, the transferee
of an oil and gas property could not claim percentage depletion with respect to
production from such property if it was "proved" at the time of the transfer.
This rule is not applicable in the case of transfers of properties after October
11, 1990. Thus, eligible unitholders that acquired units after that date are
entitled to claim an allowance for percentage depletion with respect to Royalty
income attributable to such units to the extent that such allowance exceeds cost
depletion as computed for the relevant period.

  BACKUP WITHHOLDING

     Distributions from the Trust are generally subject to backup withholding at
a rate of 31% of such distributions. Backup withholding will not normally apply
to distributions to a unitholder, however, unless such unitholder fails to
properly provide to the Trust his taxpayer identification number ("TIN") or
the IRS notifies the Trust that the TIN provided by such unitholder is
incorrect.

  SALE OF UNITS

     Generally, except for recapture items, the sale, exchange or other
disposition of a unit will result in capital gain or loss measured by the
difference between the basis in the unit and the amount realized. Such gain or
loss would be capital gain or loss if such unit was held by the unitholder as a
capital asset. For units sold on or prior to May 6, 1997, such capital gain will
be long-term if such unitholder's holding period exceeded one year as of the
date of sale or exchange. The Taxpayer Relief Act of 1997 reduced the maximum
long-term capital gains rate to 20% for capital assets sold after May 6, 1997,
but

                                       3
<PAGE>
the holding period necessary to qualify for the reduced rate increased to 18
months effective for sales after July 28, 1997. A special "mid-term" rate
(generally 28%) applies to capital assets sold after July 28, 1997 with a
holding period of over one year but not over 18 months. Effective for property
placed in service after December 31, 1986, the amount of gain, if any, realized
upon the disposition of oil and gas property is treated as ordinary income to
the extent of the intangible drilling and development costs incurred with
respect to the property and depletion claimed with respect to such property to
the extent it reduced the taxpayer's basis in the property. Depletion
attributable to a positive Section 743(b) basis adjustment of a unit acquired
after 1986 will be subject to recapture as ordinary income upon disposition of
the unit or upon disposition of the oil and gas property to which the depletion
is attributable. The balance of any gain or any loss will be capital gain or
loss, if such unit was held by the unitholder as a capital asset.

  FOREIGN UNITHOLDERS

     In general, a unitholder who is a nonresident alien individual or which is
a foreign corporation (each, a "Foreign Taxpayer") will be subject to tax on
the gross income produced by the Royalty at a rate equal to 30% (or lower treaty
rate, if applicable). This tax will be withheld by the Trustee and remitted
directly to the United States Treasury. A Foreign Taxpayer may elect to treat
the income from the Royalty as effectively connected with the conduct of a
United States trade or business under Section 871 or Section 882 of the Internal
Revenue Code of 1986, as amended (the "Code"), (or pursuant to any similar
provisions of applicable treaties). Upon making this election such unitholder is
entitled to claim all deductions with respect to such income, but he must file a
United States federal income tax return to claim such deductions. This election
once made is irrevocable (unless an applicable treaty allows the election to be
made annually). However, for tax years beginning after December 31, 1987, such
effectively connected income will be subjected to withholding equal to the
highest applicable percentage (tax rate)-39.6% for individual foreign
unitholders and 35% for corporate foreign unitholders.

     Section 897 of the Code and the Treasury Regulations thereunder treat the
publicly traded Trust as if it were a United States real property holding
corporation. Accordingly, Foreign Taxpayers owning greater than 5% of the
outstanding units are subject to United States federal income tax on the gain on
the disposition of their units. Foreign unitholders owning 5% or less of the
outstanding units are not subject to United States federal income tax on the
gain on the disposition of their units.

     Federal income taxation of a Foreign Taxpayer is a highly complex matter
which may be affected by many other considerations. Therefore, each Foreign
Taxpayer should consult with his own tax adviser as to the advisability of his
ownership of units.

  TAX-EXEMPT ORGANIZATIONS

     Investments in publicly traded partnerships are treated the same as
investments in other partnerships for purposes of the rules governing unrelated
business taxable income. The Royalty and interest income should not be unrelated
business taxable income so long as, generally, a unitholder did not incur debt
to acquire a unit or otherwise incur or maintain a debt that would not have been
incurred or maintained if such unit had not been acquired. Legislative proposals
have been made from time to time which, if adopted, would result in the
treatment of Royalty income as unrelated business income. Tax-exempt unitholders
should consult their own tax advisors with respect to the treatment of royalty
income.

                                       4
<PAGE>
                             PENDING SALE AGREEMENT

     In December 1998, PNR signed a purchase and sale agreement (the
"Agreement") with Costilla Energy, Inc. ("Costilla") to sell certain PNR oil and
gas properties. Included with the properties to be sold are PNR's interest in
all of the Trust properties. The consummation of this Agreement is primarily
dependent upon the Costilla's ability to finance the purchase as well as certain
other contingencies defined in the Agreement. The sale is expected to close by
March 31, 1999. Subsequent to the closing, PNR expects to continue to operate
the Trust properties for a limited period of time; however, Costilla will become
the Managing General Partner of the Partnership. There can be no assurance that
the sale of any or all of these properties will be completed. In addition, if
such a sale is consummated, the Trust has been advised that there should be no
significant impact on the Trust, although the precise nature of any effects
cannot be predicted or quantified at this time.

                            TERMINATION OF THE TRUST

     As discussed above under "Description of the Trust", the terms of the Mesa
Offshore Trust Indenture provide that the Trust will terminate upon the first to
occur of the following events: (1) the total amount of cash received per year by
the Trust for each of three successive years commencing after December 31, 1987
is less than ten times one-third of the total amount payable to the Trustee as
compensation for such three year period (the "Termination Threshold") or (2) a
vote by the unitholders in favor of termination. Because the Trust will
terminate in the event the total amount of cash received per year by the Trust
falls below certain levels, it would be possible for the Trust to terminate even
though some of the Royalty Properties continued to have remaining productive
lives. For information regarding the estimated remaining life of each of the
Royalty Properties and the estimated future net revenues of the Trust based on
information provided by PNR, see pages 12 and 13 of this Form 10-K and Note 6 in
the Notes to Financial Statements included elsewhere in this Form 10-K. Upon
termination of the Trust, the Trustee will sell for cash all the assets held in
the Trust estate and make a final distribution to unitholders of any funds
remaining after all Trust liabilities have been satisfied. The discussion set
forth above is qualified in its entirety by reference to the Trust Indenture
itself, which is an exhibit to this Form 10-K and is available upon request from
the Trustee.

     In addition, in the event of a dissolution of the Partnership (which could
occur under the circumstances described above under "Description of the
Trust") and a subsequent winding up and termination thereof, the assets of the
Partnership (i.e., the Royalty interest) could either (1) be distributed in kind
ratably to the Managing General Partner and the Trustee or (2) be sold and the
proceeds thereof distributed ratably to the Managing General Partner and the
Trustee. In the event of a sale of the Royalty and a distribution of the cash
proceeds to the Trustee, the Trustee would make a final distribution to
unitholders of such cash proceeds plus any other cash held by the Trust after
the payment of or provision for all liabilities of the Trust, and the Trust
would be terminated.

     The December 31, 1998 reserve report prepared for the Partnership indicates
that Royalty income expected to be received by the Trust in 1999 and 2000 could
be at or near the Termination Threshold. The reserve report estimates that 
future Royalty income to the Trust is approximately $5.2 million while the
Termination Threshold for 1998 was approximately $1.4 million. It is therefore
possible (depending on the timing of future production, market conditions,
recoupment of unrecovered capital costs, the receipt of amounts withheld from
the Trust related to MMS royalty claims, and other matters) that in either 1999
or 2000 Royalty income received by the Trust may be below the Termination
Threshold. If Royalty income falls below the Termination Threshold for three
successive years, the Trust would terminate pursuant to the terms discussed
above. There are numerous uncertainties inherent in estimating and projecting
the quantity and value of proved reserves for the Trust properties as many of
the Trust properties are nearing the end of their productive lives and are
therefore subject to unforeseen changes in production rates. As such, there can
be no assurance that Royalty income received by the Trust in 1999 or 2000 will
be above the Termination Threshold.

                                       5
<PAGE>
                       DESCRIPTION OF ROYALTY PROPERTIES

PRODUCING ACREAGE AND WELLS AS OF DECEMBER 31, 1998
<TABLE>
<CAPTION>
                                                                         PRODUCING WELLS(1)
                                                             ------------------------------------------
                                         PRODUCING ACRES            GROSS                  NET
                                       --------------------  --------------------  --------------------
              PROPERTY                   GROSS     NET(2)       OIL        GAS        OIL        GAS
-------------------------------------  ---------  ---------     ---        ---        ---        ---
<S>                                    <C>        <C>           <C>        <C>        <C>        <C>
Offshore Louisiana--
  South Marsh
     Island 155......................      5,000      2,625         --         --         --         --
  South Marsh
     Island 156......................      5,000      2,625         --         --         --         --
  West Delta 61......................      5,000      3,750         --          1         --         .8
  West Delta 62......................      5,000      3,750         --          1         --         .1
Offshore Texas--
  Brazos A-7.........................      5,760      2,160         --          2         --         .8
  Brazos A-39........................      5,760      2,160         --          1         --         .4
  Matagorda
     Island 624......................      5,617      1,369         --          1         --         .3
                                       ---------  ---------        ---        ---        ---        ---
           Total.....................     37,137     18,439          0          6          0        2.4
                                       =========  =========        ===        ===        ===        ===
</TABLE>
------------
(1) Dual completions are counted as one well. For information regarding wells
    producing at December 31, 1998, see "Net Proceeds, Production and Average
    Prices" on page 21 of this Form 10-K.

(2) Net Producing Acres are calculated by multiplying gross producing acres by
    the net Royalty interest (as defined by the Trust Indenture) attributable to
    the Trust for each property.

RESERVES

     A study of the proved oil and gas reserves attributable to the Partnership
as of December 31, 1998, has been made by PNR. The following letter (the
"Reserve Report") summarizes such reserve study. The Reserve Report reflects
estimated reserve quantities and future net revenue based upon estimates of the
future timing of actual production without regard to when received in cash by
the Trust, which differs from the manner in which the Trust recognizes and
accounts for its royalty income. For further information regarding the Net
Overriding Royalty Interest, the Basis of Accounting for the Trust and Reserves,
see Notes 2, 3 and 6, respectively, in the Notes to Financial Statements
contained in Item 8 of this Form 10-K.

                                       6
<PAGE>
                                     [LOGO]
                                    PIONEER
                               NATURAL RESOURCES

                                 SUMMARY REPORT
                                DATED MARCH 1999


                                       ON


                              RESERVES AND REVENUE
                             AS OF DECEMBER 31, 1998


                             FROM CERTAIN PROPERTIES
                                    OWNED BY


                               MESA OFFSHORE TRUST


                                       7
<PAGE>
                                     [LOGO]

March 17, 1999


MESA Offshore Trust
Chase Bank of Texas, N.A. (as Trustee)
Chase Tower, Suite 1150
600 Travis Street
Houston TX  77002

Ladies and Gentlemen:

Pursuant to your request, we have prepared estimates, as of December 31, 1998,
of the extent and value of the proved crude oil, condensate, natural gas
liquids, and natural gas reserves of certain properties subject to a net profits
interest owned by the Mesa Offshore Royalty Partnership, hereinafter referred to
as the "Partnership," a partnership owned 99.99 percent by the Mesa Offshore
Trust. The interest appraised is referred to herein as the "Partnership
Interest" and consists of a 90 percent net profits interest in ten Pioneer
Natural Resources USA, Inc. (hereinafter referred to as "Pioneer") leases
located in the Gulf of Mexico offshore from Louisiana and Texas. The ten
offshore leases subject to the net profits interest are hereinafter referred to
as the "Subject Properties." Three of these leases have been abandoned; reserves
of the remaining seven leases are reported herein.

The reserve estimates are based on a detailed study of the Subject Properties.
The method or combination of methods used in the study of each reservoir was
tempered by experience in the area, consideration of the stage of development of
the reservoir, and the quality and completeness of basic data.

Estimates of oil, condensate, natural gas liquids and gas reserves and future
net revenue should be regarded only as estimates that may change as further
production history and additional information become available. Not only are
such reserve and revenue estimates based on that information which is currently
available, but such estimates are also subject to the uncertainties inherent in
the application of judgment factors in interpreting such information.

In the preparation of this report, Pioneer has used internal information with
respect to property interests owned by the Partnership, production from such
properties, current costs of operation and development, current prices for
production, agreements relating to current and future operations and sale of
production, and various other information.

The development status shown herein represents the status applicable as of
December 31, 1998. Data available from wells drilled on the appraised properties
through December 31, 1998 were used in estimating gross ultimate recovery. Gross
production estimated to December 31, 1998, was deducted from gross ultimate
recovery to arrive at the estimates of gross reserves. In some fields, this
required that the production rates be estimated for a portion of 1998 since
production data for these properties were not available throughout 1998.

The reserve volumes and revenue values shown in this report for Partnership
Interest were estimated from projections of reserves and revenue attributable to
the combined interests consisting of the Partnership Interest and the retained
Pioneer Interest in the Subject Properties (Combined Interest). Net reserves
attributable to the Partnership Interest were estimated by allocating to the
Partnership a portion of the estimated combined net reserves of the Subject
Properties based on future revenue. Because the net reserve volumes attributable
to the


                                       8
<PAGE>
MESA Offshore Trust
March 17, 1999
Page 2


Partnership Interest are estimated using an allocation of reserves based on
estimates of future revenue, a change in prices or costs will result in changes
in the estimated net reserves. Therefore, the estimated net reserves
attributable to the Partnership Interest will vary if different future price and
cost assumptions are used.

Petroleum reserves included in this report are classified as proved and are
judged to be economically producible in future years from known reservoirs under
existing economic and operating conditions and assuming continuation of current
regulatory practices using conventional production methods and equipment. In the
analysis, reserves were estimated only to the limit of economic rates of
production under existing economic and operating conditions using prices and
costs as of the date the estimate is made, including consideration of changes in
existing prices provided only by contractual arrangements but not including
escalations based upon future conditions. The petroleum reserves are classified
as follows:

o  Proved - Reserves that have been proved to a high degree of certainty by
   analysis of the producing history of a reservoir and/or by volumetric
   analysis of adequate geological and engineering data. Commercial productivity
   has been established by actual production, successful testing, or in certain
   cases by favorable core analyses and electrical-log interpretation when the
   producing characteristics of the formation are known from nearby fields.
   Volumetrically, the structure, areal extent, volume, and characteristics of
   the reservoir are well defined by a reasonable interpretation of adequate
   subsurface well control and by known continuity of hydrocarbon-saturated
   material above known fluid contacts, if any, or above the lowest known
   structural occurrence of hydrocarbons.

o  Developed - Reserves that are recoverable from existing wells with current
   operating methods and expenses. Developed reserves include both producing and
   nonproducing reserves. Estimates of producing reserves assume recovery by
   existing wells producing from present completion intervals with normal
   operating methods and expenses. Developed nonproducing reserves are in
   reservoirs behind the casing or at minor depths below the producing zone and
   are considered proved by production from other wells in the field, by
   successful drill-stem tests, or by core analysis from the particular zones.
   Nonproducing reserves require only moderate expense to be brought into
   production.

o  Undeveloped - Reserves that are recoverable from additional wells yet to be
   drilled. Undeveloped reserves are those considered proved for production by
   reasonable geological interpretation of adequate subsurface control in
   reservoirs that are producing or proved by other wells but are not
   recoverable from existing wells. This classification of reserves requires
   drilling of additional wells, major deepening of existing wells, or
   installation of enhanced recovery or other facilities.

Estimates of the net proved reserves attributable to the Partnership Interest,
as of December 31, 1998, are as follows:

    TOTAL PROVED RESERVES:
         Natural Gas (Mcf)............................      2,280,001
         Oil and Condensate (bbl).....................        404,272
         Natural Gas Liquids (bbl)....................              0

    PROVED DEVELOPED RESERVES
         Natural Gas (Mcf)............................        933,684
         Oil and Condensate (bbl).....................          5,628
         Natural Gas Liquids (bbl)....................              0

                                       9
<PAGE>
MESA Offshore Trust
March 17, 1999
Page 3


Revenue values attributable to the net proved reserves of the Partnership
Interest are expressed in terms of estimated future net revenue and present
worth of future net revenue. Future net revenue attributable to the Partnership
Interest was estimated monthly from a projection of the combined Pioneer and
Partnership future net revenue. Combined future net revenue values were
calculated by deducting operating expenses and capital costs from the future
gross revenue of the Combined Interest. The monthly values for the aggregate of
the Combined Interest in the Subject Properties were reduced by an overhead
charge, by a monthly amount necessary for Pioneer to accrue the abandonment
costs over the life of the properties, by the deficit balance as described below
from the previous month, and by the interest on that deficit balance when such
deficits occur. If the adjusted revenue resulting from this calculation was
negative, it was carried forward to the next month as a deficit balance. If the
adjusted revenue was greater than zero, it was multiplied by a factor of 90
percent to arrive at the future net revenue of the Partnership Interest. The
above calculations were made monthly in the aggregate for the Subject
Properties. Interest was charged monthly on the net profits deficit balance
(cost not recovered currently) at the rate of 9.0 percent per year. The deficit
balance as of December 31, 1998 was $1,029,737.

Future oil and gas producing rates estimated for this report are based on
production rates considering the most recent figures available or, in certain
cases, are based on estimates tempered by Pioneer's experience in the area. The
rates used for future production are rates that Pioneer has determined are
within the capacity of the well or reservoir to produce.

Gas volumes shown herein are expressed at standard conditions of 60 degrees
Fahrenheit and a 15.025 pounds per square inch absolute. Condensate reserves
estimated herein are those to be obtained from normal separator recovery.

Revenue values in this report were estimated using current prices and costs.
Future prices were estimated using guidelines established by the Securities and
Exchange Commission and the Financial Accounting Standards
Board.

The assumptions used for estimating future prices and costs are as follows:

    o    Oil and Condensate Prices - Oil and condensate prices were held
         constant for the life of the properties.

    o    Natural Gas Prices - Gas prices were held constant for the life of the
         properties.

    o    Natural Gas Liquids Prices - Natural gas liquids prices were held
         constant for the life of the properties.

    o    Operating and Capital Costs - Current estimates of operating costs
         were used for the life of the properties with no increases in the
         future based on inflation. Future capital expenditures were estimated
         using 1998 values and were not adjusted for inflation.

A summary of estimated revenue and costs attributable to the Combined Interest
in proved reserves and the future net revenue and present worth attributable to
the Partnership Interest, as of December 31, 1998 is as follows:


                                       10
<PAGE>
MESA Offshore Trust
March 17, 1999
Page 4


    COMBINED INTEREST:
          Future Gross Revenue ($)....................         8,740,898
          Production and Ad Valorem Taxes ($).........                 0
          Operating Costs ($).........................        (1,804,756)
          Capital Costs ($)(1)........................       (10,497,250)
          Future Net Revenue ($)......................        (3,561,108)

          Accrued Revenue for Abandonment Costs ($)...        10,010,271
          Future Accrued Revenue for Abandonment
            Costs ($).................................           470,733
          Cumulative Net Profits Deficit @ 12/31/98 ..        (1,144,152)
          Revenue Subject to Net Profits Interest ($).         5,775,744


    PARTNERSHIP INTEREST:
          Future Net Revenue ($)(2)...................         5,198,165
          Present Worth at 10 Percent ($).............         3,977,242

          (1) Includes abandonment costs.
          (2) Future income tax expenses were not taken into account in the
              preparation of these estimates.

The information relating to estimated proved reserves, estimated future net
revenue from proved reserves, and present worth of estimated future net revenue
from proved reserves of oil, condensate, natural gas liquids, and gas contained
in this report has been prepared in accordance with Paragraphs 10-13, 15 and
30(a)-(b) of Statement of Financial Accounting Standards No. 69 (November 1982)
of the Financial Accounting Standards Board and Rules 4-10(a)(1)-(13) of
Regulation S-X and Rule 302(b) of Regulation S-K of the Securities and Exchange
Commission; provided, however, future income tax expenses have not been taken
into account in estimating the future net revenue and present worth values set
forth herein.

To the extent the above enumerated rules, regulations, and statements require
determinations of an accounting or legal nature or information beyond the scope
of this report, we are necessarily unable to express an opinion as to whether
the above-described information is in accordance therewith or sufficient
therefor.

                                  Submitted,

                                  /s/ RICHARD MASSENGILL
                                  D. Richard Massengill

                                       11

<PAGE>
     There are numerous uncertainties inherent in estimating quantities of
proved reserves and in projecting the future rates of production and timing of
development expenditures, including many factors beyond the control of the
producer. The preceding reserve data in the Reserve Report represent estimates
only and should not be construed as being exact. Reserve assessment is a
subjective process of estimating the recovery from underground accumulations of
gas and oil that cannot be measured in an exact way, and estimates of other
persons might differ materially from those of PNR. Accordingly, reserve
estimates are often different from the quantities of hydrocarbons that are
ultimately recovered.

     Also, while estimates of reserves attributable to the Royalty Properties
are shown in order to comply with requirements of the Securities and Exchange
Commission (the "SEC"), there is no precise method of allocating estimates of
physical quantities of reserves between PNR and the Partnership, since the
Royalty is not a working interest and the Partnership does not own and is not
entitled to receive any specific volume of reserves from the Royalty. Reserve
quantities in the previously mentioned reserve study have been allocated based
on the method referenced in the Reserve Report. The quantities of reserves
attributable to the Partnership will be affected by future changes in various
economic factors utilized in estimating future gross and net revenues from the
Royalty Properties. Therefore, the estimates of reserves set forth in the
Reserve Report are to a large extent hypothetical and differ in significant
respects from estimates of reserves attributable to a working interest.

     Moreover, the discounted present values in the Reserve Report should not be
construed as the current market value of the estimated gas and oil reserves
attributable to the Royalty Properties or the costs that would be incurred to
obtain equivalent reserves, since a market value determination would include
many additional factors. In accordance with applicable regulations of the SEC,
estimated future net revenues were based, generally, on current prices and
costs, whereas actual future prices and costs may be materially greater or less.
The estimates in the Reserve Report use market prices as of December 31, 1998
pursuant to gas contracts in effect on January 1, 1999. These prices (having a
weighted average of $1.83 per Mcf as of December 31, 1998) were held constant
over the estimated life of the Royalty Properties. Such prices were influenced
by seasonal demand for natural gas and may not be the most appropriate or
representative prices to use for estimating future revenues or related reserve
data. The average price of natural gas sold from the Royalty Properties during
1998 was $2.31 per Mcf, representing a combination of contract prices and spot
market prices.

     The following is a summary of the estimated remaining life for each of the
Royalty Properties provided to the Trustee by PNR as of December 31, 1998. There
are numerous uncertainties present in estimating the remaining productive lives
for the Royalty Properties. The following summary represents an estimate only
and should not be construed as being exact. The estimated remaining productive
life of each property varies depending on the recoverable reserves and annual
production assumed by PNR. In addition, future economic and operating conditions
may cause significant changes in such estimates.

                    PROPERTY
------------------------------------------------
South Marsh Island 155/156......................            --
West Delta 61/62................................         15-20 years
Brazos A-7......................................           4-5 years
Brazos A-39.....................................           1-2 years
Matagorda Island 624............................           3-4 years
------------
(1) The Trust will terminate in the event the total amount of cash received per
    year by the Trust falls below certain levels. Accordingly, it would be
    possible for the Trust to terminate even though some of the Royalty
    Properties continued to have remaining productive lives. See "Termination
    of the Trust" on page 5 of this Form 10-K.

(2) Estimates of remaining lives may vary significantly from year to year.

                                       12
<PAGE>
     The future net revenues contained in the Reserve Report have not been
reduced for future general and administrative costs and expenses of the Trust,
which are expected to approximate $500,000 annually. The general and
administrative costs and expenses of the Trust may increase in future years,
depending on the amount of royalty income, increases in accounting, engineering,
legal and other professional fees and other factors.

     PNR has advised the Trust that there have been no events subsequent to
December 31, 1998 that have caused a significant change in the estimated proved
reserves referred to in the Reserve Report.

PROCEEDS, PRODUCTION AND AVERAGE PRICES

     Reference is made to "Net Proceeds, Production and Average Prices" under
Item 7 of this Form 10-K.

ASSETS

     Reference is made to Item 6 of this Form 10-K for information relating to
the assets of the Trust.

                                   CONTRACTS

     GENERAL.  PNR has advised the Trust that during 1998 its offshore gas
production was marketed under short-term contracts at spot market prices
primarily to H&N, Limited. PNR has further advised the Trust that it expects to
continue to market its production under short-term contracts for the foreseeable
future; however, it is not known whether Costilla will change the current
marketing practices. Spot market prices for natural gas in 1998 were generally
lower than spot market prices in 1997. Information regarding recent prices
received for production from the Royalty Properties is provided below.

          BRAZOS A-7 AND A-39.  In March 1999, most of the gas from this
     property was being sold to H&N, Limited at an average price of $1.59 per
     MMBtu.

          SOUTH MARSH ISLAND 155 AND 156.  In March 1999, most of the gas from
     this property was being sold to H&N, Limited at an average price of $1.61
     per MMBtu.

          WEST DELTA 61 AND 62.  In March 1999, most of the gas from this
     property was being sold to H&N, Limited at an average price of $1.57 per
     MMBtu.

          MATAGORDA ISLAND 624.  In March 1999, most of the gas from this
     property was being sold to H&N, Limited at an average price of $1.57 per
     MMBtu.

MARKET FOR NATURAL GAS

     The amount of cash distributions by the Trust is dependent on, among other
things, the sales prices for natural gas produced from the Royalty Properties
and the quantities of gas sold. The natural gas industry in the United States
during the past decade has been affected generally by a surplus in natural gas
deliverability in comparison to demand. Demand for gas declined during this
period due to a number of factors including the implementation of energy
conservation programs, a shift in economic activity away from energy intensive
industries and competition from alternative fuel sources such as residual fuel
oil, coal and nuclear energy. The surplus of natural gas deliverability caused a
general deterioration in gas prices. The annual average wellhead price for
natural gas peaked in 1984 at $2.66 per Mcf and declined to $1.55 per Mcf in
1995. Annual wellhead prices generally increased from 1995 to $2.17 per MCF in
1996 and $2.32 per MCF in 1997 and decreased to an estimated $1.90 in 1998,
according to the Natural Gas Monthly published by the Energy Information
Administration of the Department of Energy. Spot prices for domestic natural gas
were negatively affected by warmer than normal weather in the winters of 1997-98
and 1998-99.

     The seasonal nature of demand for natural gas and its effects on sales
prices and production volumes may cause the amounts of cash distributions by the
Trust to vary substantially on a seasonal basis. Generally, production volumes
and prices are higher during the first and fourth quarters of each

                                       13
<PAGE>
calendar year due primarily to peak demand in these periods. Because of the time
lag between the date on which PNR receives payment for production from the
Royalty Properties and the date on which distributions are made to unitholders,
the seasonality that generally affects production volumes and prices is
generally reflected in distributions to unitholders in later periods.

COMPETITION

     The production and sale of gas from the areas in which the Royalty
Properties are located is highly competitive and PNR has a number of competitors
in these areas. PNR has advised the Trust that it believes that its competitive
position in these areas is affected by price, contract terms and quality of
service. PNR's business is affected not only by such competition, but also by
general economic developments, governmental regulations and other factors.

MARKETING OF LIQUIDS

     PNR generally reserves in its gas purchase contracts the right to extract
condensate and other liquid and liquifiable hydrocarbons from all gas produced.
PNR is currently selling the condensate and other liquids to various purchasers
under contracts with terms of one year or less.

     A PNR subsidiary owns a 100% interest in a pipeline which transports crude
oil from South Marsh Island 155 and 156 to an underwater connection with
Marathon Pipe Line Company's ("Marathon") pipeline on South Marsh Island 139.
In 1998, PNR charged $3.60 per barrel for transportation of crude oil from these
properties, which included Marathon's currently posted tariff of $1.55 per
barrel and the PNR subsidiary's tariff of $2.05 per barrel. Tariffs are subject
to approval by the Federal Energy Regulatory Commission (the "FERC").

     Future pipeline construction and operation arrangements may be necessary
for the marketing of crude oil and other liquid hydrocarbon production, if any,
from the other Royalty Properties. PNR could be involved in such
arrangements.

                                       14
<PAGE>
                             REGULATION AND PRICES

GENERAL

     The production and sale of natural gas from the Royalty Properties are
affected from time to time in varying degrees by political developments and
federal, state and local laws and regulations. In particular, oil and gas
production operations and economics are, or in the past have been, affected by
price controls, taxes, conservation, safety, environmental and other laws
relating to the petroleum industry, by changes in such laws and by constantly
changing administrative regulations.

OPERATING HAZARDS AND UNINSURED RISKS

     PNR's oil and gas activities are subject to all of the risks normally
incident to exploration for and production of oil and gas, including blowouts,
cratering and fires, each of which could result in damage to life and property.
Offshore operations are subject to a variety of operating risks, such as
hurricanes and other adverse weather conditions and lack of access to existing
pipelines or other means of transporting production. Furthermore, offshore oil
and gas operations are subject to extensive governmental regulations, including
certain regulations that may, in certain circumstances, impose absolute
liability for pollution damages, and to interruption or termination by
governmental authorities based on environmental or other considerations. In
accordance with customary industry practices, PNR carries insurance against
some, but not all, of these risks. Losses and liabilities resulting from such
events would reduce revenues and increase costs to the Trust to the extent not
covered by insurance.

FERC REGULATION

     In recent years, the FERC has required interstate pipeline companies to
"unbundle" their services. To the extent a pipeline company or its sales
affiliate makes gas sales as a merchant in the future, it does so pursuant to
private contracts in direct competition with all other sellers, such as PNR. In
recent years, the FERC also has pursued a number of other policy initiatives
which could significantly affect the marketing of natural gas. Several of these
initiatives are intended to enhance competition in natural gas markets, although
some, such as "spin-downs," may have the adverse effect of increasing the cost
of doing business on some in the industry. On July 29, 1998, the FERC issued two
orders in which the FERC is considering revisions to its regulations of
short-term and long-term transportation markets. As to all of these recent FERC
initiatives, PNR has advised the Trust that the on-going, or, in some instances,
preliminary evolving nature of these regulatory initiatives makes it impossible
at this time to predict their ultimate impact on the prices, markets or terms of
sale of natural gas related to the Trust.

STATE REGULATION

     State regulation of gathering facilities generally includes various safety,
environmental, and in some circumstances, non-discriminatory take requirements.
Recently some states have implemented more stringent legislation to regulate
gathering rates charged by gas gathering companies but to date the effect to PNR
is minimal.

ENVIRONMENTAL

     PNR's operations are subject to numerous federal, state and local laws and
regulations controlling the discharge of materials into the environment or
otherwise relating to the protection of the environment, including the
Comprehensive Environmental Response, Compensation and Liability Act ("CERCLA"
or "Superfund"), the Solid Waste Disposal Act, the Clean Air Act, and the
Federal Water Pollution Control Act. These laws and regulations, including their
state counterparts, can impose liability upon the lessee under a lease for the
cost of cleanup of discharged materials resulting from a lessee's operations or
can subject the lessee to liability for damages to natural resources. Violations
of environmental laws, regulations, or permits can result in civil and criminal
penalties as well as potential injunctions curtailing operations in affected
areas and restrictions on the injection of liquids into the subsurface that may
contaminate groundwater. PNR maintains insurance for costs of cleanup
operations, but it is not fully insured against all such risks. A serious
release of regulated materials could result in the DOI requiring lessees under
federal leases to suspend or cease operations in the

                                       15
<PAGE>
affected area. In addition, the recent trend toward stricter standards and
regulations in environmental legislation is likely to continue. For example,
legislation has been proposed in Congress that would reclassify certain oil and
gas production wastes as "hazardous wastes" which would subject the handling,
disposal and cleanup of these wastes to more stringent requirements and result
in increased operating costs for the Royalty Properties, as well as the oil and
gas industry in general. State initiatives to further regulate the disposal of
oil and gas wastes are also pending in certain states, and these initiatives
could have a similar impact on the Royalty Properties.

     From time to time, federal and state environmental agencies propose
regulations which could have a direct and material impact on PNR's operations.
For example, under the Oil Pollution Act of 1990, as amended by the Coast Guard
Authorization Act of 1996, (collectively, "OPA"), parties responsible for
offshore facilities must establish and maintain evidence of oil-spill financial
responsibility ("OSFR") for costs attributable to potential oil spills. OPA
requires a minimum of $35 million in OSFR for offshore facilities located on the
OCS. This amount is subject to upward regulatory adjustment up to $150 million.
Responsible parties for more than one offshore facility are required to provide
OSFR only for their offshore facility requiring the highest OSFR. In 1998, the
Minerals Management Service adopted regulations for establishing the amount of
OSFR required for particular facilities. The amount of OSFR increases as the
volume of a facility's worst-case oil spill increases. Accordingly, for
facilities with worst-case spills of less than 35,000 barrels, only $35 million
in OSFR is required; for worst-case spills of over 35,000 barrels, $70 million
is required; for worst-case spills of over 70,000 barrels, $105 million is
required; and for worst-case spills of over 105,000 barrels, $150 million is
required. In addition, all OSFR below $150 million remains subject to upward
regulatory adjustment if warranted by the particular operational, environmental,
human health or other risks involved with a facility. Under this regulation, PNR
is required to maintain $ 35 million in OSFR for its offshore facilities. PNR is
maintaining its OSFR in this amount by insurance. Although the working interest
owners have advised the Trust that current environmental regulation has had no
material adverse effect on the working interest owners' present method of
operations, the impact of the recently adopted regulatory changes, and of future
environmental regulatory developments such as stricter environmental regulation
and enforcement policies, cannot presently be quantified. By letter dated
November 9, 1995, PNR was advised by the MMS that it does not qualify for a
waiver from supplemental bond requirements and that PNR may be required to post
supplemental bonds covering its potential obligations with respect to offshore
operations. PNR executed a guaranty of abandonment liability (area wide) with
the MMS on April 26, 1996, in satisfaction of these obligations.

     PNR has advised the Trust that it is not involved in any administrative or
judicial proceedings relating to the Royalty Properties arising under federal,
state, or local environmental protection laws and regulations which would have a
material adverse effect on the Trust's financial position or results of
operations.

PLATFORM ABANDONMENT AND REMOVAL

     PNR is responsible for the abandonment and removal of its offshore drilling
and production structures within one year after the cessation of production,
although extensions can be requested.

ITEM 2.  PROPERTIES.

     Reference is made to Item 1 of this Form 10-K.

ITEM 3.  LEGAL PROCEEDINGS.

     There are no pending legal proceedings to which the Trust is a party.

ITEM 4.  SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

     There were no matters submitted to a vote of unitholders during the fourth
quarter of 1998.

                                       16
<PAGE>
                                    PART II

ITEM 5.  MARKET FOR THE REGISTRANT'S COMMON EQUITY AND RELATED UNITHOLDER
MATTERS.

     The units of beneficial interest of Mesa Offshore Trust are traded on the
Pacific Exchange -- ticker symbol MOS. The high and low sales prices and
distributions per unit for each quarter in the two years ended December 31, 1998
were as follows:

<TABLE>
<CAPTION>
                                                            1998                                    1997
                                            -------------------------------------   -------------------------------------
                                                                    DISTRIBUTION                            DISTRIBUTION
                                              HIGH        LOW           PAID          HIGH        LOW           PAID
                                            ---------  ---------    -------------   ---------  ---------    -------------
<S>                                         <C>        <C>          <C>             <C>        <C>          <C>
First Quarter.............................  $    .219  $    .156       $ .0091      $    .344  $    .219       $ .0070
Second Quarter............................  $    .188  $    .094       $ .0045      $    .344  $    .250       $ .0248
Third Quarter.............................  $    .125  $    .063       $ .0070      $    .250  $    .188       $ .0219
Fourth Quarter............................  $    .094  $    .031       $   --       $    .250  $    .188       $ .0143
</TABLE>

     At March 26, 1999, the 71,980,216 units outstanding were held by 14,525
unitholders of record.

ITEM 6.  SELECTED FINANCIAL DATA.

<TABLE>
<CAPTION>
                                        1998            1997            1996           1995           1994
                                   --------------  --------------  --------------  -------------  -------------
<S>                                <C>             <C>             <C>             <C>            <C>
Royalty income...................  $    1,683,664  $    5,737,644  $       36,014  $   3,139,620  $   9,104,615
Distributable income.............  $    1,487,139  $    4,900,814  $        --     $   2,803,862  $   8,783,711
Distributable income per unit..    $        .0206  $        .0681  $        --     $       .0390  $       .1220
Excess cost carryforward.........  $   (1,109,013) $        --     $   (3,149,598) $    (138,514) $       --
Total assets at year end.........  $    1,915,901  $    3,274,532  $    2,602,742  $   3,103,451  $   4,724,878
</TABLE>

ITEM 7.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
         OF OPERATIONS.

FINANCIAL REVIEW

  YEARS 1998 AND 1997

     Royalty income decreased to $1,683,664 in 1998 as compared to $5,737,644 in
1997, primarily as a result of lower natural gas production and prices and the
recovery of capital costs associated with completion costs on the Brazos A-7 No.
5 well in the fourth quarter of 1998.

     Production volumes for natural gas decreased to 1,277,464 Mcf in 1998
compared with 4,030,273 Mcf in 1997. The decrease was due primarily to natural
production decline. The average sale price received for natural gas in 1998 was
$2.31 per Mcf compared with $2.66 per Mcf in 1997.

     Crude oil, condensate and natural gas liquids production volumes decreased
to 51,066 barrels in 1998 compared with 170,158 barrels in 1997. The decrease
was due primarily to natural production decline at South Marsh Island 155 and
156. The average sale price in 1998 for crude oil, condensate and natural gas
liquids was $13.03 per barrel compared with $16.97 per barrel in 1997.

  YEARS 1997 AND 1996

     Royalty income was $5,737,644 in 1997 as compared to $36,014 in 1996. The
increase in Royalty income was primarily due to the recovery of 1996 drilling
costs on South Marsh Island blocks 155 and 156 by PNR in the first quarter of
1997. Distributable income increased to $4,900,814 ($.0681 per unit) in 1997 as
compared to no distributable income in 1996.

     Production volumes for natural gas decreased to 4,030,273 Mcf in 1997
compared with 4,499,242 Mcf in 1996. The decrease was due primarily to natural
production decline. The average sale price received for natural gas in 1997 was
$2.66 per Mcf compared with $2.25 per Mcf in 1996.

     Crude oil, condensate and natural gas liquids production volumes increased
to 170,158 barrels in 1997 compared with 162,405 barrels in 1996. The increase
was due primarily to increased production

                                       17
<PAGE>
on South Marsh Island. The average sale price in 1997 for crude oil, condensate
and natural gas liquids was $16.97 per barrel compared with $15.83 per barrel in
1996.

  GENERAL

     From inception of the Trust on December 1, 1982 through December 31, 1987,
PNR, as working interest owner, spent $110 million ($99 million net to the
Trust) to explore and develop the Royalty Properties. No significant
expenditures regarding exploration and development were made during 1988, 1989
or 1990. Beginning in late 1991 and continuing in 1992, PNR spent $9.6 million
($8.7 million net to the Trust) on exploration and development. No significant
exploration and development expenditures were made in 1993 or 1994. As discussed
below, PNR spent $3.4 million ($1.2 million net to the Trust) on exploration and
development during 1995, $21.9 million ($13.8 million net to the Trust) in 1996,
$2.9 million ($1.8 million net to the Trust) in 1997, and $7.5 million ($746,000
net to the Trust) in 1998. PNR anticipates spending up to approximately $72,000
($45,000 net to the Trust) primarily on a possible workover on South Marsh
Island 155 and 156 in 1999, and recompletions on Brazos 155 and 156 in 1999.

LIQUIDITY AND CAPITAL RESOURCES

     In accordance with the provisions of the Trust conveyance, generally all
revenues received by the Trust, net of Trust administrative expenses and any
cash reserves established for the payment of contingent or future obligations of
the Trust, are distributed currently to the unitholders.

     The Trust's source of cash is the Royalty income received from its share of
the net proceeds from the Royalty Properties. Reference is made to Note 6 in the
Notes to Financial Statements under Item 8 of this Form 10-K for a discussion of
estimated future Royalty income attributable to the Partnership, of which the
Trust has a 99.99% interest.

     PNR farmed out a portion of the Brazos A-7 block to another operator and
participated at a 10% working interest in the completion of an exploratory gas
well drilled in the second quarter of 1997. During the fourth quarter of 1998,
PNR incurred $7.35 million ($661,000 net to the Trust) of completion costs for
the Brazos A-7 No. 5 well. At December 31, 1998, the cost carryforward resulting
from the completion costs on the Brazos A-7 No. 5 well, other capital
expenditures and over distributions by PNR over the last twelve months was
approximately $1.1 million. As such, beginning in the fourth quarter of 1998,
the Trust stopped receiving royalty income from PNR and no such royalty income
will resume until the $1.1 million of cost carryforwards are recouped by PNR. In
addition, no distributions to unitholders will be made until the Trust recovers
administrative expenses paid from the Trust's reserve fund during the period in
which royalty income is not paid to the Trust (approximately $140,500 at
December 31, 1998).

     The December 31, 1998 reserve report prepared for the Partnership indicates
that Royalty income expected to be received by the Trust in 1999 and 2000 could
be at or near the Termination Threshold. The reserve report estimates that
future Royalty income to the Trust is approximately $5.2 million while the
Termination Threshold for 1998 was approximately $1.4 million. It is therefore
possible (depending on the timing of future production, market conditions,
recoupment of unrecovered capital costs, the receipt of amounts withheld from
the Trust related to MMS royalty claims, and other matters) that in either 1999
or 2000 Royalty income received by the Trust may be below the Termination
Threshold. If Royalty income falls below the Termination Threshold for three
successive years, the Trust would terminate pursuant to the terms discussed
above. There are numerous uncertainties inherent in estimating and projecting
the quantity and value of proved reserves for the Trust properties as many of
the Trust properties are nearing the end of their productive lives and are
therefore subject to unforeseen changes in production rates. As such, there can
be no assurance that Royalty income received by the Trust in 1999 or 2000 will
be above the Termination Threshold.

     During the mid-1980's, PNR withheld approximately $3.5 million ($3.1
million net to the Trust) as a reserve for potential liabilities for royalty
claims made by the MMS. The claims by the MMS

                                       18
<PAGE>
included, among other things, disputed transportation allowances attributable to
the Trust's South Marsh Island properties and payments received by PNR from
purchasers as settlements under gas purchase contracts. During 1998, PNR settled
all known claims with the MMS for $3.6 million ($3.2 million net to the Trust)
which significantly reduced the amount in the reserve. As of March 31, 1999, the
balance of the reserve, including accrued interest, was approximately $3.4
million ($3.1 million net to the Trust). PNR is currently in the process of
determining whether there are any additional claims related to the Trust
properties that would warrant the need to maintain this reserve. Once the review
is complete, which should be in the second quarter of 1999, PNR anticipates
releasing the excess reserve, if any, that is not deemed necessary to be
maintained in the reserve to the Trust.

OPERATIONAL REVIEW

     As discussed in Item 1 of this Form 10-K, PNR has advised the Trust that
during 1998, its offshore gas production was marketed under short-term contracts
at spot market prices primarily to H&N, Limited and that it expects to continue
to market its production under short-term contracts for the foreseeable future;
however, it is not known whether Costilla will change the current marketing
practices.

     The amount of cash distributed by the Trust is dependent on, among other
things, the sales prices and quantities of gas, crude oil, condensate and
natural gas liquids produced from the Royalty Properties and the quantities
sold. Substantial uncertainties exist with regard to future gas and oil prices,
which are subject to fluctuations due to the regional supply and demand for
natural gas and oil, production levels and other activities of the Organization
of the Petroleum Exporting Countries ("OPEC") and other oil and gas producers,
weather, storage levels, industrial growth, conservation measures, competition
and other variables.

     The Brazos A-39 block experienced a decrease in natural gas production in
1998 as compared to 1997, primarily due to natural production decline. The
Brazos A-7 block also experienced a decrease in natural gas production in 1998
compared to 1997, primarily due to natural production decline. PNR farmed out a
portion of the Brazos A-7 block to another operator and participated at a 10%
working interest in the completion of an exploratory gas well that was drilled
in the second quarter of 1997. The No. 5 well encountered gas pay and was
suspended pending completion operations. Production facilities were installed
and the No. 5 well commenced production late in the fourth quarter of 1998 at a
rate of approximately 10 MMcf per day. The combined completion and facility
costs are expected to total $7.35 million ($661,000 net to the Trust).

     The South Marsh Island 155 and 156 blocks experienced a decrease in
production in 1998 as compared to 1997, primarily due to natural production
decline and the cessation of production in November of 1998 of the A-19 well. 
PNR purchased 3D seismic data for the South Marsh Island 156 block at a cost of
$300,000 ($189,000 net to the Trust). The data has been evaluated and PNR has no
current plans for additional drilling.

     The West Delta 61 and 62 blocks experienced a decrease in production in
1998 as compared to 1997, primarily due to the cessation of production of PNR
operated wells. These wells are currently uneconomic to produce. In portions of
West Delta Block 62, the Trust is receiving royalty income from this property
pursuant to a farmout agreement with another operator. The interest in the
farmout wells which is attributable to the Trust consists of a 7.5% overriding
royalty interest. In West Delta Block 61, PNR farmed out portions of the block
to another operator, retaining a 10% (9% net to the Trust) overriding royalty
interest. As previously reported, a new well was drilled in the third quarter of
1998 which encountered 320 net feet of pay in eight Miocene sands below a true
vertical depth of 7,500 feet. In the fourth quarter of 1998, the operator
drilled one development well and one exploratory well. The development well
encountered 250 net feet of pay in seven Miocene sands. The operator has elected
to set a four pile platform and production is expected in the second quarter of
1999. The exploratory well tested a new fault block which was determined to be
non-commercial. The exploratory well was subsequently plugged in the first
quarter of 1999. The Trust will receive an 11.25% overriding royalty interest in
these wells.

                                       19
<PAGE>
     Matagorda Island 624 production decreased in 1998 as compared to 1997,
primarily due to natural production decline. Gross production for the block is
currently 1.5 MMcf per day and 23 barrels of condensate per day as of March
1999.

INFORMATION SYSTEMS FOR THE YEAR 2000

     The inability of some computer programs and embedded chips to distinguish
between the year 1900 and year 2000 (the "Year 2000 problem") poses a serious
threat of business disruption to any organization that utilizes computer
technology and computer chip technology in their business systems or equipment.
In proactive response to the Year 2000 problem, PNR established a "Year 2000"
project to assess, to the extent possible, PNR's internal Year 2000 problem; to
take remedial actions necessary to minimize the Year 2000 risk exposure to PNR
and significant third parties with whom it has data interchange; and, to test
its systems and processes once remedial actions have been taken. PNR has
contracted with IBM Global Services to perform the assessment and remedial
phases of its Year 2000 project.

     As of December 31, 1998, PNR estimates that the assessment phase is
approximately 86% complete on a worldwide basis and has included, among other
procedures, (1) the identification of necessary remediation, upgrade and/or
replacement of existing information technology applications and systems; (2) the
assessment of non-information technology exposures, such as telecommunications
systems, security systems, elevators and process control equipment; (3) the
initiation of inquiry and dialogue with significant third party business
partners, customers and suppliers in an effort to understand and assess their
Year 2000 problems, readiness and potential impact on PNR and its Year 2000
problem; (4) the implementation of processes designed to reduce the risk of
reintroduction of Year 2000 problems into PNR's systems and business processes;
and, (5) the formulation of contingency plans for mission-critical information
technology systems.

     PNR expects to complete the assessment phase of its Year 2000 project by
the end of the first quarter of 1999 but is being delayed by limited responses
received on inquiries made of third party businesses.

     As of December 31, 1998, PNR estimates that the remedial phase is
approximately 54% complete, on a worldwide basis, subject to the continuing
results of the third party inquiry assessments and the testing phase. The
remedial phase has included the upgrade and/or replacement of certain
applications and hardware systems. The remediation of non-information technology
is expected to be completed during July 1999. PNR's Year 2000 remedial actions
have not significantly delayed other information technology projects or
upgrades. The testing phase of PNR's Year 2000 project is expected to be
completed by March 1999 and all other information technology systems and
non-information technology remediation by the end of the third quarter of 1999.
None of PNR's costs related to the Year 2000 are passed through to the Trust.

     A failure to remedy a critical Year 2000 problem could have a materially
adverse effect on PNR's results of operations and financial condition. The most
likely worst case scenario which may be encountered as a result of a Year 2000
problem could include information and non-information system failures, the
receipt or transmission of erroneous data, lost data or a combination of similar
problems of a magnitude to PNR that cannot be accurately assessed at this time.

     In the assessment phase of PNR's Year 2000 project, contingency plans are
being designed to mitigate the exposure to mission critical information
technology systems, such as oil and gas sales receipts; vendor and royalty cash
distributions; debt compliance; accounting; and, employee compensation. Such
contingency plans anticipate the extensive utilization of third-party data
processing services, personal computer applications and the substitution of
courier and mail services in place of electronic data interchange. Given the
uncertainties regarding the scope of the Year 2000 problem and the compliance of
significant third parties, there can be no assurance that contingency plans will
have anticipated all Year 2000 scenarios.

     The Trustee has developed and is implementing a program to prepare its
systems and applications for the Year 2000, including those used to render
services to the Trust. In that connection, the Trustee intends to have such
systems and applications capable of processing, on and after January 1, 2000,
date, and date-related data consistent with the functionality of such systems
and applications, without a

                                       20
<PAGE>
material adverse effect upon its performance of services as Trustee. Third
parties that the Trust conducts business with could be prone to Year 2000
problems that could not be assessed or detected by the Trust. The Trust is
contacting the major third parties to determine whether they will be able to
resolve, in a timely manner, any Year 2000 problems directly affecting the Trust
and to inform them of the Trust's internal assessment of its Year 2000 review.

     Information above with respect to PNR is based upon information provided by
PNR to the Trustee for use in this Form 10-K.

                                       21
<PAGE>
            NET PROCEEDS, PRODUCTION AND AVERAGE PRICES (UNAUDITED)
<TABLE>
<CAPTION>
                                                         SOUTH      
                                                         MARSH        WEST     MATAGORDA
                                          BRAZOS       ISLAND 155     DELTA      ISLAND
YEAR ENDED DECEMBER 31, 1998:          A-7 AND A-39     AND 156     61 AND 62     624        TOTAL
                                       -------------   ----------   ---------  ----------  ----------
<S>                                    <C>             <C>          <C>        <C>         <C>       <C>
  90% of--                                                          
    Gross proceeds...................    $ 872,631     $1,527,059   $ 456,750  $  761,902  $3,618,342
  Less 90% of--                                                     
    Operating costs..................     (299,732)      (795,642)   (580,501)   (153,745) (1,829,620)
    Capital costs recovered..........      --             (23,007)     --          (1,883)    (24,890)
    Accrual for future abandonment                                  
      costs and interest                                            
      on cost carryforward...........      (46,908)        (5,999)    (23,392)     (3,701)    (80,000)
                                       -------------   ----------   ---------  ----------  ----------
  Net Proceeds                                                      
    (Excess Costs)...................    $ 525,991     $  702,411   $(147,143) $  602,573  $1,683,832
                                       =============   ==========   =========  ==========  ==========
Trust share of net proceeds                                         
  (99.99%)...........................                                                      $1,683,664
                                                                                           ==========
90% of Production Volumes and Average                               
  Sales Prices:                                                     
    Crude oil, condensate and natural                               
      gas liquids (Bbls).............        1,668         43,589       1,013       4,796      51,066
                                       =============   ==========   =========  ==========  ==========
    Average sales price per Bbl......    $   11.04     $    12.53   $   13.09  $    18.24  $    13.03
                                       =============   ==========   =========  ==========  ==========
    Natural gas (Mcf)................      384,969        419,725     170,106     302,664   1,277,464
                                       =============   ==========   =========  ==========  ==========
    Average sales price per Mcf......    $    2.22     $     2.34   $    2.61  $     2.23  $     2.31
                                       =============   ==========   =========  ==========  ==========
Producing wells (gross)..............            4              2           3           1          10
YEAR ENDED DECEMBER 31, 1997:                                       
  90% of--                                                          
    Gross proceeds...................   $1,736,576     $8,909,206  $1,730,818  $1,226,177 $13,602,777
  Less 90% of--                                                     
    Operating costs..................     (431,282)    (1,192,448)   (748,218)   (245,669) (2,617,617)
    Capital costs recovered..........       (1,178)    (4,917,298)    (69,128)     (4,644) (4,992,248)
    Accrual for future abandonment                                  
      costs..........................     (123,115)       (60,448)    (61,395)     (9,716)   (254,674)
                                       -------------   ----------   ---------  ----------  ----------
  Net Proceeds.......................   $1,181,001     $2,739,012   $ 852,077  $  966,148  $5,738,238
                                       =============   ==========   =========  ==========  ==========
Trust share of net proceeds                                         
  (99.99%)...........................                                                      $5,737,644
                                                                                           ==========
90% of Production Volumes and Average                               
  Sales Prices:                                                     
    Crude oil, condensate and natural                               
      gas liquids (Bbls).............        1,215        145,493      13,891       9,559     170,158
                                       =============   ==========   =========  ==========  ==========
    Average sales price per Bbl......    $   18.36     $    16.66   $   18.24  $    19.65  $    16.97
                                       =============   ==========   =========  ==========  ==========
    Natural gas (Mcf)................      682,333      2,383,150     565,919     398,871   4,030,273
                                       =============   ==========   =========  ==========  ==========
    Average sales price per Mcf......    $    2.51     $     2.72   $    2.61  $     2.60  $     2.66
                                       =============   ==========   =========  ==========  ==========
Producing wells (gross)..............            3              3           3           1          10
YEAR ENDED DECEMBER 31, 1996:                                       
  90% of--                                                          
    Gross proceeds...................   $1,011,764     $7,714,044  $3,070,880  $  906,788  $12,703,476
  Less 90% of--                                                     
    Operating costs..................     (600,885)      (807,674)   (727,325)   (377,206) (2,513,090)
    Capital costs recovered..........      --          (9,329,717)     (5,335)   (344,793) (9,679,845)
    Accrual for future abandonment                                  
      costs and interest                                            
      on cost carryforward...........      (86,181)      (143,018)   (231,185)    (14,139)   (474,523)
                                       -------------   ----------   ---------  ----------  ----------
  Net Proceeds (Excess Costs)........    $ 324,698    $(2,566,365) $2,107,035  $  170,650  $   36,018
                                       =============   ==========   =========  ==========  ==========
Trust share of net proceeds (99.99%).                                                      $   36,014
                                                                                           ==========
90% of Production Volumes and Average                               
  Sales Prices:                                                     
    Crude oil, condensate and natural                               
      gas liquids (Bbls).............          477        148,046       5,719       8,163     162,405
                                       =============   ==========   =========  ==========  ==========
    Average sales price per Bbl......    $     N/A     $    15.74   $   17.20  $    20.41  $    15.83
                                       =============   ==========   =========  ==========  ==========
    Natural gas (Mcf)................      521,846      2,397,012   1,220,306     360,078   4,499,242
                                       =============   ==========   =========  ==========  ==========
    Average sales price per Mcf......    $    1.99     $     2.25   $    2.44  $     2.06  $     2.25
                                       =============   ==========   =========  ==========  ==========
Producing wells (gross)..............            3              5           4           3          15
</TABLE>
------------
o  The amounts shown are for the Mesa Offshore Royalty Partnership.

o  Producing wells indicates the gross number of wells capable of production as
   of the end of the period.

o  Gross proceeds is based on actual production for a twelve-month period ending
   on October 31 of each year, respectively.

o  Capital costs recovered represent capital costs incurred during the current
   or prior period to the extent that such costs have been recovered by PNR from
   gross proceeds.

o  At December 31, 1998 the cost carryforward was $1.1 million of which $0.8
   million primarily related to well completion costs on the Brazos A-7 No. 5
   and other unrecovered capital costs, and $0.3 million related to over
   distributions by Pioneer over the last twelve month period.

                                       22
<PAGE>
ITEM 8.  FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA.

                              MESA OFFSHORE TRUST

                       STATEMENTS OF DISTRIBUTABLE INCOME

<TABLE>
<CAPTION>
                                                YEARS ENDED DECEMBER 31,
                                       -----------------------------------------
                                           1998           1997          1996
                                       -------------  -------------  -----------
<S>                                    <C>            <C>            <C>
Royalty income.......................  $   1,683,664  $   5,737,644  $    36,014
Interest income......................        121,430        123,268       63,253
General and administrative expense...       (317,955)      (960,098)     (99,267)
                                       -------------  -------------  -----------
Distributable income.................  $   1,487,139  $   4,900,814  $   --
                                       =============  =============  ===========
Distributable income per unit........  $      0.0206  $      0.0681  $   --
                                       =============  =============  ===========
</TABLE>

               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS

<TABLE>
<CAPTION>
                                                                                         DECEMBER 31,
                                                                             ------------------------------------
                                                                                   1998               1997
<S>                                                                          <C>                <C>
                                                                             -----------------  -----------------
                                  ASSETS
Cash and short-term investments............................................  $       1,836,398  $       2,993,764
Interest receivable........................................................             23,102             32,568
Net overriding royalty interest in oil and gas properties..................        380,905,000        380,905,000
     Less: accumulated amortization........................................       (380,848,599)      (380,656,800)
                                                                             -----------------  -----------------
Total assets...............................................................  $       1,915,901  $       3,274,532
                                                                             =================  =================
                       LIABILITIES AND TRUST CORPUS
Reserve for trust expenses.................................................  $       1,859,500  $       2,000,000
Distribution payable.......................................................             --              1,026,332
Trust corpus (71,980,216 units of beneficial
  interest authorized and outstanding).....................................             56,401            248,200
                                                                             -----------------  -----------------
Total liabilities and trust corpus.........................................  $       1,915,901  $       3,274,532
                                                                             =================  =================
</TABLE>

                     STATEMENTS OF CHANGES IN TRUST CORPUS

<TABLE>
<CAPTION>
                                                                             YEARS ENDED DECEMBER 31,
                                                                  ----------------------------------------------
                                                                       1998            1997            1996
<S>                                                               <C>             <C>             <C>
                                                                  --------------  --------------  --------------
Trust corpus, beginning of year.................................  $      248,200  $    1,062,405  $    1,067,160
     Distributable income.......................................       1,487,139       4,900,814        --
     Distributions to unitholders...............................      (1,487,139)     (4,900,814)       --
     Amortization of net overriding royalty interest............        (191,799)       (814,205)         (4,755)
                                                                  --------------  --------------  --------------
Trust corpus, end of year.......................................  $       56,401  $      248,200  $    1,062,405
                                                                  ==============  ==============  ==============
</TABLE>

   The accompanying notes are an integral part of these financial statements.

                                       23

<PAGE>
                              MESA OFFSHORE TRUST
                         NOTES TO FINANCIAL STATEMENTS

(1)  TRUST ORGANIZATION AND PROVISIONS

  THE TRUST

     The Mesa Offshore Trust (the "Trust") was created effective December 1,
1982. On that date, Mesa Petroleum Co., predecessor to Mesa Limited Partnership,
which was predecessor to MESA Inc., transferred to the Trust a 99.99% interest
in the Mesa Offshore Royalty Partnership (the "Partnership"). The Trust is an
independent trust administered by Chase Bank of Texas National Association, as
trustee (the "Trustee").

     The terms of the Mesa Offshore Trust Indenture (the "Trust Indenture")
provide, among other things, that:

        (a) the Trust cannot engage in any business or investment activity or
        purchase any assets;

        (b) the interest in the Partnership can be sold in part or in total for
        cash upon approval of the unitholders;

        (c) the Trustee can establish cash reserves and borrow funds to pay
        liabilities of the Trust and can pledge the assets of the Trust to
        secure payment of the borrowings;

        (d) the Trustee will make cash distributions to the unitholders in
        January, April, July and October of each year as discussed more fully in
        Note 4; and

        (e) the Trust will terminate upon the first to occur of the following
        events: (i) the total amount of cash received per year by the Trust for
        each of three successive years commencing after December 31, 1987 is
        less than ten times one-third of the total amount payable to the Trustee
        as compensation for such three-year period (the "Termination
        Threshold") or (ii) a vote by the unitholders in favor of termination.
        Amounts earned by the Trustee as compensation were $128,000, $173,000
        and $123,000 for the years 1998, 1997 and 1996, respectively. Upon
        termination of the Trust, the Trustee will sell for cash all the assets
        held in the Trust estate and make a final distribution to unitholders of
        any funds remaining after all Trust liabilities have been satisfied.

  THE PARTNERSHIP

     The Partnership was created to receive and hold a net overriding royalty
interest (the "Royalty") in ten producing and nonproducing oil and gas
properties located in federal waters offshore Louisiana and Texas (the "Royalty
Properties"). MESA Inc. created the Royalty out of its working interest in the
Royalty Properties and transferred it to the Partnership. Until August 7, 1997,
MESA Inc. owned and operated its assets through Mesa Operating Co. ("Mesa"),
the operator and the managing general partner of the Royalty Properties. On
August 7, 1997, MESA Inc. merged with and into Pioneer Natural Resources Company
("Pioneer"), formerly a wholly owned subsidiary of MESA, Inc., and Parker &
Parsley Petroleum Company merged with and into Pioneer Natural Resources USA,
Inc. (successor to Mesa), a wholly owned subsidiary of Pioneer ("PNR")
(collectively, the mergers are referred to herein as the "Merger"). Subsequent
to the Merger, Pioneer owns and operates its assets through PNR and is also the
managing general partner of the Partnership.

     The Partnership is owned 99.99% by the Trust and 0.01% by PNR. PNR serves
as the managing general partner of the Partnership. PNR receives no compensation
for serving as managing general partner other than the income it receives
attributable to its interest in the Partnership.

  STATUS OF THE TRUST

     The December 31, 1998 reserve report prepared for the Partnership (See Note
6) indicates that Royalty income expected to be received by the Trust in 1999
and 2000 could be at or near the Termination Threshold. The reserve report
estimates that the future Royalty income to the Trust is approximately $5.2
million while the Termination Threshold for 1998 was approximately $1.4 million.
It is therefore possible (depending on the timing of production, market

                                       24
<PAGE>
                              MESA OFFSHORE TRUST
                    NOTES TO FINANCIAL STATEMENTS--CONTINUED

     conditions, recoupment of unrecovered capital costs, the receipt of amounts
withheld from the Trust related to MMS royalty claims, and other matters) that
in either 1999 or 2000 Royalty income received by the Trust may be below the
Termination Threshold. If Royalty income falls below the Termination Threshold
for three successive years, the Trust would terminate pursuant to the terms
discussed above. There are numerous uncertainties inherent in estimating and
projecting the quantity and value of proved reserves for the Trust properties as
many of the Trust properties are nearing the end of their productive lives and
are therefore subject to unforeseen changes in production rates. As such, there
can be no assurance that Royalty income received by the Trust in 1999 or 2000
will be above the Termination Threshold.

(2)  NET OVERRIDING ROYALTY INTEREST

     The instruments conveying the Royalty to the Partnership provide that PNR
will calculate and pay to the Partnership each month an amount equal to 90% of
aggregate net proceeds for the preceding month. Generally, net proceeds means
the excess of the amounts received by PNR from sales of its share of oil and gas
from the Royalty Properties (gross proceeds) over the operating and capital
costs incurred. Costs exceeding gross proceeds for any month are recovered by
PNR, with interest thereon at the prime rate of the Bank of America plus
one-half percent, out of future gross proceeds prior to making further royalty
payments to the Partnership.

     The initial carrying value of the Royalty represented the net book value
assigned by PNR to the Royalty Properties at the date of transfer to the Trust.
Amortization of the Royalty, which is calculated on the basis of current royalty
income in relation to estimated future royalty income, is charged directly to
trust corpus since such amounts do not affect distributable income.

(3)  BASIS OF ACCOUNTING

     The financial statements of the Trust are prepared on the following basis:

        (a) Royalty income recorded for a month is the Trust's interest in the
        amount computed and paid by the working interest owner to the
        Partnership for such month rather than either the value of a portion of
        the oil and gas produced by the working interest owner for such month or
        the amount subsequently determined to be 90% of the net proceeds for
        such month;

        (b) Interest income, interest receivable and distributions payable to
        unitholders include interest to be earned on short-term investments from
        the financial statement date through the next date of distribution; and

        (c) Trust general and administrative expenses are recorded in the month
        they accrue.

     This basis for reporting distributable income is considered to be the most
meaningful because distributions to the unitholders for a month are based on net
cash receipts for such month. However, it will differ from the basis used for
financial statements prepared in accordance with generally accepted accounting
principles because, under such accounting principles, royalty income for a month
would be based on net proceeds from production for such month without regard to
when calculated or received and interest income for a month would be calculated
only through the end of such month.

(4)  DISTRIBUTIONS TO UNITHOLDERS

     Under the terms of the Trust Indenture, the Trustee must distribute to the
unitholders all cash receipts, after paying liabilities and providing for cash
reserves as determined necessary by the Trustee. The amounts distributed are
determined on a monthly basis and are payable to unitholders of record as of the
last business day of each month. However, cash distributions are made quarterly
in January,

                                       25
<PAGE>
                              MESA OFFSHORE TRUST
                    NOTES TO FINANCIAL STATEMENTS--CONTINUED

April, July and October, and include interest earned from the monthly record
dates to the dates of distribution.

(5)  FEDERAL INCOME TAXES

     The Trustee reports on the basis that the Trust is a grantor trust. Based
on its previous audit policy, the Internal Revenue Service (the "IRS") is
expected to concur with such action. No IRS ruling has been received or
requested with respect to the Trust, however, and no court case has been decided
involving identical facts and circumstances. It is possible, therefore, that the
IRS would assert upon audit that the Trust is taxable as a corporation and that
a court might agree with such assertion.

     As a grantor trust, the Trust will incur no federal income tax liability.
In addition, it will incur little or no federal income tax liability if it is
held to be a non-grantor trust. If the Trust were held to be taxable as a
corporation, it would have to pay tax on its net taxable income at the corporate
rate.

(6)  SUPPLEMENTAL RESERVE INFORMATION (UNAUDITED)

     Estimates of the proved oil and gas reserves attributable to the Royalty as
of December 31, 1998, 1997 and 1996 are based on a report prepared by PNR. The
estimates were prepared in accordance with guidelines established by the
Securities and Exchange Commission (the "SEC"). Accordingly, the estimates
were based on existing economic and operating conditions. The reserve volumes
and revenue values contained in the reserve report for the Partnership interest
were estimated by allocating to the Partnership a portion of the estimated
combined net reserve volumes of the Royalty Properties based on future net
revenue. Production volumes are allocated based on royalty income. Because the
net reserve volumes attributable to the Partnership interest are estimated using
an allocation of reserve volumes based on estimates of future net revenue, a
change in prices or costs will result in changes in the estimated net reserve
volumes. Therefore, the estimated net reserve volumes attributable to the
Partnership interest will vary if different future price and cost assumptions
are used. Only costs necessary to develop and produce existing proved reserve
volumes were assumed in the allocation of reserve volumes to the Royalty.

     Future prices for natural gas were based on prices in effect as of each
year end and existing contract terms. Prices being received as of each year end
were used for sales of oil, condensate and natural gas liquids. Operating costs,
production and ad valorem taxes and future development and abandonment costs
were based on current costs as of each year end, with no escalation.

     There are numerous uncertainties inherent in estimating the quantities and
value of proved reserves and in projecting the future rates of production and
timing of expenditures. The reserve data below represent estimates only and
should not be construed as being exact. Moreover, the discounted values should
not be construed as representative of the current market value of the Royalty. A
market value determination would include many additional factors including: (i)
anticipated future oil and gas prices; (ii) the effect of federal income taxes,
if any, on the future royalties; (iii) an allowance for return on investment;
(iv) the effect of governmental legislation; (v) the value of additional
reserves, not considered proved at present, which may be recovered as a result
of further exploration and development activities; and (vi) other business
risks.

     Estimates of reserve volumes attributable to the Royalty are shown in order
to comply with requirements of the SEC. There is no precise method of allocating
estimates of physical quantities of reserve volumes between PNR and the
Partnership, since the Royalty is not a working interest and the Partnership
does not own and is not entitled to receive any specific volume of reserves from
the Royalty. The quantities of reserves attributable to the Partnership have
been and will be affected by changes in various economic factors utilized in
estimating net revenues from the Royalty Properties, as well as any exploration
activities which may be conducted by PNR. Therefore, the estimates of reserve

                                       26
<PAGE>
                              MESA OFFSHORE TRUST
                    NOTES TO FINANCIAL STATEMENTS--CONTINUED

volumes set forth below are to a large extent hypothetical and differ in
significant respects from estimates of reserves attributable to a working
interest.

     The future net revenues contained in the previously mentioned reserve
report have not been reduced for future general and administrative costs and
expenses of the Trust, which are expected to approximate $500,000 annually. The
general and administrative costs and expenses of the Trust may increase in
future years, depending on the amount of royalty income, increases in
accounting, engineering, legal, and other professional fees and other factors.

     The following schedules set forth (i) the estimated net quantities of
proved and proved developed oil, condensate and natural gas liquids and natural
gas reserves attributable to the Royalty, and (ii) the standardized measure of
the discounted future royalty income attributable to the Royalty and the nature
of changes in such standardized measure between years. These schedules are
prepared on the accrual basis, which is the basis on which PNR maintains its
production records and is different from the basis on which the Royalty is
computed. Certain reclassifications have been made to prior year amounts to
conform to the current year presentation.

    ESTIMATED QUANTITIES OF PROVED AND PROVED DEVELOPED RESERVES (UNAUDITED)

<TABLE>
<CAPTION>
                                            OIL,
                                         CONDENSATE
                                        AND NATURAL       NATURAL
                                        GAS LIQUIDS         GAS
                                        ------------   -------------
<S>                                     <C>            <C>
                                           (BBLS)          (MCF)
Proved Reserves:
     December 31, 1995...............      153,168         2,281,262
           Revisions of previous
              estimates..............      (10,158)         (319,134)
           Extensions, discoveries
              and other additions....      133,190         2,111,233
           Production................         (460)          (12,755)
                                        ------------   -------------
     December 31, 1996...............      275,740         4,060,606
           Revisions of previous
              estimates..............     (131,509)         (672,227)
           Extensions, discoveries
              and other additions....       --               831,732
           Production................      (74,114)       (1,755,429)
                                        ------------   -------------
     December 31, 1997...............       70,117         2,464,682
           Revisions of previous
              estimates..............      115,088          (615,111)
           Extensions, discoveries
              and other additions....      241,200           984,112
           Production................      (22,133)         (553,682)
                                        ------------   -------------
     December 31, 1998...............      404,272         2,280,001
                                        ============   =============
Proved Developed Reserves:
     December 31, 1996...............      275,740         4,060,606
                                        ============   =============
     December 31, 1997...............       70,117         2,464,682
                                        ============   =============
     December 31, 1998...............        5,628           933,684
                                        ============   =============
</TABLE>
------------

  (See Notes on following page.)

                                       27
<PAGE>
                              MESA OFFSHORE TRUST
                    NOTES TO FINANCIAL STATEMENTS--CONTINUED

               STANDARDIZED MEASURE OF FUTURE ROYALTY INCOME FROM
      PROVED OIL AND GAS RESERVES, DISCOUNTED AT 10% PER ANNUM (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                                 DECEMBER 31,
                                                                                             --------------------
                                                                                               1998       1997
                                                                                             ---------  ---------
<S>                                                                                          <C>        <C>
                                                                                                (IN THOUSANDS)
Ninety percent of future gross proceeds....................................................  $   7,867  $   6,863
Less ninety percent of --
     Future operating costs................................................................     (1,201)    (3,723)
     Future capital costs, net of amounts previously accrued...............................     (1,468)      (971)
                                                                                             ---------  ---------
Future royalty income......................................................................      5,198      2,169
Discount at 10% per annum..................................................................     (1,221)      (285)
                                                                                             ---------  ---------
Standardized measure of future royalty
  income from proved oil and gas reserves..................................................  $   3,977  $   1,884
                                                                                             =========  =========
</TABLE>

       CHANGES IN THE STANDARDIZED MEASURE OF FUTURE ROYALTY INCOME FROM
      PROVED OIL AND GAS RESERVES, DISCOUNTED AT 10% PER ANNUM (UNAUDITED)

<TABLE>
<CAPTION>
                                                                                    YEARS ENDED DECEMBER 31,
                                                                              -----------------------------------
                                                                                1998        1997         1996
                                                                              ---------  -----------  -----------
<S>                                                                           <C>        <C>          <C>
                                                                                        (IN THOUSANDS)
Standardized measure at beginning of year...................................  $   1,884  $    18,585  $     5,639
                                                                              ---------  -----------  -----------
     Revisions of previous estimates........................................       (559)       3,826        1,317
     Net changes in prices and production costs.............................      1,188      (17,362)       1,263
     Extensions, discoveries and other additions............................      2,960          714        9,838
     Royalty income.........................................................     (1,684)      (5,738)         (36)
     Accretion of discount..................................................        188        1,859          564
                                                                              ---------  -----------  -----------
     Net changes in standardized measure....................................      2,093      (16,701)      12,946
                                                                              ---------  -----------  -----------
Standardized measure at end of year.........................................  $   3,977  $     1,884  $    18,585
                                                                              =========  ===========  ===========
</TABLE>
------------
o  The estimated quantities of proved reserves for oil, condensate and natural
   gas liquids include oil and condensate reserves at December 31, of the
   respective years as follows: 1998, 404,272 Bbls; 1997, 54,769 Bbls; 1996,
   192,574 Bbls.

o  The estimated quantities of proved reserves, standardized measure of future
   royalty income and changes in the standardized measure represent 100% of
   amounts for the Partnership in which the Trust has a 99.99% interest.

o  The "Future capital costs, net of amounts previously accrued" at December 31,
   1998 includes, in thousands, $9,433 of future abandonment costs net of $9,009
   previously accrued by PNR.

                                       28
<PAGE>
                              MESA OFFSHORE TRUST
                    NOTES TO FINANCIAL STATEMENTS--CONTINUED

(7)  SELECTED QUARTERLY FINANCIAL DATA (UNAUDITED)
<TABLE>
<CAPTION>
                                                                   SUMMARIZED QUARTERLY RESULTS
                                                                        THREE MONTHS ENDED
                                                  --------------------------------------------------------------
                                                    MARCH 31        JUNE 30       SEPTEMBER 30      DECEMBER 31
                                                  -------------  -------------    -------------     ------------
<S>                                               <C>            <C>              <C>               <C>
1998:
Royalty income..................................  $     694,318  $     440,956      $ 535,215        $    13,175
Distributable income............................  $     659,659  $     324,206      $ 503,274        $      --
Distributable income per unit...................  $       .0091  $       .0045      $   .0070        $      -- 

1997:
Royalty income..................................  $   1,111,555  $   1,786,585      $1,756,412       $ 1,083,092
Distributable income............................  $     509,533  $   1,791,954      $1,572,995       $ 1,026,332
Distributable income per unit...................  $       .0070  $       .0248      $   .0219        $     .0144
</TABLE>

                                       29
<PAGE>
                    REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS

TO CHASE BANK OF TEXAS, NATIONAL ASSOCIATION (TRUSTEE)
AND THE UNITHOLDERS OF THE MESA OFFSHORE TRUST:

     We have audited the accompanying statements of assets, liabilities and
trust corpus of the Mesa Offshore Trust as of December 31, 1998 and 1997, and
the related statements of distributable income and changes in trust corpus for
each of the three years in the period ended December 31, 1998. These financial
statements are the responsibility of the Trustee. Our responsibility is to
express an opinion on these financial statements based on our audits.

     We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.

     These financial statements were prepared on the basis of accounting
described in Note 3, which is a comprehensive basis of accounting other than
generally accepted accounting principles.

     In our opinion, the financial statements referred to above present fairly,
in all material respects, the assets, liabilities and trust corpus of the Mesa
Offshore Trust as of December 31, 1998 and 1997, and its distributable income
and changes in trust corpus for each of the three years in the period ended
December 31, 1998, on the basis of accounting described in Note 3.

                                          ARTHUR ANDERSEN LLP

Houston, Texas
March 26, 1999

                                       30
<PAGE>
ITEM 9.  CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND
FINANCIAL DISCLOSURE.

     None.

                                    PART III

ITEM 10.  DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT.

     There are no directors or executive officers of the Registrant. The Trustee
is a corporate trustee which may be removed by the affirmative vote of a
majority of the units then outstanding at a meeting of the holders of units of
beneficial interest of the Trust at which a quorum is present.

ITEM 11.  EXECUTIVE COMPENSATION.

     Not applicable.

ITEM 12.  SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT.

     (a) SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS. Not applicable.

     (b) SECURITY OWNERSHIP OF MANAGEMENT. Not applicable.

     (c) CHANGES IN CONTROL. Registrant knows of no arrangement, including the
         pledge of securities of the Registrant, the operation of which may at a
         subsequent date result in a change in control of the Registrant.

ITEM 13.  CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS.

     Not Applicable.

                                    PART IV

ITEM 14.  EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND REPORTS ON FORM 8-K.

     (a)(1) FINANCIAL STATEMENTS

     The following financial statements are set forth under Part II, Item 8 of
this Annual Report on Form 10-K on the pages indicated.

<TABLE>
<CAPTION>
                                                                                                        PAGE IN THIS
                                                                                                          FORM 10-K
<S>                                                                                                     <C>
Statements of Distributable Income...................................................................      22
Statements of Assets, Liabilities and Trust Corpus...................................................      22
Statements of Changes in Trust Corpus................................................................      22
Notes to Financial Statements........................................................................      23
Report of Independent Public Accountants.............................................................      29
</TABLE>

     (a)(2) SCHEDULES

     Schedules have been omitted because they are not required, not applicable
or the information required has been included elsewhere herein.

     (a)(3) EXHIBITS

<TABLE>
<CAPTION>
                                                                                      SEC FILE
                                                                                         OR
                                                                                    REGISTRATION       EXHIBIT
                                                                                        NUMBER          NUMBER
                                                                                        ------          ------
<S>              <C>                                                                   <C>                <C>
      4(a)      *Mesa Offshore Trust Indenture between Mesa Petroleum Co. and Texas
                 Commerce Bank National Association, as Trustee, dated December 15,
                 1982...............................................................   2-79673         10(gg)

      4(b)      *Overriding Royalty Conveyance between Mesa Petroleum Co. and Mesa
                 Offshore Royalty Partnership, dated December 15, 1982..............   2-79673         10(hh)

      4(c)      *Partnership Agreement between Mesa Offshore Management Co. and
                 Texas Commerce Bank National Association, as Trustee, dated
                 December 15, 1982..................................................   2-79673         10(ii)
</TABLE>

                                       31
<PAGE>

<TABLE>
<CAPTION>
                                                                                          SEC FILE
                                                                                             OR
                                                                                        REGISTRATION       EXHIBIT
                                                                                           NUMBER          NUMBER
                                                                                           ------          ------
<S>               <C>                                                                   <C>                <C>
      4(d)      * Amendment to Partnership Agreement between Mesa Offshore Management
                  Co., Texas Commerce Bank National Association, as Trustee, and Mesa
                  Operating Limited Partnership, dated December 27, 1985 (Exhibit
                  4(d) to Form 10-K for year ended December 31, 1992 of Mesa Offshore
                  Trust).............................................................    1-8432             4(d)

      4(e)      * Amendment to Partnership Agreement between Texas Commerce Bank
                  National Association, as Trustee, and Mesa Operating dated as of
                  January 5, 1994 (Exhibit 4(e) to Form 10-K for year ended December
                  31, 1993 of Mesa Offshore Trust)...................................    1-8432             4(e)

     27           Financial Data Schedule
</TABLE>

------------
 * Previously filed with the Securities and Exchange Commission and incorporated
   herein by reference.

(B) REPORTS ON FORM 8-K

     None.

                                       32
<PAGE>
                                   SIGNATURES

     PURSUANT TO THE REQUIREMENTS OF SECTION 13 OR 15(d) OF THE SECURITIES
EXCHANGE ACT OF 1934, THE REGISTRANT HAS DULY CAUSED THIS REPORT TO BE SIGNED ON
ITS BEHALF BY THE UNDERSIGNED, THEREUNTO DULY AUTHORIZED.

                                          MESA OFFSHORE TRUST

                                          By  CHASE BANK OF TEXAS, NATIONAL
                                              ASSOCIATION, TRUSTEE

                                          By /s/ PETE FOSTER
                                                 Pete Foster
                                             Senior Vice President
                                               & Trust Officer

March 26, 1999

     The Registrant, Mesa Offshore Trust, has no principal executive officer,
principal financial officer, board of directors or persons performing similar
functions. Accordingly, no additional signatures are available and none have
been provided.

                                       33
<PAGE>
                                 EXHIBIT INDEX
<TABLE>
<CAPTION>
                                                                                      SEC FILE
                                                                                         OR
                                                                                    REGISTRATION       EXHIBIT
                                                                                        NUMBER          NUMBER
                                                                                        ------          ------
<S>              <C>                                                                   <C>                <C>
      4(a)      *Mesa Offshore Trust Indenture between Mesa Petroleum Co. and Texas
                 Commerce Bank National Association, as Trustee, dated December 15,
                 1982...............................................................   2-79673         10(gg)

      4(b)      *Overriding Royalty Conveyance between Mesa Petroleum Co. and Mesa
                 Offshore Royalty Partnership, dated December 15, 1982..............   2-79673         10(hh)

      4(c)      *Partnership Agreement between Mesa Offshore Management Co. and
                 Texas Commerce Bank National Association, as Trustee, dated
                 December 15, 1982..................................................   2-79673         10(ii)

      4(d)      * Amendment to Partnership Agreement between Mesa Offshore Management
                  Co., Texas Commerce Bank National Association, as Trustee, and Mesa
                  Operating Limited Partnership, dated December 27, 1985 (Exhibit
                  4(d) to Form 10-K for year ended December 31, 1992 of Mesa Offshore
                  Trust).............................................................    1-8432             4(d)

      4(e)      * Amendment to Partnership Agreement between Texas Commerce Bank
                  National Association, as Trustee, and Mesa Operating dated as of
                  January 5, 1994 (Exhibit 4(e) to Form 10-K for year ended December
                  31, 1993 of Mesa Offshore Trust)...................................    1-8432             4(e)

     27           Financial Data Schedule
</TABLE>

------------
 * Previously filed with the Securities and Exchange Commission and incorporated
   herein by reference.