<PAGE>   1
 
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                                   FORM 10-Q
 
                       SECURITIES AND EXCHANGE COMMISSION
 
                             Washington, D.C. 20549
 
(Mark One)
 
[X]          QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE
                      SECURITIES AND EXCHANGE ACT OF 1934
 
For the quarterly period ended September 30, 1998.
 
                                       OR
 
[ ]          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 1-8581
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                                            <C>
                         TEXAS                                                72-6108468
     (State or other jurisdiction of incorporation                         (I.R.S. Employer
                    or organization)                                      Identification No.)
 
   CHASE BANK OF TEXAS, NATIONAL ASSOCIATION, TRUSTEE                            77002
                    712 MAIN STREET                                           (Zip Code)
                     HOUSTON, TEXAS
        (Address of principal executive offices)
</TABLE>
 
       Registrant's telephone number, including area code: (713) 216-5712
 
                      ....................................
 
   (Former name, former address and former fiscal year, if changed since last
                                    report)
 
     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  ______
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<PAGE>   2
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                                PAGE
                                                              --------
<S>                                                           <C>
Part I.  Financial Information
 
  Item 1.  Financial Statements:
     Statements of Royalty Proceeds and Distributable
      Cash..................................................    3
     Statements of Assets, Liabilities and Trust Corpus.....    3
     Statements of Changes in Trust Corpus..................    3
     Notes to Financial Statements..........................    4
     Report of Independent Public Accountants...............    7
 
  Item 2.  Management's Discussion and Analysis of Financial
     Condition and Results of Operations....................    8
 
Part II.  Other Information
 
  Item 6.  Exhibits and Reports on Form 8-K.................    13
 
Signature...................................................    14
</TABLE>
 
                                      --2--
<PAGE>   3
 
                         PART I.  FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS.
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
             STATEMENTS OF ROYALTY PROCEEDS AND DISTRIBUTABLE CASH
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                            THREE MONTHS ENDED            NINE MONTHS ENDED
                                              SEPTEMBER 30,                 SEPTEMBER 30,
                                        --------------------------    --------------------------
                                           1998           1997           1998           1997
                                        -----------    -----------    -----------    -----------
<S>                                     <C>            <C>            <C>            <C>
Royalty proceeds......................  $        --    $        --    $        --    $        --
Trust administrative expenses.........     (126,010)      (135,042)      (289,994)      (307,378)
Interest income.......................       17,870         20,597         56,099         58,824
Reserve for future Trust expenses.....      108,140        114,445        233,895        248,554
                                        -----------    -----------    -----------    -----------
Distributable cash....................  $        --    $        --    $        --    $        --
                                        ===========    ===========    ===========    ===========
Distributable cash per Unit...........  $        --    $        --    $        --    $        --
                                        ===========    ===========    ===========    ===========
Units outstanding.....................   14,975,390     14,975,390     14,975,390     14,975,390
                                        ===========    ===========    ===========    ===========
</TABLE>
 
               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
 
<TABLE>
<CAPTION>
                                                              SEPTEMBER 30,    DECEMBER 31,
                                                                  1998             1997
                           ASSETS                             -------------    -------------
<S>                                                           <C>              <C>
Cash and short-term investments.............................  $   1,471,687    $   1,705,582
Net overriding royalty interest in oil and gas properties...    189,875,741      189,875,741
Less, adjustments to recorded cost of net overriding royalty
  interest in oil and gas properties........................    (25,614,756)     (25,614,756)
Less, accumulated amortization of net overriding royalty
  interest..................................................   (164,260,985)    (164,260,985)
                                                              -------------    -------------
          Total assets......................................  $   1,471,687    $   1,705,582
                                                              =============    =============
                LIABILITIES AND TRUST CORPUS
Reserve for future Trust expenses...........................  $   1,471,687    $   1,705,582
Trust corpus (14,975,390 Units of Beneficial Interest
  authorized,
  issued and outstanding)...................................             --               --
                                                              -------------    -------------
          Total liabilities and trust corpus................  $   1,471,687    $   1,705,582
                                                              =============    =============
</TABLE>
 
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                               NINE MONTHS ENDED
                                                                 SEPTEMBER 30,
                                                              --------------------
                                                                1998        1997
                                                              --------    --------
<S>                                                           <C>         <C>
Trust corpus, beginning of year.............................  $     --    $183,213
Royalty proceeds and interest income, net of trust
  administrative expenses and reserve for future Trust
  expenses..................................................        --          --
Distributions payable to Unit holders.......................        --          --
Amortization of net overriding royalty interest.............        --          --
                                                              --------    --------
Trust corpus, end of period.................................  $     --    $183,213
                                                              ========    ========
</TABLE>
 
   The accompanying notes are an integral part of these financial statements.
 
                                      --3--
<PAGE>   4
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                         NOTES TO FINANCIAL STATEMENTS
1. THE TRUST
 
     Freeport-McMoRan Oil and Gas Royalty Trust (the Trust) was created
effective September 30, 1983. On that date, Freeport-McMoRan Inc. (FTX)
transferred a net overriding royalty interest in certain offshore oil and gas
properties to a Partnership (the Partnership) equal to 90 percent of the Net
Proceeds (as defined in the Conveyance referred to below) from FTX's working
interests in such properties and conveyed a 99.9 percent general partnership
interest in the Partnership to the Trust. Such net overriding royalty interest
is referred to herein as the "Royalty." The Overriding Royalty Conveyance which
created the Royalty is referred to herein as the "Conveyance." The Trust is
passive, with Chase Bank of Texas, National Association as Trustee. The Trustee
has only such powers as are necessary for the collection and distribution of
revenues attributable to the Royalty, the payment of Trust liabilities and the
protection of Trust assets.
 
     The Trust Indenture provides generally that the Trust shall terminate upon
the first to occur of (i) the sale of all the Trust's interest in the
Partnership, or the sale by the Partnership of all the assets of the Partnership
including the Royalty, or (ii) a decision to terminate the Trust by the
affirmative vote of Unit holders representing a majority of the Units. The
Trustee is required to sell the Trust's interest in the Partnership, or cause
the Partnership to sell the Royalty, if the Trust's cash receipts for each of
three successive years are less than $3 million, thereby terminating the Trust
pursuant to (i) above. Upon the termination of the Trust under (ii) above, the
Trustee will sell the Trust's interest in the Partnership (or will cause the
Partnership to sell all of the assets of the Partnership). The Trustee will as
promptly as possible distribute the proceeds of any such sales according to the
respective interests and rights of the Unit holders after discharging all of the
liabilities of the Trust and, if necessary, setting up reserves in such amounts
as the Trustee in its discretion deems appropriate for contingent liabilities.
 
     The Trust's cash receipts last reached $3 million during 1995 and there
were no cash receipts in 1996 or 1997. Continued significant development of West
Cameron Block 498 has contributed to no cash being received during the first
nine months of 1998. Additionally, the Class A cost carry-forward has increased
to $23.4 million at September 30, 1998 (Note 3). This cost carry-forward must be
recouped by the Working Interest Owner before any distribution may be made to
the Trust. Unless the Trust has cash receipts of at least $3 million during
1998, the Trust will be terminated by one of the means described above. The
Working Interest Owner has informed the Trustee that there will be no Royalty
payments during 1998. Accordingly, under the Trust Agreement, the Trustee will
be required to sell the Trust's interest in the Partnership or cause the
Partnership to sell the Royalty.
 
     The Working Interest Owner has advised the Trustee that, based on an
independent review of the oil and gas interests burdened by the Royalty, the net
present value of the reserves contained therein is substantially less than the
cumulative excess Class A cost carry-forward. The Working Interest Owner is
entitled to recover this carry-forward amount from production (as well as other
costs) prior to resuming payments in respect of the Royalties. The Working
Interest Owner has also advised that it believes that production from such
reserves, together with gas imbalance payments that may be received in the
future, will be insufficient to
 
                                      --4--
<PAGE>   5
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
eliminate the cumulative Class A cost carry-forward and cover other costs taken
into account in calculating the Royalties. This information indicates that it is
unlikely that any additional Royalty payments will be received by the Trust
prior to its termination and liquidation. It also indicates that the Royalties
may have little or no value, based on the net present value of reserves
determined as a result of the independent review. In connection with the
termination of the Trust, the Trustee intends to sell the Trust's interest in
the Partnership, or to cause the Partnership to sell the Royalty, for cash to
the highest bidder. Although the Trustee will endeavor to offer the Partnership
interest, or to cause the Partnership to offer the Royalty, pursuant to
procedures intended to maximize the proceeds to the Trust, the Trustee can give
no assurance regarding the amounts, if any, to be realized as a result of such
offer.
 
     A trust unitholder has advised the Trustee that he intends to seek
unitholder approval to convert the Trust into a corporation. The Trustee has not
received any formal proposal from the unitholder, nor is the Trustee aware of
any likely method by which such a conversion can be accomplished.
 
2. THE ROYALTY
 
     IMC Global Inc. (IGL) succeeded to FTX effective December 22, 1997,
following the merger of FTX into IGL. Accordingly, IGL is now the Working
Interest Owner and presently owns the oil and gas interests burdened by the
Royalty. The Conveyance provides that the owner of the interests burdened by the
Royalty will calculate and pay monthly to the Partnership an amount equal to 90
percent of the net proceeds for the preceding month. Net proceeds generally
consist of the excess of gross revenues received from the Royalty Properties
(Gross Proceeds), on a cash basis, over operating costs, capital expenditures
and other charges, on an accrual basis (Net Proceeds). Included in the
calculation of expenses is a cost-carryforward. See Note 3.
 
3. DISTRIBUTIONS TO UNIT HOLDERS
 
     As a result of capital costs incurred in recent years, a cumulative excess
Class A cost carry-forward of $23,377,874 existed as of September 30, 1998. This
carry-forward is subject to and includes an interest factor, calculated at the
prime rate, which totaled $1,434,799 ($1,291,319, net to the Trust) during the
nine month period of 1998 and cumulatively totaled $2,391,572 ($2,150,262, net
to the Trust). This excess Class A cost carry-forward must be recouped by the
Working Interest Owner out of future Net Proceeds before Royalty distributions
can be resumed. Given the amount of the cumulative excess Class A cost
carry-forward and the imminent termination of the Trust, it is highly unlikely
that distributions to Unitholders will ever be resumed. In addition, the Working
Interest Owner has given the Trustee information indicating that it is unlikely
that any additional Royalty payments will be received by the Trust prior to its
termination and liquidation. See Note 1.
 
4. GAS BALANCING ARRANGEMENTS
 
     As a result of past curtailments in gas taken by the former principal
purchaser of production from the Royalty Properties, certain quantities of gas
have been sold by other parties with interests in the Royalty Properties
pursuant to gas balancing arrangements. Proceeds from gas produced from the
Royalty Properties
                                      --5--
<PAGE>   6
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
but sold by other parties pursuant to such balancing arrangements
(underproduction) are not included in Gross Proceeds for purposes of calculating
the Royalty. In the future, the Working Interest Owner will be entitled to sell
volumes equal to such underproduction or receive cash settlements. On certain of
the Royalty Properties, a cash settlement may be required, depending on future
results, because of the lack of sufficient remaining reserves from which to
makeup any underproduction. As of September 30, 1998, the unrecovered quantity
of gas sold by third parties pursuant to such gas balancing arrangements since
inception of the Trust was approximately 1.6 billion cubic feet (bcf) (1.4 bcf
net to the Trust). Gross Proceeds will be increased in future periods when the
Working Interest Owner is compensated either through the sale of gas or through
cash settlements, the amount and timing of which are uncertain. Because the
cumulative excess Class A carry-forward is relatively large and the Working
Interest Owner is entitled to recover such carry-forward from Gross Proceeds, it
is unlikely that the receipt of compensation, if any, from gas balancing
arrangements will result in the payment of Royalties. See Notes 1 and 2.
 
5. ESTABLISHMENT OF AN EXPENSE RESERVE
 
     Because of the decline in Royalty income, at certain times since late 1993
the Trust has been unable to pay its ongoing administrative expenses. To permit
the Trust to pay its routine administrative expenses until such time, if ever,
as the Trust once again receives Royalty payments, the Trustee, in accordance
with the Trust Indenture, established an expense reserve of $2.4 million, of
which $1,471,687 remained as of September 30, 1998. Because no Royalty payments
were received during the first nine months of 1998 (Note 3), $233,895 was
withdrawn from the expense reserve to pay Trust administrative expenses during
the period. There will be income tax consequences to the Unit holders for such
reserve as described in Note 6 below.
 
     The funding for this reserve is deposited with Chase Bank of Texas and
invested in Chase Bank of Texas collateralized certificates of deposit. The
average interest rate earned on these funds for the third quarter of 1998 was
4.65 percent per annum.
 
6. FEDERAL INCOME TAX MATTERS
 
     Unit holders are required to report taxable income for the interest earned
on the expense reserve even if no distributions are received by the Unit
holders. The expense reserve established for Trust administrative expenses
described in Note 5 above will give rise to income tax deductions as
administrative expenses are incurred and paid with funds deposited in the
reserve.
 
7. WORKING INTEREST OWNER'S RESERVE FOR FUTURE ABANDONMENT COSTS
 
     Estimated future abandonment costs are accrued by the Working Interest
Owner over the life of the properties burdened by the Royalty based on current
laws and regulations. During the 1997 fourth quarter an updated assessment of
estimated future abandonment costs was undertaken by the Working Interest Owner,
taking into consideration current labor and equipment costs levels and permitted
abandonment practices. This assessment resulted in a revision of estimated
remaining future abandonment costs to an amount that is
                                      --6--
<PAGE>   7
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
approximately equal to amounts previously included as abandonment costs for
purposes of calculating the Royalty. Such costs are by their nature imprecise
and can be expected to be revised over time because of changes in general and
specific cost levels, government regulations, operation or technology. As of
December 31, 1997, the estimated remaining aggregate abandonment costs to be
incurred for all of the properties burdened by the Royalty totaled $9.5 million
net to the Trust, all of which has been included as abandonment costs for
purposes of calculating the Royalty. Any further adjustments to estimated
abandonment costs or variances to actual costs will reduce or increase amounts
deducted for the purpose of calculating the Royalty.
 
                             ---------------------
 
     THE INFORMATION FURNISHED HEREIN SHOULD BE READ IN CONJUNCTION WITH THE
FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST FINANCIAL STATEMENTS FOR THE YEAR
ENDED DECEMBER 31, 1997, WHICH ARE CONTAINED IN ITS ANNUAL REPORT ON FORM 10-K
FOR 1997.
 
                                      --7--
<PAGE>   8
 
                   FREEPORT-MCMORAN OIL AND GAS ROYALTY TRUST
 
                    REPORT OF INDEPENDENT PUBLIC ACCOUNTANTS
 
To Chase Bank of Texas National Association (Trustee)
and the Unit Holders of Freeport-McMoRan Oil and Gas Royalty Trust:
 
     We have reviewed the accompanying statement of assets, liabilities and
trust corpus of Freeport-McMoRan Oil and Gas Royalty Trust as of September 30,
1998, the related statements of royalty proceeds and distributable cash for the
three month and nine month periods ended September 30, 1998 and 1997 and the
statement of changes in trust corpus for the nine month periods ended September
30, 1998 and 1997. These financial statements are the responsibility of the
Working Interest Owner.
 
     We conducted our reviews in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical review
procedures to financial data and making inquiries of persons responsible for
financial and accounting matters. It is substantially less in scope than an
audit in accordance with generally accepted auditing standards, the objective of
which is the expression of an opinion regarding the financial statements taken
as a whole. Accordingly, we do not express such an opinion.
 
     These financial statements were prepared on the cash basis of accounting,
which is a comprehensive basis of accounting other than generally accepted
accounting principles.
 
     Based on our reviews, we are not aware of any material modifications that
should be made to the financial statements referred to above for them to be in
conformity with the cash basis of accounting.
 
     We have previously audited, in accordance with generally accepted auditing
standards, the statement of assets, liabilities and trust corpus of
Freeport-McMoRan Oil and Gas Royalty Trust as of December 31, 1997 and, in our
report dated March 30, 1998, we expressed an unqualified opinion on that
statement.
 
                                          ARTHUR ANDERSEN LLP
 
New Orleans, Louisiana
October 20, 1998
 
                                      --8--
<PAGE>   9
 
ITEM 2.MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
       OF OPERATIONS.
 
     The information contained herein regarding operations and exploration and
development activities on the properties burdened by the Royalty has been
furnished by the Working Interest Owner who obtained this information from the
relevant operators. For convenience, references are made to the Notes to
Financial Statements.
 
     The following discussion includes forward-looking statements within the
meaning of Section 27A of the Securities Act of 1933 and Section 21E of the
Securities Exchange Act of 1934. Although it is believed that these
forward-looking statements are based on reasonable assumptions, important
factors could cause actual results to differ materially from those in the
forward-looking statements herein, including the timing and extent of changes in
commodity prices for oil and gas, environmental risks, drilling and operating
risks, risks related to exploration and development, uncertainties about oil and
gas reserves in respect of properties burdened by the Royalty, government
regulations and other matters beyond the control of the Trustee and the Working
Interest Owner.
 
LIKELIHOOD OF TRUST TERMINATION
 
     As discussed in "Capital Resources and Liquidity" below and Notes 1, 3 and
10 to the financial statements included in the 1997 Annual Report on Form 10-K,
several factors occurring during 1997 increased the likelihood of the Trust
being terminated. The combination of a significant increase in the Class A cost
carryforward and negative reserve quantity revisions during 1997, combined with
declines in oil and gas prices received by the Working Interest Owner at
December 31, 1997 from those received at December 31, 1996, caused there to be
no proved oil and gas reserve quantities and related discounted future net cash
flows attributable to the Trust at December 31, 1997. Such proved reserve
estimates are based on various assumptions, many of which are subject to
uncertainties, as more fully discussed in the Trust's 1997 Annual Report on Form
10-K. These reserves estimates do not consider changes in prices and costs
subsequent to December 31, 1997, or the possibility of additional potentially
recoverable reserves not currently classified as proved, and therefore should
not be considered to be a prediction of actual amounts to be paid to the trustee
or an estimate of fair market value. Further, as discussed in Note 1, the Trust
must have $3 million or more in cash receipts during 1998 to avoid termination.
The Working Interest Owner has informed the Trustee that there will be no
Royalty payments in 1998, in which case the Trustee will be required to sell the
Trust's interest in the Partnership or cause the Partnership to sell the
Royalty, thereby terminating the Trust. The Working Interest Owner has advised
the Trustee that, based on an independent review of the oil and gas interests
burdened by the Royalty, the net present value of the reserves contained therein
is substantially less than the cumulative excess Class A cost carryforward. See
Note 1 to the Financial Statements. The information from the Working Interest
Owner indicates that the Royalties may have little or no value, based on the net
present value of reserves determined as a result of the independent review. In
connection with the termination of the Trust, the Trustee intends to sell the
Trust's interest in the Partnership, or to cause the Partnership to sell the
Royalty, for cash to the highest bidder. Although the Trustee will endeavor to
offer the Partnership interest, or to cause the Partnership to offer the
Royalty, pursuant to procedures intended to maximize the proceeds to the Trust,
the Trustee can give no assurance regarding the amounts, if any, to be realized
as a result of such offer.
 
                                      --9--
<PAGE>   10
 
     On June 11, 1998, a Trust unitholder announced his intention to seek
unitholder approval to convert the Trust's units into common stock of a
newly-formed corporation. The Trustee has not received any formal proposal from
the unitholder, nor is the Trustee aware of any likely method by which such a
conversion can be accomplished.
 
OPERATIONAL ACTIVITIES
 
     Exploratory drilling on West Cameron Block 498 began in June 1994 and
ultimately resulted in four successful wells, which were saved for future
production. A 12 slot four pile drilling platform was set in March 1997, from
which four additional wells were drilled during the remainder of 1997 and early
1998. An auxiliary platform was set in October 1997, with production facilities
capable of handling 55 million cubic feet (Mmcf) of natural gas and 15,000
barrels of oil per day. In February 1998, Coastal Oil & Gas Corporation
(Coastal), the operator, announced intended future development plans for
additional drilling and construction activity in this block during the remainder
of 1998, including drilling and completing four additional wells and setting a
six-well satellite platform during the third-quarter. At September 30, 1998,
West Cameron Block 498 had ten development wells that contributed to production
during the third quarter of 1998. In June 1998, one of these wells was
temporarily shut in, re-completed and placed back on production in early July
1998. The B-9 well commenced during April 1998, was completed and logged in late
June and placed on production in early July 1998. The B-10 development well
commenced drilling in early July 1998 and was completed in early August 1998.
The drilling rig has been moved off location. The #6 exploratory well commenced
drilling during April 1998, was drilled and temporarily abandoned. A new
platform has been fabricated for developing the #6 well. The platform was
scheduled to be set at a separate surface location from existing platforms in
the field during the third quarter, but unexpected delays, due mainly to
tropical storms and hurricanes in the Gulf of Mexico, have pushed the
installation of this platform into the fourth quarter. The average gross daily
production relating to revenue received by the Trust from this field during the
third quarter was approximately 8,500 barrels of oil and 26 Mmcf of gas. The
average gross daily production figures may vary throughout the life of the
field. These variations may be attributable to a number of factors, including
the number of wells on production at a given point in time, natural depletion of
wells, production techniques, and adjustments to flow rates in order to
optimally produce the related reserves. Total capital expenditures of the
Working Interest Owner during the nine months ended September 30, 1998 were
approximately $11.3 million for this block, in which the Working Interest Owner
owns a 23.1 percent working interest and a 19.2 net revenue interest prior to
taking into account the Trust's Royalty interest.
 
                                     --10--
<PAGE>   11
 
RESULTS OF OPERATIONS
 
     There were no cash distributions to the Unit holders during the first nine
months of 1998 or 1997, primarily because of significant capital expenditures
incurred by the Working Interest Owner. During the three months and nine months
ended September 30, 1998, Total Costs exceeded Gross Proceeds by approximately
$1.9 and $6.6 million, respectively, primarily because of the capital costs
incurred to explore and develop West Cameron Block 498. As a result, the Class A
cost carry-forward increased to $23.4 million (Note 3) as of September 30, 1998.
Because of the Class A cost carry-forward, there were no payments in respect of
the Royalty, and the Trust administrative expenses were paid from the expense
reserve during the 1998 and 1997 periods. The calculation of the Royalty and the
Trust's distributable cash for each period follows:
 
<TABLE>
<CAPTION>
                                          THREE MONTHS ENDED             NINE MONTHS ENDED
                                            SEPTEMBER 30,                  SEPTEMBER 30,
                                      --------------------------    ----------------------------
                                         1998           1997            1998            1997
                                      -----------    -----------    ------------    ------------
<S>                                   <C>            <C>            <C>             <C>
Gross Proceeds(1)...................  $ 3,830,172    $   611,008    $  9,138,615    $  2,225,635
Total Costs(2)......................   (5,749,455)    (4,936,236)    (15,732,625)    (11,904,354)
Excess Class A cost (recovery)
  carry-forward, net(3).............    1,919,283      4,325,228       6,594,010       9,678,719
                                      -----------    -----------    ------------    ------------
Net Proceeds........................           --             --              --              --
Percentage attributable to
  Royalty...........................         90.0%          90.0%           90.0%           90.0%
                                      -----------    -----------    ------------    ------------
Amounts payable attributable to
  Royalty...........................           --             --              --              --
Percentage attributable to the
  Trust.............................         99.9%          99.9%           99.9%           99.9%
                                      -----------    -----------    ------------    ------------
Royalty Proceeds....................           --             --              --              --
Trust administrative expenses.......     (126,010)      (135,042)       (289,994)       (307,378)
                                      -----------    -----------    ------------    ------------
                                         (126,010)      (135,042)       (289,994)       (307,378)
Interest income.....................       17,870         20,597          56,099          58,824
Reserve for future Trust
  expenses(4).......................      108,140        114,445         233,895         248,554
                                      -----------    -----------    ------------    ------------
Distributable cash..................  $        --    $        --    $         --    $         --
                                      ===========    ===========    ============    ============
</TABLE>
 
---------------
 
(1) Represents amounts received by the Working Interest Owner during the three
    and nine month periods ended in August of such year.
(2) Represents amounts accrued by the Working Interest Owner during the three
    and nine month periods ended in August of such year. Includes accrued
    interest of $478,630 and $1,291,319 for the three and nine months during
    1998 as well as $202,345 and $371,692 for the three and nine months during
    1997.
(3) Represents Class A costs incurred in the applicable period that remained
    outstanding as of the end of such period.
(4) Represents withdrawals from the Trust administrative expense reserve during
    the respective periods.
 
                                     --11--
<PAGE>   12
 
     Gross Proceeds, which includes gas and oil revenues, are calculated based
on amounts received by the Working Interest Owner. Operating information
follows:
 
<TABLE>
<CAPTION>
                                                      THIRD QUARTER            NINE MONTHS
                                                   -------------------     -------------------
                                                     1998       1997         1998       1997
                                                   --------   --------     --------   --------
<S>                                                <C>        <C>          <C>        <C>
Natural Gas
  Revenues (in millions).........................   $  1.4     $  0.3       $  4.1     $  1.2
  Sales volumes (in million cubic feet)..........      639        146        1,779        444
  Average realization (per thousand cubic
     feet).......................................   $ 2.26     $ 2.23       $ 2.30     $ 2.63
Oil
  Revenues (in millions).........................   $  2.4     $  0.3       $  5.0     $  1.1
  Sales volumes (in thousands of barrels)........    178.5       15.4        351.5       50.0
  Average realization (per barrel)...............   $13.39     $18.47       $14.34     $21.20
</TABLE>
 
     Revenues and volumes for oil and gas during the nine months and three
months ended September 30, 1998 increased substantially over the comparable
periods during 1997 primarily reflecting the increased development and
subsequent production at West Cameron Block 498. Production at West Cameron
Block 498 commenced during the fourth quarter of 1997 from six wells and the
number of producing wells has increased to ten as of September 30, 1998. The
increased revenues from West Cameron Block 498 were offset in part by normal
production declines at the other properties burdened by the Royalty and by lower
oil and natural gas prices, which fell significantly during the second quarter
of 1998.
 
     Costs consist of the following (in millions):
 
<TABLE>
<CAPTION>
                                                          THIRD QUARTER             NINE MONTHS
                                                       --------------------     --------------------
                                                         1998        1997         1998        1997
                                                       --------    --------     --------    --------
<S>                                                    <C>         <C>          <C>         <C>
Lease operating expenses.............................    $1.4        $0.4        $ 2.7       $ 0.6
Exploration and development costs....................     3.7         4.4         11.3        10.8
Interest, abandonment costs withheld and other.......     0.6         0.1          1.7         0.5
                                                         ----        ----        -----       -----
                                                         $5.7        $4.9        $15.7       $11.9
                                                         ====        ====        =====       =====
</TABLE>
 
     Lease operating expenses for the nine months and third quarter ended
September 30, 1998 increased from the comparable periods during 1997 primarily
because of the increasing production costs associated with West Cameron Block
498 as well as, $0.2 million being recorded during the third quarter to settle a
disputed liability at Vermilion Block 310. In addition, the nine months ended
September 30, 1997 contains a first quarter adjustment, affecting insurance,
which resulted in an approximate $0.4 million credit to lease operating expense
during that period. Exploration and development costs for the nine months and
third quarter of both 1998 and 1997 primarily reflects the drilling activity at
West Cameron Block 498. The increase in interest is the result of the Class A
carry-forward escalating throughout 1997 and the first nine months of 1998.
Abandonment costs, which have been accrued each period on the estimate of costs
required to abandon the properties burdened by the Royalty, are now fully
accrued based on current estimates. See further discussion under "Capital
Resources and Liquidity" and Note 7 to the Financial Statements.
 
                                     --12--
<PAGE>   13
 
CAPITAL RESOURCES AND LIQUIDITY
 
     The Trustee may sell or dispose of the Trust's interest in the Partnership,
or permit the Partnership to sell or dispose of all or any part of the Royalty
only as authorized by a vote of the Unit holders in accordance with the Trust
Indenture, upon termination of the Trust and in certain other limited
circumstances. However, the Trust is directed to effect such a sale (without
such vote) if the Trust's cash receipts for each of three successive years are
less than $3 million. The Trustee must distribute the net proceeds of such sale
(after satisfaction of any outstanding liabilities) to the Unit holders.
 
     The Trust's cash receipts last reached $3 million during 1995 and there
were no cash receipts in 1996 or 1997. Significant development costs, primarily
at West Cameron Block 498, resulted in no cash receipts during the first nine
months of 1998. Additionally, the Class A cost carry-forward has increased to
$23.4 million at September 30, 1998 (Note 3). This cost carry-forward must be
recouped by the Working Interest Owner before any distribution may be made to
the Trust. The Working Interest Owner has informed the Trustee that there will
be no Royalty payments during 1998. Thus, it is anticipated that the Trust will
be terminated by one of the means described above.
 
     A trust unitholder has advised the Trustee that he intends to seek
unitholder approval to convert the Trust into a corporation. The Trustee has not
received any formal proposal from the unitholder, nor is the Trustee aware of
any likely method by which such a conversion can be accomplished.
 
     Total committed exploration and development costs for the remainder of 1998
are presently estimated by the Working Interest Owner to be approximately $2.2
million net to the Trust, primarily for the development of West Cameron Block
498. This estimate is derived from cost estimates provided by the operators of
the Royalty Properties and may vary from actual costs depending on the success
of drilling, particular circumstances encountered during drilling and many other
factors outside the control of the operators. These expenditures can be expected
to delay resumption of Royalty payments. For the reasons stated above and in
Note 1 to the Financial Statements, it is unlikely that any additional Royalty
payments will be received by the Trust prior to its termination and liquidation.
 
     Estimated future abandonment costs, based on current laws and regulations,
are accrued over the life of the properties burdened by the Royalty (Note 7). As
of September 30, 1998, the estimated remaining aggregate abandonment costs to be
incurred by the Working Interest Owner for all of the properties burdened by the
Royalty totaled $10.6 million ($9.5 million net to the Trust), of which all has
been included as a cost for the purpose of calculating the Royalty. Any
adjustments to the estimated abandonment costs or variances will reduce or
increase costs included for the purpose of calculating the Royalty.
 
     At certain times since late 1993, the Trust has been unable to pay its
ongoing administrative expenses. To permit the Trust to pay its administrative
expenses during the time the Trust is not receiving Royalty payments, the
Trustee, in accordance with the Trust Indenture, established a $2.4 million
Trust administrative expense reserve to pay such expenses (Note 5), of which
$1.5 million remained at September 30, 1998.
 
                                     --13--
<PAGE>   14
 
IMPACT OF YEAR 2000 COMPLIANCE
 
     Chase Bank of Texas, National Association (Chase) 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 connection
therewith, Chase 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 material
adverse effect upon its performance of services as Trustee.
 
                          PART II.  OTHER INFORMATION
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.
 
  (a) Not applicable
 
  (b) Reports on Form 8-K:
 
      No reports on Form 8-K were filed by the registrant during the quarter for
      which this report is filed.
 
                                     --14--
<PAGE>   15
 
                                   SIGNATURE
 
     PURSUANT TO THE REQUIREMENTS 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.
 
                                           FREEPORT-McMoRan OIL AND GAS
                                           ROYALTY TRUST
 
                                           By: Chase Bank of Texas, National
                                               Association, Trustee
 
                                           By:       /s/ PETE FOSTER
                                             -----------------------------------
                                                         PETE FOSTER
                                               SENIOR VICE PRESIDENT AND TRUST
                                                            OFFICER
 
Date: November 13, 1998
<PAGE>   16
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                       DESCRIPTION
         ------                                       -----------
<C>                           <S>
           27                 Financial Data Schedule
</TABLE>