<PAGE>   1
 
================================================================================
                                   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 March 31, 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  ______
================================================================================
<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.................    12
 
Signature...................................................    13
</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
                                                                      MARCH 31,
                                                              --------------------------
                                                                 1998           1997
                                                              -----------    -----------
<S>                                                           <C>            <C>
Royalty proceeds............................................  $        --    $        --
Trust administrative expenses...............................      (36,116)       (87,615)
Interest income.............................................       19,364         18,811
Reserve for future Trust expenses...........................       16,752         68,804
                                                              -----------    -----------
Distributable cash..........................................  $        --    $        --
                                                              ===========    ===========
Distributable cash per Unit.................................  $        --    $        --
                                                              ===========    ===========
Units outstanding...........................................   14,975,390     14,975,390
                                                              ===========    ===========
</TABLE>
 
               STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
 
<TABLE>
<CAPTION>
                                                                MARCH 31,      DECEMBER 31,
                                                                  1998             1997
                           ASSETS                             -------------    -------------
<S>                                                           <C>              <C>
Cash and short-term investments.............................  $   1,688,830    $   1,705,582
Net overriding royalty interest in oil and gas properties...    189,875,741      189,875,741
Less, adjustment 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......................................  $   1,688,830    $   1,705,582
                                                              =============    =============
                LIABILITIES AND TRUST CORPUS
Reserve for future Trust expenses...........................  $   1,688,830    $   1,705,582
Trust corpus (14,975,390 Units of Beneficial Interest
  authorized,
  issued and outstanding)...................................             --               --
                                                              -------------    -------------
          Total liabilities and trust corpus................  $   1,688,830    $   1,705,582
                                                              =============    =============
</TABLE>
 
                     STATEMENTS OF CHANGES IN TRUST CORPUS
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                     MARCH 31,
                                                              -----------------------
                                                                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. Significant development costs, primarily at West
Cameron Blocks 498 and 215, resulted in no cash receipts during 1997 or the
first three months of 1998. Additionally, the Class A cost carry-forward has
increased to $20.5 million at March 31, 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 actual level of cash receipts, if any, during the remainder of 1998 will
depend primarily on the timing and the rate of production from West Cameron
Block 498, the costs and results of future exploration and development costs on
West Cameron Block 498, oil and gas prices and other factors. Based on current
circumstances, it is unlikely that cash receipts to the Trust will total $3
million or more in 1998, in which case the Trustee would be required to sell the
Trust's interest in the Partnership or cause the Partnership to sell the
Royalty.
 
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
 
                                      --4--
<PAGE>   5
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
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).
 
3. DISTRIBUTIONS TO UNIT HOLDERS
 
     As a result of the capital cost incurred in recent years, a cumulative
excess Class A cost carry-forward of $20,458,295 existed as of March 31, 1998.
This carry-forward is subject to and includes interest due the Working Interest
Owner at the prime rate, which totaled $366,303, net to the Trust during the
three month period of 1998. This excess Class A cost carry-forward must be
recouped out of future Net Proceeds before distributions to the Unitholders can
be resumed.
 
4. GAS BALANCING ARRANGEMENTS
 
     As a result of past curtailments in gas takes by the 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
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 March 31, 1998, the unrecovered quantity of
gas sold by third parties pursuant to such gas balancing arrangements since
inception of the Trust was approximately 1.4 billion cubic feet (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 is uncertain.
 
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 during the time the Trust
incurs a Class A cost deficit, the Trustee, in accordance with the Trust
Indenture, established an expense reserve of $2.4 million, of which $1,688,830
remained as of March 31, 1998. Because of the cumulative excess Class A cost
carry-forward (Note 3), $16,752 was withdrawn from the expense reserve to pay
Trust administrative expenses during the first three months of 1998. 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 first quarter of 1998 was
4.6 percent.
 
                                      --5--
<PAGE>   6
                  NOTES TO FINANCIAL STATEMENTS -- (CONTINUED)
 
6. FEDERAL INCOME TAX MATTERS
 
     Unit holders are required to report taxable income for the Royalty income
received by the Trust and deposited to the expense reserve even if no
distributions were received by the Unit holders. The expense reserve established
for Trust administrative expenses described in Note 5 above will give rise to
future income tax deductions as additional administrative expenses are incurred
and paid with funds deposited in the reserve.
 
7. RESERVE FOR FUTURE ABANDONMENT COSTS
 
     Estimated future abandonment costs are accrued over the life of the Trust's
properties based on current laws and regulations. During the 1997 fourth quarter
an updated assessment of estimated future abandonment costs was undertaken,
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 approximately equal to
amounts previously withheld from distributions to Unitholders. 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 Trust's properties totaled $9.5
million net to the Trust, all of which has been withheld from distributions to
Unit holders. Any further adjustments to estimated abandonment costs or
variances to actual costs will reduce or increase future distributable cash
accordingly.
 
                             ---------------------
 
     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.
 
                                      --6--
<PAGE>   7
 
                   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 March 31, 1998,
the related statements of royalty proceeds and distributable cash and changes in
trust corpus for the three month periods ended March 31, 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
April 21, 1998
 
                                      --7--
<PAGE>   8
 
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 Trust's
reserves, 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 future changes in prices and
costs, the use of discount rates other than 10 percent 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. Based on current circumstances, it is unlikely
that cash receipts to the Trust will total $3 million or more in 1998, in which
case the Trustee would be required to sell the Trust's interest in the
Partnership or cause the Partnership to sell the Royalty.
 
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 of natural gas and 15,000 barrels of
oil per day. In February 1998, Coastal Oil & Gas Corporation ("Coastal"), the
operator, announced average gross daily production from the initial six wells
drilled of 52 million cubic feet of gas and 7,800 barrels of oil. Coastal also
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 in the third quarter. One well commenced
                                      --8--
<PAGE>   9
 
production in early April 1998, and another well is scheduled to be placed on
production during the remainder of the second quarter of 1998. The operator
commenced drilling the B-9 development well on April 18, 1998 and the #6
exploratory well on April 27, 1998. The average gross daily production for the
week ending May 11, 1998 was approximately 33 million cubic feet of gas and
11,000 barrels of oil. Total capital expenditures net to the Trust during the
first quarter of 1998 were $2.3 million for this block, in which the Working
Interest Owner owns a 23.1 percent working interest and a 19.2 net revenue
interest.
 
RESULTS OF OPERATIONS
 
     There were no cash distributions to the Unit holders during the first three
months of 1998 or 1997, primarily because of significant capital expenditures.
During the first quarter of 1998, Total Costs exceeded Gross Proceeds by
approximately $3.3 million, primarily because of the capital costs incurred to
develop West Cameron Block 498. As a result, the Class A cost carry-forward
increased to $20.5 million (Note 3) net to the Trust as of March 31, 1998.
Because of the Class A cost carry-forward, the Trust administrative expenses
were paid from the expense reserve during the 1998 and 1997 periods. The
calculation of distributable cash for each period follows:
 
<TABLE>
<CAPTION>
                                                                  THREE MONTHS ENDED
                                                                      MARCH 31,
                                                              --------------------------
                                                                 1998           1997
                                                              -----------    -----------
<S>                                                           <C>            <C>
Gross Proceeds(1)...........................................  $   764,281    $   815,212
Total Costs(2)..............................................   (4,111,067)    (2,221,790)
Excess Class A cost carry-forward, net(3)...................    3,346,786      1,406,578
                                                              -----------    -----------
Net Proceeds................................................           --             --
Percentage attributable to Royalty..........................         90.0%          90.0%
                                                              -----------    -----------
Amounts payable attributable to Royalty.....................           --             --
Percentage attributable to the Trust........................         99.9%          99.9%
                                                              -----------    -----------
Royalty Proceeds............................................           --             --
Trust administrative expenses...............................      (36,116)       (87,615)
                                                              -----------    -----------
                                                                  (36,116)       (87,615)
Interest income.............................................       19,364         18,811
Reserve for future Trust expenses(4)........................       16,752         68,804
                                                              -----------    -----------
Distributable cash..........................................  $        --    $        --
                                                              ===========    ===========
</TABLE>
 
---------------
 
(1) Represents amounts received by the Working Interest Owner during the three
     month period ended in February of such year.
 
(2) Represents amounts accrued by the Working Interest Owner during the three
     month period ended in February of such year. Includes accrued interest of
     $366,303 in 1998 and $58,473 in 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.
 
                                      --9--
<PAGE>   10
 
     Gross Proceeds, which includes gas and oil revenues, are calculated based
on amounts received by the Working Interest Owner. Operating information
follows:
 
<TABLE>
<CAPTION>
                                                                  FIRST QUARTER
                                                              ---------------------
                                                                1998         1997
                                                              --------     --------
<S>                                                           <C>          <C>
Natural Gas
  Revenues (in millions)....................................   $  0.7       $  0.4
  Sales volumes (in million cubic feet).....................      249          137
  Average realization (per thousand cubic feet).............   $ 2.74       $ 2.82
Oil
  Revenues (in millions)....................................   $  0.1       $  0.4
  Sales volumes (in thousands of barrels)...................      4.3         18.2
  Average realization (per barrel)..........................   $19.38       $23.50
</TABLE>
 
     Gas volumes for the 1998 period increased over the 1997 period because of
the commencement of production at West Cameron Block 498 from six development
wells during the fourth quarter of 1997 and another development well in March
1998. The new production at West Cameron Block 498 was offset in part by normal
production declines on the remaining properties. Oil volumes for the 1998 period
decreased from 1997 levels because of normal production declines. Receipt of
initial oil revenue from West Cameron Block 498 did not commence until April
1998. Revenues for the 1998 period were adversely affected by declining natural
gas and oil prices.
 
     Costs consist of the following (in millions):
 
<TABLE>
<CAPTION>
                                                                  FIRST QUARTER
                                                              ---------------------
                                                                1998         1997
                                                              --------     --------
<S>                                                           <C>          <C>
Lease operating expenses....................................    $0.4        $(0.1)
Exploration and development costs...........................     3.2          2.2
Interest, abandonment costs withheld and other..............     0.5          0.1
                                                                ----        -----
                                                                $4.1        $ 2.2
                                                                ====        =====
</TABLE>
 
     Lease operating expenses for the 1998 period increased over the 1997 period
because an insurance accrual adjustment resulted in an approximate $0.4 million
credit in the first quarter of 1997, and increased lease operating expense for
West Cameron Block 498 during 1998. Exploration and development costs for the
first quarter 1998 relate primarily to development and exploration at West
Cameron Block 498. First quarter 1997 costs related to the development of West
Cameron Block 498 and Breton Sound Block 55. Abandonment costs, which have been
accrued each period based on the estimate of costs required to abandon the
Trust's properties, are now fully accrued. See further discussion under "Capital
Resources and Liquidity" and Note 7 to the Financial Statements.
 
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, upon termination of the Trust
and in certain other limited circumstances. However, the Trust is directed to
effect such a sale
 
                                     --10--
<PAGE>   11
 
(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. Significant development costs, primarily at West
Cameron Blocks 498 and 215, resulted in no cash receipts during 1997, or the
first three months of 1998. Additionally, the Class A cost carry-forward has
increased to $20.5 million at March 31, 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 actual level of cash receipts, if any, during the remainder of 1998 will
depend primarily on the timing and the rate of production from West Cameron
Block 498, the costs and results of future exploration and development costs on
West Cameron Blocks 498, oil and gas prices and other factors. Based on current
circumstances, it is unlikely that cash receipts to the Trust will total $3
million or more in 1998, in which case the Trustee would be required to sell the
Trust's interest in the Partnership or cause the Partnership to sell the
Royalty.
 
     Additional exploration may be proposed by the operators of certain other
Royalty Properties. After analyzing each proposal, the Working Interest Owner
will determine whether or not to participate in additional exploratory
operations.
 
     Total committed exploration and development costs for the remainder of 1998
are presently estimated by the Working Interest Owner to be approximately $3.5
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 operator. These expenditures can be expected
to reduce and could further delay resumption of distributions to Unit holders.
 
     Estimated future abandonment costs, based on current laws and regulations,
are accrued over the life of the Trust's properties (Note 7). As of March 31,
1998, the estimated remaining aggregate abandonment costs to be incurred for all
of the Trust's properties totaled $9.5 million net to the Trust, of which all
has been withheld from distributions to Unit holders. Any adjustments to the
estimated abandonment costs or variances will reduce or increase future
distributable cash accordingly.
 
     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 incurs a Class A cost deficit, 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 $1.7
million remained at March 31, 1998.
 
                                     --11--
<PAGE>   12
 
                          PART II.  OTHER INFORMATION
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.
 
  (a) Not applicable
 
  (b) Reports on Form 8-K:
 
      One report on Form 8-K and one report on Form 8-K/A, both reporting events
      under Item 5, were filed by the registrant on February 3, 1998.
 
                                     --12--
<PAGE>   13
                                   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.
 
<TABLE>
<S>                                                      <C>
                                                         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
</TABLE>
 
Date: May 15, 1998
 
                                     --13--
<PAGE>   14
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
NO.                          DESCRIPTION
---  ------------------------------------------------------------
<C>  <S>
27   Financial Date Schedule
</TABLE>