<PAGE>   1
 
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                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
                             ---------------------
                                   FORM 10-K
(Mark One)
[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
 
                                       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 1-8033
                          PERMIAN BASIN ROYALTY TRUST
 
   (Exact Name of Registrant as Specified in the Permian Basin Royalty Trust
                                   Indenture)
 
<TABLE>
<S>                                            <C>
                    TEXAS                                        75-6280532
       (State or Other Jurisdiction of                        (I.R.S. Employer
        Incorporation or Organization)                      Identification No.)
 
              NATIONSBANK, N.A.
               TRUST DEPARTMENT
                P.O. BOX 1317
              FORT WORTH, TEXAS                                    76101
   (Address of Principal Executive Offices)                      (Zip Code)
</TABLE>
 
                                 (817) 390-6905
              (Registrant's Telephone Number, Including Area Code)
 
          Securities registered pursuant to Section 12(b) of the Act:
 
<TABLE>
<CAPTION>
             TITLE OF EACH CLASS                 NAME OF EACH EXCHANGE ON WHICH REGISTERED
             -------------------                 -----------------------------------------
<S>                                            <C>
         UNITS OF BENEFICIAL INTEREST                     NEW YORK STOCK EXCHANGE
</TABLE>
 
          Securities registered pursuant to Section 12(g) of the Act:
                                      NONE
                                (Title of Class)
 
     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]
 
     At March 5, 1999, there were 46,608,796 Units of Beneficial Interest of the
Trust outstanding with an aggregate market value on that date of $186,435,184.
 
                      DOCUMENTS INCORPORATED BY REFERENCE
 
     "Units of Beneficial Interest" at page 1; "Trustee's Discussion and
Analysis for the Three-Year Period Ended December 31, 1998" at pages 5 through
6; "Results of the 4th Quarters of 1998 and 1997" at page 7; and "Statements of
Assets, Liabilities and Trust Corpus," "Statements of Distributable Income,"
"Statements of Changes in Trust Corpus," "Notes to Financial Statements" and
"Independent Auditors' Report" at page 8 et seq., in registrant's Annual Report
to security holders for fiscal year ended December 31, 1998 are incorporated
herein by reference for Item 5 (Market for Units of the Trust and Related
Security Holder Matters), Item 7 (Management's Discussion and Analysis of
Financial Condition and Results of Operation) and Item 8 (Financial Statements
and Supplementary Data) of Part II of this Report.
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<PAGE>   2
 
FORWARD LOOKING INFORMATION
 
     Certain information included in this report contains, and other materials
filed or to be filed by the Trust with the Securities and Exchange Commission
(as well as information included in oral statements or other written statements
made or to be made by the Trust) may contain or include, forward looking
statements within the meaning of Section 21E of the Securities Exchange Act of
1934, as amended, and Section 27A of the Securities Act of 1933, as amended.
Such forward looking statements may be or may concern, among other things,
capital expenditures, drilling activity, development activities, production
efforts and volumes, hydrocarbon prices and the results thereof, and regulatory
matters. Although the Trustee believes that the expectations reflected in such
forward-looking statements are reasonable, such expectations are subject to
numerous risks and uncertainties and the Trustee can give no assurance that they
will prove correct. There are many factors, none of which is within the
Trustee's control, that may cause such expectations not to be realized,
including, among other things, factors such as actual oil and gas prices and the
recoverability of reserves, capital expenditures, general economic conditions,
actions and policies of petroleum-producing nations and other changes in the
domestic and international energy markets. Such forward looking statements
generally are accompanied by words such as "estimate," "expect," "anticipate,"
"goal," "should," "assume," "believe," or other words that convey the
uncertainty of future events or outcomes.
 
                                     PART I
 
ITEM 1. BUSINESS
 
     The Permian Basin Royalty Trust (the "Trust") is an express trust created
under the laws of the state of Texas by the "Permian Basin Royalty Trust
Indenture" (the "Trust Indenture") entered into on November 3, 1980, between
Southland Royalty Company ("Southland Royalty") and The First National Bank of
Fort Worth, as Trustee. NationsBank, N.A. (formerly known as NationsBank of
Texas, N.A. and NCNB Texas National Bank), a banking association organized under
the laws of the United States, as the successor of The First National Bank of
Fort Worth, is now the Trustee of the Trust. The principal office of the Trust
(sometimes referred to herein as the "Registrant") is located at 500 West
Seventh Street, Fort Worth, Texas (telephone number 817/390-6905).
 
     On October 23, 1980, the stockholders of Southland Royalty approved and
authorized that company's conveyance of net overriding royalty interests
(equivalent to net profits interests) to the Trust for the benefit of the
stockholders of Southland Royalty of record at the close of business on the date
of the conveyance consisting of a 75% net overriding royalty interest carved out
of that company's fee mineral interests in the Waddell Ranch properties in Crane
County, Texas and a 95% net overriding royalty interest carved out of that
company's major producing royalty properties in Texas. The conveyance of these
interests (the "Royalties") was made on November 3, 1980, effective as to
production from and after November 1, 1980 at 7:00 a.m.
 
     The function of the Trustee is to collect the income attributable to the
Royalties, to pay all expenses and charges of the Trust, and then distribute the
remaining available income to the Unit holders. The Trust is not empowered to
carry on any business activity and has no employees, all administrative
functions being performed by the Trustee.
 
     The Royalties were carved out of and now burden those properties and
interests as are more particularly described under "Item 2. PROPERTIES" herein.
 
     The Royalties constitute the principal asset of the Trust and the
beneficial interests in the Royalties are divided into that number of Units of
Beneficial Interest (the "Units") of the Trust equal to the number of shares of
the common stock of Southland Royalty outstanding as of the close of business on
November 3, 1980. Each stockholder of Southland Royalty of record at the close
of business on November 3, 1980, received one Unit for each share of the common
stock of Southland Royalty then held.
 
     In 1985, Southland Royalty became a wholly-owned subsidiary of Burlington
Northern Inc. ("BNI"). In 1988, BNI transferred its natural resource operations
to Burlington Resources Inc. ("BRI") as a result of which Southland Royalty
became a wholly-owned indirect subsidiary of BRI. As a result of these
transactions,
 
                                        1
<PAGE>   3
 
El Paso Natural Gas Company ("El Paso") also became an indirect subsidiary of
BRI. In March 1992, El Paso completed an initial public offering of 5,750,000
newly issued shares of El Paso common stock, thereby decreasing BRI's ownership
of El Paso to approximately eighty-five percent (85%). On June 30, 1992, BRI
distributed all of the shares of El Paso common stock owned by BRI to BRI's
stockholders of record as of June 15, 1992. See "Pricing Information" under
"Item 2. PROPERTIES" herein.
 
     Effective January 1, 1996, Southland Royalty, a wholly-owned subsidiary of
Meridian Oil Inc. ("MOI") was merged with and into MOI, by which action the
separate corporate existence of Southland Royalty ceased and MOI survived and
succeeded to the ownership of all of the assets, has the rights, powers and
privileges and assumed all of the liabilities and obligations of Southland
Royalty. In 1996, MOI changed its name to Burlington Resources Oil & Gas Company
("BROG").
 
     The term "net proceeds" as used in the above conveyance means the excess of
"gross proceeds" received by BROG during a particular period over "production
costs" for such period. "Gross proceeds" means the amount received by BROG (or
any subsequent owner of the interests from which the Royalties were carved) from
the sale of the production attributable to the properties and interests from
which the Royalties were carved, subject to certain adjustments. "Production
costs" means, generally, costs incurred on an accrual basis in operating the
properties and interests out of which the Royalties were carved, including both
capital and non-capital costs; for example, development drilling, production and
processing costs, applicable taxes, and operating charges. If production costs
exceed gross proceeds in any month, the excess is recovered out of future gross
proceeds prior to the making of further payment to the Trust, but the Trust is
not liable for any production costs or liabilities attributable to these
properties and interests or the minerals produced therefrom. If at any time the
Trust receives more than the amount due from the Royalties, it shall not be
obligated to return such overpayment, but the amounts payable to it for any
subsequent period shall be reduced by such amount, plus interest, at a rate
specified in the conveyance.
 
     To the extent it has the legal right to do so, BROG is responsible for
marketing the production from such properties and interests, either under
existing sales contracts or under future arrangements at the best prices and on
the best terms it shall deem reasonably obtainable in the circumstances. BROG
also has the obligation to maintain books and records sufficient to determine
the amounts payable to the Trustee. BROG, however, can sell its interests in the
properties from which the Royalties were carved.
 
     Proceeds from production in the first month are generally received by BROG
in the second month, the net proceeds attributable to the Royalties are paid by
BROG to the Trustee in the third month and distribution by the Trustee to the
Unit holders is made in the fourth month. The identity of Unit holders entitled
to a distribution will generally be determined as of the last business day of
each calendar month (the "monthly record date"). The amount of each monthly
distribution will generally be determined and announced ten days before the
monthly record date. Unit holders of record as of the monthly record date will
be entitled to receive the calculated monthly distribution amount for each month
on or before ten business days after the monthly record date. The aggregate
monthly distribution amount is the excess of (i) net revenues from the Trust
properties, plus any decrease in cash reserves previously established for
contingent liabilities and any other cash receipts of the Trust over (ii) the
expenses and payments of liabilities of the Trust plus any net increase in cash
reserves for contingent liabilities.
 
     Cash held by the Trustee as a reserve for liabilities or contingencies
(which reserves may be established by the Trustee in its discretion) or pending
distribution is placed, at the Trustee's discretion, in obligations issued by
(or unconditionally guaranteed by) the United States or any agency thereof,
repurchase agreements secured by obligations issued by the United States or any
agency thereof, or certificates of deposit of banks having a capital surplus and
undivided profits in excess of $50,000,000, subject, in each case, to certain
other qualifying conditions.
 
     The income to the Trust attributable to the Royalties is not subject in
material respects to seasonal factors nor in any manner related to or dependent
upon patents, licenses, franchises or concessions. The Trust conducts no
research activities. The Trust has no employees since all administrative
functions are performed by the Trustee.
 
                                        2
<PAGE>   4
 
     BROG has advised the Trustee that it believes that comparable revenues
could be obtained in the event of a change in purchasers of production.
 
ITEM 2. PROPERTIES
 
     The net overriding royalties conveyed to the Trust include: (1) a 75% net
overriding royalty carved out of Southland Royalty's fee mineral interests in
the Waddell Ranch in Crane County, Texas (the "Waddell Ranch properties"); and
(2) a 95% net overriding royalty carved out of Southland Royalty's major
producing royalty interests in Texas (the "Texas Royalty properties"). The net
overriding royalty for the Texas Royalty properties is subject to the provisions
of the lease agreements under which such royalties were created. References
below to "net" wells and acres are to the interests of Southland Royalty (from
which the Royalties were carved) in the "gross" wells and acres.
 
     The following information in Item 2 is based upon data and information
furnished to the Trustee by Southland Royalty or BROG.
 
PRODUCING ACREAGE, WELLS AND DRILLING
 
     Waddell Ranch Properties. The Waddell Ranch properties consist of 78,175
gross (34,205 net) producing acres. A majority of the proved reserves are
attributable to six fields: Dune, Sand Hills (Judkins), Sand Hills (McKnight),
Sand Hills (Tubb), University-Waddell (Devonian) and Waddell. At December 31,
1998, the Waddell Ranch properties contained 853 gross (354 net) productive oil
wells, 166 gross (70 net) productive gas wells and 368 gross (146 net) injection
wells.
 
     BROG is operator of record of the Waddell Ranch properties. All field,
technical and accounting operations have been contracted by an agreement between
the working interest owners and Coastal Management Corporation ("CMC") but
remain under the direction of BROG.
 
     The Waddell Ranch properties are mature producing properties, and all of
the major oil fields are currently being waterflooded. Proved reserves and
estimated future net revenues attributable to the properties are included in the
reserve reports summarized below. BROG does not own the full working interest in
any of the tracts constituting the Waddell Ranch properties and, therefore,
implementation of any development programs will require approvals of other
working interest holders as well as BROG. In addition, implementation of any
development programs will be dependent upon oil and gas prices currently being
received and anticipated to be received in the future. During 1998 there were 52
gross (22.75 net) wells drilled on the Waddell Ranch properties. At December 31,
1998 there were 3 gross (1.375 net) wells in progress on the Waddell Ranch
properties. During 1997 there were 23 gross (9.25 net) wells drilled on the
Waddell Ranch properties. At December 31, 1997 there were 19 gross (7.875 net)
wells in progress on the Waddell Ranch properties. During 1996 there were 22
gross (8.375 net) oil wells drilled on the Waddell Ranch properties. At December
31, 1996 there were no wells in progress on the Waddell Ranch properties.
 
     BROG has advised the Trustee that the total amount of capital expenditures
for 1998 with regard to the Waddell Ranch properties totalled $15,874,193.
Capital expenditures include the cost of the 1998 drilling program and remedial
and maintenance activities. This amount spent is approximately $1,764,808 less
than the budgeted amount projected by BROG for 1998. BROG has advised the
Trustee that the capital expenditures budget for 1999 totals approximately
$6,066,000, of which approximately $1,352,000 is attributable to the 1999
drilling program, $4,056,000 to workovers and recompletions and $658,000 to
facility upgrades and replacements. Accordingly, there is an estimated 62%
decrease in capital expenditures for 1999 as compared with the 1998 capital
expenditures.
 
     Texas Royalty Properties. The Texas Royalty properties consist of royalty
interests in mature producing oil fields, such as Yates, Wasson, Sand Hills,
East Texas, Kelly-Snyder, Panhandle Regular, N. Cowden, Todd, Keystone, Kermit,
McElroy, Howard-Glasscock, Seminole and others. The Texas Royalty properties
contain approximately 303,000 gross (approximately 51,000 net) producing acres.
Detailed information concerning the number of wells on royalty properties is not
generally available to the owners of royalty
 
                                        3
<PAGE>   5
 
interests. Consequently, an accurate count of the number of wells located on the
Texas Royalty properties cannot readily be obtained.
 
     Approximately $1.3 million in ad valorem taxes related to 1991 through 1994
for the Texas Royalty properties that Southland Royalty did not previously
charge to gross proceeds attributable to the Trust was charged to the Trust over
12 months beginning March 1995. Such amount was charged by deducting $87,000 per
month from gross proceeds attributable to the Texas Royalty properties in
calculating royalty income from such properties. To the extent charges were made
to gross proceeds, the amount of funds available for distribution to Unit
holders was reduced. As of November 1996, the Trustee was advised that this
original charge of $1.3 million and all subsequent adjustments to that charge
had been paid.
 
     In February 1997, BROG sold its interests in the Texas Royalty properties
that are subject to the Net Overriding Royalty Conveyance to the Trust dated
effective November 1, 1980 ("Texas Royalty Conveyance") to Riverhill Energy
Corporation ("Riverhill Energy"), which was then a wholly-owned subsidiary of
Riverhill Capital Corporation ("Riverhill Capital") and an affiliate of CMC. At
the time of such sale, Riverhill Capital was a privately owned Texas corporation
with offices in Bryan and Midland, Texas. The Trustee was informed by BROG that,
as required by the Texas Royalty Conveyance, Riverhill Energy succeeded to all
of the requirements upon and the responsibilities of BROG under the Texas
Royalty Conveyance with regard to the Texas Royalty properties. BROG and
Riverhill Energy further advised the Trustee that all accounting operations
pertaining to the Texas Royalty properties were being performed by CMC under the
direction of Riverhill Energy. BROG indicated to the Trustee that BROG will work
together with CMC and Riverhill Energy in an effort to assure that various
administrative functions and reporting requirements assumed by Riverhill Energy
are met. The Trustee has been advised that independent auditors representing
Riverhill Energy and CMC are Arthur Andersen LLP.
 
     The Trustee has been advised that in the first quarter of 1998 Schlumberger
Technology Corporation ("Schlumberger"), acquired all of the shares of stock of
Riverhill Capital. Prior to such acquisition by Schlumberger, CMC and Riverhill
Energy were wholly-owned subsidiaries of Riverhill Capital. The Trustee has
further been advised that in connection with Schlumberger's acquisition of
Riverhill Capital, the shareholders of Riverhill Capital acquired ownership of
all of the shares of stock of Riverhill Energy. Thus, the ownership in the Texas
Royalty properties referenced above remained in Riverhill Energy, the stock
ownership of which was acquired by the former shareholders of Riverhill Capital.
Accounting operations pertaining to the Texas Royalty properties are being
performed by CMC under the direction of Riverhill Energy. CMC also currently
conducts all field, technical and accounting operations on behalf of BROG with
regard to the Waddell Ranch properties.
 
                                        4
<PAGE>   6
 
OIL AND GAS PRODUCTION
 
     The Trust recognizes production during the month in which the related
distribution is received. Production of oil and gas attributable to the
Royalties and the properties from which the Royalties were carved and the
related average sales prices attributable to the properties from which the
Royalties were carved for the three years ended December 31, 1998, excluding
portions attributable to the adjustments discussed below, were as follows:
 
<TABLE>
<CAPTION>
                                           WADDELL                           TEXAS
                                            RANCH                           ROYALTY
                                         PROPERTIES                       PROPERTIES                          TOTAL
                              ---------------------------------   ---------------------------   ---------------------------------
                                1998        1997        1996       1998      1997      1996       1998        1997        1996
                              ---------   ---------   ---------   -------   -------   -------   ---------   ---------   ---------
<S>                           <C>         <C>         <C>         <C>       <C>       <C>       <C>         <C>         <C>
ROYALTIES:
  Production
    Oil (barrels)...........     87,187     426,127     418,991   369,823   391,665   352,833     457,010     817,792     771,824
    Gas (Mcf)...............    666,864   1,875,965   1,915,649   766,085   840,790   724,732   1,432,949   2,716,755   2,640,381
PROPERTIES FROM WHICH THE
  ROYALTIES WERE CARVED:
  Production
    Oil (barrels)...........  1,475,258   1,387,056   1,338,340   434,444   438,963   450,397   1,909,702   1,826,019   1,788,737
    Gas (Mcf)...............  6,458,411   6,409,242   6,376,201   915,025   945,920   932,205   7,373,436   7,355,162   7,308,406
  Average Price
    Oil/barrel..............     $12.76      $19.54      $19.97    $12.44    $19.20    $18.32      $12.69      $19.46      $19.55
    Gas/Mcf.................     $ 2.13      $ 2.67      $ 2.20    $ 2.06    $ 2.45    $ 2.04      $ 2.12      $ 2.64      $ 2.18
</TABLE>
 
     Since the oil and gas sales attributable to the Royalties are based on an
allocation formula that is dependent on such factors as price and cost
(including capital expenditures), the production amounts do not provide a
meaningful comparison.
 
     In calculating Trust royalty income for the months of June through December
1998, costs exceeded revenues in the Waddell Ranch properties by $1,218,732.
Pursuant to the Waddell Ranch Net Overriding Royalty Conveyance dated effective
November 1, 1980 ("Waddell Ranch Conveyance"), excess costs plus accrued
interest must be recovered from future net proceeds relating to the underlying
Waddell Ranch properties before the properties can again contribute to Trust
royalty income. As a result of this, no royalty income was received for those
months. Production attributable to the Trust is calculated based on net royalty
income. As there was no royalty income, no production was reported for the
Waddell Ranch properties at the Trust level for those months. Production at the
Trust level for the Waddell Ranch properties was not recorded again until
February 1999 when the cumulative excess amounts had been recovered.
 
     In September 1998, the Trust received $1,041,340 from BROG which
represented the Trust's portion of amounts that had been previously held in
suspense by BROG relating to the Texas Royalty properties. The Trustee was
advised that these amounts relate to revenues received by BROG prior to the
conveyance of its interest in the Texas Royalty properties to Riverhill Energy
in February 1997. In October 1998, Riverhill Energy advised the Trustee that an
overpayment of $521,183 with regard to the suspended funds had been made to the
Trust. Pursuant to the Texas Royalty Conveyance, Riverhill Energy offset the
overpayment against royalty income attributable to the Texas Royalty properties
for the months of October and November 1998. The suspense amounts are not
reflected in Trust production or used in calculating average prices in 1998 or
prior years.
 
     As reported in Item 3 below, the Trustee was notified in the third quarter
of 1996 of the settlement of a class action lawsuit pending in the 270th
District Court of Harris County, Texas (the "Court") styled Caroline Altheide
and Langdon Harrison vs. Meridian Oil Inc., Meridian Oil Holding Inc., Meridian
Oil Trading Inc., Meridian Oil Production Inc., Southland Royalty Company, El
Paso Production Company, Meridian Oil Hydrocarbons Inc., Meridian Oil Gathering
Inc., Meridian Oil Services Inc. and Edward Parker ("Class Action"), in which
the Trust was a class member. The judgment approving the settlement of the Class
Action was the subject of an appeal. The Trustee was advised that such appeal
was dismissed and in October 1998, the Trust's portion of such settlement
proceeds, in the amount of $766,051 was received by the Trustee. The proceeds
were subsequently distributed with the regular monthly Trust distribution on
 
                                        5
<PAGE>   7
 
November 16, 1998, to the Trust's Unit holders of record on October 31, 1998.
The settlement proceeds are not reflected in Trust production in 1998 or prior
years.
 
PRICING INFORMATION
 
     Reference is made to "Regulation" for information as to federal regulation
of prices of natural gas. The following paragraphs provide information regarding
sales of oil and gas from the Waddell Ranch properties. As a royalty owner,
Southland Royalty is not furnished detailed information regarding sales of oil
and gas from the Texas Royalty properties.
 
     Oil. The Trustee has been advised by BROG that for the period August 1,
1993 through June 30, 1999, the oil from the Waddell Ranch properties is being
sold under a competitive bid to independent third parties.
 
     Gas. The gas produced from the Waddell Ranch properties is processed
through a natural gas processing plant and sold at the tailgate of the plant.
Plant products are marketed by Burlington Resources Hydrocarbons Inc., an
indirect subsidiary of BRI. The processor of the gas (Warren Petroleum Company,
L.P.) receives 15% of the liquids and residue gas as a fee for gathering,
compression, treating and processing the gas.
 
OIL AND GAS RESERVES
 
     The following are definitions adopted by the Securities and Exchange
Commission ("SEC") and the Financial Accounting Standards Board which are
applicable to terms used within this Item:
 
          "Proved reserves" are those estimated quantities of crude oil, natural
     gas and natural gas liquids, which, upon analysis of geological and
     engineering data, appear with reasonable certainty to be recoverable in the
     future from known oil and gas reservoirs under existing economic and
     operating conditions.
 
          "Proved developed reserves" are those proved reserves which can be
     expected to be recovered through existing wells with existing equipment and
     operating methods.
 
          "Proved undeveloped reserves" are those proved reserves which are
     expected to be recovered from new wells on undrilled acreage, or from
     existing wells where a relatively major expenditure is required.
 
          "Estimated future net revenues" are computed by applying current
     prices of oil and gas (with consideration of price changes only to the
     extent provided by contractual arrangements and allowed by federal
     regulation) to estimated future production of proved oil and gas reserves
     as of the date of the latest balance sheet presented, less estimated future
     expenditures (based on current costs) to be incurred in developing and
     producing the proved reserves, and assuming continuation of existing
     economic conditions. "Estimated future net revenues" are sometimes referred
     to herein as "estimated future net cash flows."
 
          "Present value of estimated future net revenues" is computed using the
     estimated future net revenues and a discount factor of 10%.
 
                                        6
<PAGE>   8
 
     The independent petroleum engineers' reports as to the proved oil and gas
reserves attributable to the Royalties conveyed to the Trust were obtained from
Cawley, Gillespie & Associates, Inc. The following table presents a
reconciliation of proved reserve quantities from December 31, 1995 through
December 31, 1998 (in thousands):
 
<TABLE>
<CAPTION>
                                                                WADDELL RANCH        TEXAS ROYALTY
                                                                  PROPERTIES          PROPERTIES              TOTAL
                                                              ------------------   -----------------   -------------------
                                                                OIL       GAS        OIL       GAS       OIL        GAS
                                                              (BBLS)     (MCF)     (BBLS)     (MCF)     (BBLS)     (MCF)
                                                              -------   --------   -------   -------   --------   --------
<S>                                                           <C>       <C>        <C>       <C>       <C>        <C>
December 31, 1995...........................................   5,952     24,843     4,577     4,873     10,529     29,716
Extensions, discoveries and other additions.................      24         24       -0-       -0-         24         24
Revisions of previous estimates.............................   1,746     11,560       448       642      2,194     12,202
Production..................................................    (419)    (1,916)     (353)     (725)      (772)    (2,641)
                                                              ------     ------     -----     -----     ------     ------
December 31, 1996...........................................   7,303     34,511     4,672     4,790     11,975     39,301
Extensions, discoveries and other additions.................      48         52       -0-       -0-         48         52
Revisions of previous estimates.............................  (1,902)    (8,512)      161       680     (1,741)    (7,832)
Production..................................................    (426)    (1,876)     (392)     (841)      (818)    (2,717)
                                                              ------     ------     -----     -----     ------     ------
December 31, 1997...........................................   5,023     24,175     4,441     4,629      9,464     28,804
Extensions, discoveries and other additions.................      10          4       -0-       -0-         10          4
Revisions of previous estimates.............................  (2,231)    (6,123)     (285)      100     (2,516)    (6,023)
Production..................................................     (87)      (667)     (370)     (766)      (457)    (1,433)
                                                              ------     ------     -----     -----     ------     ------
December 31, 1998...........................................   2,715     17,389     3,786     3,963      6,501     21,352
                                                              ======     ======     =====     =====     ======     ======
</TABLE>
 
     Estimated quantities of proved developed reserves of crude oil and natural
gas as of December 31, 1998, 1997 and 1996 were as follows (in thousands):
 
<TABLE>
<CAPTION>
                                                              CRUDE OIL    NATURAL GAS
                                                               (BBLS)         (MCF)
                                                              ---------    -----------
<S>                                                           <C>          <C>
1998........................................................    5,476        17,444
1997........................................................    8,116        23,054
1996........................................................   10,154        32,008
</TABLE>
 
     The Financial Accounting Standards Board requires supplemental disclosures
for oil and gas producers based on a standardized measure of discounted future
net cash flows relating to proved oil and gas reserve quantities. Under this
disclosure, future cash inflows are computed by applying year-end prices of oil
and gas relating to the enterprise's proved reserves to the year-end quantities
of those reserves. Future price changes are only considered to the extent
provided by contractual arrangements in existence at year-end. The standardized
measure of discounted future net cash flows is achieved by using a discount rate
of 10% a year to reflect the timing of future cash flows relating to proved oil
and gas reserves.
 
     Estimates of proved oil and gas reserves are by their very nature
imprecise. Estimates of future net revenue attributable to proved reserves are
sensitive to the unpredictable prices of oil and gas and other variables.
 
     The 1998, 1997 and 1996 change in the standardized measure of discounted
future net cash flows related to future royalty income from proved reserves
discounted at 10% is as follows (in thousands):
 
<TABLE>
<CAPTION>
                                     WADDELL RANCH PROPERTIES       TEXAS ROYALTY PROPERTIES                 TOTAL
                                   -----------------------------   ---------------------------   ------------------------------
                                    1998       1997       1996      1998      1997      1996       1998       1997       1996
                                   -------   --------   --------   -------   -------   -------   --------   --------   --------
<S>                                <C>       <C>        <C>        <C>       <C>       <C>       <C>        <C>        <C>
January 1........................  $63,179   $150,170   $ 74,070   $40,956   $52,457   $36,324   $104,135   $202,627   $110,394
Extensions, discoveries and other
  additions......................       81        619        447       -0-       -0-       -0-         81        619        447
Accretion of discount............    6,318     15,017      7,407     4,096     5,246     3,632     10,414     20,263     11,039
Revisions of prior year
  estimates, changes in price and
  other..........................  (39,982)   (89,235)    80,524   (16,796)   (7,540)   20,153    (56,778)   (96,775)   100,677
Royalty income...................   (4,553)   (13,392)   (12,278)   (6,225)   (9,207)   (7,652)   (10,778)   (22,599)   (19,930)
                                   -------   --------   --------   -------   -------   -------   --------   --------   --------
December 31......................  $25,043   $ 63,179   $150,170   $22,031   $40,956   $52,457   $ 47,074   $104,135   $202,627
                                   =======   ========   ========   =======   =======   =======   ========   ========   ========
</TABLE>
 
                                        7
<PAGE>   9
 
     Oil and gas prices of $8.56 and $9.96 per barrel and $1.74 and $1.88 per
Mcf were used to determine the estimated future net revenues from the Waddell
Ranch properties and the Texas Royalty properties, respectively, at December 31,
1998. The extension, discoveries and other additions for the Waddell Ranch
properties are proved developed producing reserves related to the RM (Clearfork)
field. The downward revisions of both reserves and discounted future net cash
flows for the Waddell Ranch properties and the Texas Royalty properties are due
to decreases in oil and gas prices from 1997 to 1998.
 
     Oil and gas prices of $15.79 and $16.75 per barrel and $2.28 and $3.14 per
Mcf were used to determine the estimated future net revenues from the Waddell
Ranch properties and the Texas Royalty properties at December 31, 1997. The
downward revision of the estimated oil reserves and the related decrease in the
discounted future net cash flow for the Waddell Ranch properties was primarily
due to the decrease in oil prices from 1996 to 1997. The downward revision in
the estimated gas reserves for the Waddell Ranch properties was primarily due to
the decrease in gas prices from 1996 to 1997.
 
     Oil and gas prices of $23.88 and $22.32 per barrel and $4.00 and $2.64 per
Mcf were used to determine the estimated future net revenues from the Waddell
Ranch properties and the Texas Royalty properties at December 31, 1996. The
extension, discoveries and other additions for the Waddell Ranch properties are
reserves added as a result of remedial activity in the Waddell Ellenberger
Field. The upward revision of the estimated oil and gas reserves and the related
increase in the discounted future net cash flow for the Waddell Ranch properties
was due to the increase in oil and gas prices from 1995 to 1996, as well as
production response from drilling and remedial activity. The largest increase in
oil reserves due to drilling and remedial activity occurred in the Waddell
Field. The revisions in the oil and gas reserves and related discounted cash
flow for the Texas Royalty properties are mainly due to the increase in oil and
gas prices at December 31, 1996.
 
     The following presents estimated future net revenue and the present value
of estimated future net revenue, for each of the years ended December 31, 1998,
1997 and 1996 (in thousands except amounts per Unit):
 
<TABLE>
<CAPTION>
                                                      1998                     1997                     1996
                                              ---------------------    ---------------------    ---------------------
                                              ESTIMATED                ESTIMATED                ESTIMATED
                                               FUTURE      PRESENT      FUTURE      PRESENT      FUTURE      PRESENT
                                                 NET        VALUE         NET        VALUE         NET        VALUE
                                               REVENUE      AT 10%      REVENUE      AT 10%      REVENUE      AT 10%
                                              ---------    --------    ---------    --------    ---------    --------
<S>                                           <C>          <C>         <C>          <C>         <C>          <C>
Total Proved
  Waddell Ranch properties..................   $50,322     $ 25,043    $126,924     $ 63,179    $294,653     $150,170
  Texas Royalty properties..................    43,290       22,031      85,254       40,956     111,181       52,457
                                               -------     --------    --------     --------    --------     --------
        Total...............................   $93,612     $ 47,074    $212,178     $104,135    $405,834     $202,627
                                               =======     ========    ========     ========    ========     ========
Total Proved Per Unit.......................   $  2.01     $   1.01    $   4.55     $   2.23    $   8.71     $   4.35
                                               =======     ========    ========     ========    ========     ========
Proved Developed
  Waddell Ranch properties..................   $35,607     $ 22,032    $ 94,493     $ 55,150    $226,174     $124,395
  Texas Royalty properties..................    43,290       22,031      85,254       40,956     111,181       52,457
                                               -------     --------    --------     --------    --------     --------
        Total...............................   $78,896     $ 44,063    $179,747     $ 96,106    $337,355     $176,852
                                               =======     ========    ========     ========    ========     ========
</TABLE>
 
     Reserve quantities and revenues shown in the preceding tables for the
Royalties were estimated from projections of reserves and revenue attributable
to the combined Southland Royalty and Trust interests in the Waddell Ranch
properties and Texas Royalty properties. Reserve quantities attributable to the
Royalties were estimated by allocating to the Royalties a portion of the total
estimated net reserve quantities of the interests, based upon gross revenue less
production taxes. Because the reserve quantities attributable to the Royalties
are estimated using an allocation of the reserves, any changes in prices or
costs will result in changes in the estimated reserve quantities allocated to
the Royalties. Therefore, the reserve quantities estimated will vary if
different future price and cost assumptions occur.
 
     Proved reserve quantities are estimates based on information available at
the time of preparation and such estimates are subject to change as additional
information becomes available. The reserves actually recovered and the timing of
production of those reserves may be substantially different from the original
estimate.
 
                                        8
<PAGE>   10
 
Moreover, the present values shown above should not be considered as the market
values of such oil and gas reserves or the costs that would be incurred to
acquire equivalent reserves. A market value determination would include many
additional factors.
 
REGULATION
 
     Many aspects of the production, pricing and marketing of crude oil and
natural gas are regulated by federal and state agencies. Legislation affecting
the oil and gas industry is under constant review for amendment or expansion,
frequently increasing the regulatory burden on affected members of the industry.
 
     Exploration and production operations are subject to various types of
regulation at the federal, state and local levels. Such regulation includes
requiring permits for the drilling of wells, maintaining bonding requirements in
order to drill or operate wells, and regulating the location of wells, the
method of drilling and casing wells, the surface use and restoration of
properties upon which wells are drilled and the plugging and abandonment of
wells. Natural gas and oil operations are also subject to various conservation
laws and regulations that regulate the size of drilling and spacing units or
proration units and the density of wells which may be drilled and unitization or
pooling of oil and gas properties. In addition, state conservation laws
establish maximum allowable production from natural gas and oil wells, generally
prohibit the venting or flaring of natural gas and impose certain requirements
regarding the ratability of production. The effect of these regulations is to
limit the amounts of natural gas and oil that can be produced and to limit the
number of wells or the locations which can be drilled.
 
  Federal Natural Gas Regulation
 
     The Federal Energy Regulatory Commission (the "FERC") is primarily
responsible for federal regulation of natural gas. The interstate transportation
and sale for resale of natural gas is subject to federal governmental
regulation, including regulation of transportation and storage tariffs and
various other matters, by FERC. The Natural Gas Wellhead Decontrol Act of 1989
("Decontrol Act") terminated federal price controls on wellhead sales of
domestic natural gas on January 1, 1993. Consequently, sales of natural gas may
be made at market prices, subject to applicable contract provisions. The FERC's
jurisdiction over natural gas transportation and storage was unaffected by the
Decontrol Act.
 
     Sales of natural gas are affected by the availability, terms and cost of
transportation. The price and terms for access to pipeline transportation remain
subject to extensive federal and state regulation. Several major regulatory
changes have been implemented by Congress and the FERC from 1985 to the present
that affect the economics of natural gas production, transportation, and sales.
In addition, the FERC continues to promulgate revisions to various aspects of
the rules and regulations affecting those segments of the natural gas industry,
most notably interstate natural gas transmission companies, that remain subject
to the FERC's jurisdiction. These initiatives may also affect the intrastate
transportation of gas under certain circumstances. The stated purpose of many of
these regulatory changes is to promote competition among the various sectors of
the natural gas industry and these initiatives generally reflect more
light-handed regulation of the natural gas industry. The ultimate impact of the
rules and regulations issued by the FERC since 1985 cannot be predicted. In
addition, many aspects of these regulatory developments have not become final
but are still pending judicial and FERC final decisions.
 
     Additional proposals and proceedings that might affect the natural gas
industry are considered from time to time by Congress, the FERC, state
regulatory bodies and the courts. The Trust cannot predict when or if any such
proposals might become effective, or their effect, if any, on the Trust. The
natural gas industry historically has been very heavily regulated; therefore,
there is no assurance that the less stringent regulatory approach recently
pursued by the FERC and Congress will continue.
 
     Sales of crude oil, condensate and gas liquids are not currently regulated
and are made at market prices. Effective as of January 1, 1995, the FERC
implemented regulations establishing an indexing system for transportation rates
for oil that could increase the cost of transporting oil to the purchaser. The
Trust is not able to predict what effect, if any, these regulations will have on
it, but other factors being equal, the regulations may tend to increase
transportation costs or reduce wellhead prices for crude oil.
 
                                        9
<PAGE>   11
 
  State Regulation
 
     The various states regulate the production and sale of oil and natural gas,
including imposing requirements for obtaining drilling permits, the method of
developing new fields, the spacing and operation of wells and the prevention of
waste of oil and gas resources. The rates of production may be regulated and the
maximum daily production allowables from both oil and gas wells may be
established on a market demand or conservation basis, or both.
 
  Other Regulation
 
     The petroleum industry is also subject to compliance with various other
federal, state and local regulations and laws, including, but not limited to,
environmental protection, occupational safety, resource conservation and equal
employment opportunity. The Trustee does not believe that compliance with these
laws by the operating parties will have any material adverse effect on the Unit
holders.
 
ITEM 3. LEGAL PROCEEDINGS
 
     In the third quarter of 1996, the Trustee was notified of the settlement of
a class action lawsuit pending in the 270th District Court of Harris County,
Texas (the "Court") Cause No. 92-026182 styled Caroline Altheide and Langdon
Harrison vs. Meridian Oil Inc., Meridian Oil Holding Inc., Meridian Oil Trading
Inc., Meridian Oil Production Inc., Southland Royalty Company, El Paso
Production Company, Meridian Oil Hydrocarbons Inc., Meridian Oil Gathering Inc.,
Meridian Oil Services Inc. and Edward Parker filed in June 1992 ("Class
Action"). The defendants in this lawsuit are collectively referred to herein as
"Meridian."
 
     The members of the class ("Class Members") involved in the Class Action
that was certified by the Court are all persons or entities who (i) at any time
between December 1, 1986 and July 1, 1996 received payments directly from
Meridian, (ii) the payments from Meridian were attributable to interests in
natural gas that was sold at the wellhead to Meridian Oil Trading Inc., and
(iii) the interests were either royalty interests, overriding royalty interests
or interests of a similar nature that burdened the working interests of
Meridian, or working interests in properties operated by Meridian, or royalty
interests, overriding royalty interests or interests of a similar nature that
burdened working interests in properties operated by Meridian. Meridian, the San
Juan Basin Royalty Trust, the Burlington Resources Coal Seam Royalty Trust and
the Commissioner of Public Lands of the New Mexico State Lands Office are not
Class Members.
 
     In summary, the claims asserted in the Class Action ("Class Claims") are
those asserted in Plaintiffs' Second Amended Original Petition filed in the
Class Action which are based upon the manner in which Meridian calculated
payments to its royalty owners and its joint working interest owners in natural
gas-producing properties. It is alleged that those payments were based on
wellhead prices that were set by a marketing affiliate, rather than upon the net
prices that Meridian received for the gas and liquid components in arm's-length
sales to non-affiliated purchasers. More specifically, such claims are based on
Meridian's conduct in basing its payments to Class Members, for natural gas sold
at the wellhead to Meridian Oil Trading Inc., on wellhead prices that resulted
from one or more of the following:
 
          (i) Meridian's use of allegedly depressed prices for gas set by
     Meridian Oil Trading Inc.;
 
          (ii) Meridian's use of allegedly inflated cost factors for
     transportation services set by Meridian Oil Trading Inc.;
 
          (iii) Meridian's use of allegedly depressed net prices for liquids set
     by Meridian Oil Hydrocarbons Inc.; and
 
          (iv) Meridian's use of allegedly inflated rates for coal seam
     gathering and treating services set by Meridian Oil Gathering Inc.
 
     It was alleged that Meridian's conduct violated applicable legal
principles. Meridian denied that its conduct had been unlawful or otherwise
wrongful. The Court has not ruled on the merits of the Class Claims or on
Meridian's defenses to such claims.
 
                                       10
<PAGE>   12
 
     The settlement reached by the parties in the Class Action provided for the
payment of up to $42 million together with interest thereon beginning on July
17, 1996 until the date the settlement checks were initially mailed to the Class
Members participating in the settlement. Such settlement amount was subject to
reduction for certain adjustments such as (i) fees, costs and expenses awarded
by the Court to the Class Counsel (Susman Godfrey L.L.P. and Dick Watt), (ii)
extra compensation awarded by the Court to the named Plaintiffs (Caroline D.
Altheide and Langdon D. Harrison), and (iii) the expense incurred in giving
notice and administering the proposed settlement ("Net Settlement Fund").
Concurrently with Meridian's payment of the Net Settlement Fund to Class Members
who did not timely and validly elect to be excluded from the Class ("Settlement
Class Members"), Meridian was obligated under the settlement to advise its then
current recipients of royalty payments that Meridian intended (i) to commence
calculating royalty payments based upon the net prices received by Meridian from
non-affiliated third parties for natural gas and the liquids extracted
therefrom, and (ii) in calculating royalty payments on gas produced from coal
seam gas wells using the Val Verde Gathering System, to commence using a
deduction for gathering and treating the gas produced from such wells that does
not exceed 75% of the fee charged by Meridian Oil Gathering Inc. for similar
services to the five largest (by volume) non-affiliated third-party shippers.
Meridian is not obligated to calculate royalty payments in such method in the
future but, if it changes such method of calculation, it is obligated to provide
notice of such change in method of calculation to the then-current recipients of
royalty payments.
 
     Of the Net Settlement Fund, (i) 48% thereof was to be distributed among
Class Members whose interests bear on "conventional" gas-producing properties
(specifically, gas not gathered on the Val Verde Gathering System) that are
located in Meridian's Farmington operating division (which is roughly
coextensive with the San Juan Basin of New Mexico and Colorado), (ii) 42%
thereof was to be distributed among the Class Members whose interests bear on
the coal seam gas producing properties located in Meridian's Farmington
operating division (specifically, gas gathered on the Val Verde Gathering
System), and (iii) 10% thereof was to be distributed among those Class Members
whose interests bear on gas-producing properties located in areas other than
Meridian's Farmington operating division. The Trust fell into the last of these
three classifications.
 
     Upon final judicial approval of the settlement, the settlement provided
that a judgment be entered in the Class Action dismissing the Class Action with
prejudice to its refiling. As a result of the settlement, Settlement Class
Members release and discharge the Released Parties, and each of them, from and
with respect to the Class Claims and such Class Members will not be able to
pursue the Class Claims against the Released Parties. "Released Parties" as used
herein means, severally and collectively, the Defendants and Meridian Oil Inc.
and all Affiliates of Burlington Resources Inc. since December 1, 1986,
collectively, and all past and present agents, employees, officers, directors,
shareholders, representatives, attorneys, predecessors, successors, assigns and
affiliates of each of the Defendants and of Meridian Oil Inc. and all Affiliates
of Burlington Resources Inc. since December 1, 1986, collectively. "Released
Parties" also includes all other persons or entities who are liable or become
liable for the conduct of any person or entity that is identified in the
preceding sentence. "Affiliates" as used herein means Burlington Resources
Inc.'s direct and indirect subsidiaries.
 
     It was determined by the Trustee that the Trust was part of the Class that
was certified by the Court in the Class Action and that it was in the best
interest of the Trust to elect to remain as part of the Class and share in the
Net Settlement Fund. The Trustee believes that the Class Claims, if true, had
little, if any, detrimental effect on the Trust and the Trust is being
adequately compensated as a result of this settlement.
 
     A judgment was signed by the Court approving the settlement. However, a
Notice of Appeal was filed by San Juan 1990-A, L.P., K&W Gas Partners, L.P., MAP
1992-A Partners, L.P. and The Board of Trustees of Leland Stanford Junior
University, Non-Profit Corporation (Stanford University) ("Objectors") on
February 7, 1997.
 
     One of the conditions set forth in the settlement agreement relating to the
Class Action relating to the distribution of the settlement proceeds was that
there would be no distribution of settlement proceeds unless and until such
judgment was no longer subject to further appeal and, if there was an appeal,
not unless and
 
                                       11
<PAGE>   13
 
until such judgment was affirmed or such appeal was dismissed and the time for
any further proceedings in the appellate court of last resort had expired. The
Trustee was advised that such appeal has been dismissed and it is the
understanding of the Trustee that the conditions and restrictions that prevented
payment of the settlement proceeds no longer existed. In the fourth quarter of
1998, the Trust received its portion of the settlement proceeds totalling
$766,050.89. Such settlement proceeds that were received by the Trust were
distributed with the regular monthly Trust distribution on November 16, 1998 to
Trust's Unit holders of record on October 31, 1998.
 
ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
 
     No matters were submitted to a vote of Unit holders, through the
solicitation of proxies or otherwise, during the fourth quarter ended December
31, 1998.
 
                                    PART II
 
ITEM 5. MARKET FOR UNITS OF THE TRUST AND RELATED SECURITY HOLDER MATTERS
 
     The information under "Units of Beneficial Interest" at page 1 of the
Trust's Annual Report to security holders for the year ended December 31, 1998,
is herein incorporated by reference.
 
ITEM 6. SELECTED FINANCIAL DATA
 
<TABLE>
<CAPTION>
                                                                    FOR THE YEAR ENDED DECEMBER 31,
                                                -----------------------------------------------------------------------
                                                   1998           1997           1996           1995           1994
                                                -----------    -----------    -----------    -----------    -----------
<S>                                             <C>            <C>            <C>            <C>            <C>
Royalty income................................  $10,777,901    $22,598,873    $19,930,354    $12,014,623    $16,646,903
Distributable income..........................   10,414,382     22,190,115     19,488,574     11,632,463     16,174,570
Distributable income per Unit.................     0.223443       0.476092       0.418131       0.249574       0.347027
Distributions per Unit........................     0.223443       0.476092       0.418131       0.249574       0.347027
Total assets, December 31.....................    3,861,776      5,220,786      5,913,931      5,252,922      6,002,283
</TABLE>
 
ITEM 7. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATION
 
     The "Trustee's Discussion and Analysis for the Three Year Period Ended
December 31, 1998" and "Results of the 4th Quarters of 1998 and 1997" at pages 5
through 7 of the Trust's Annual Report to security holders for the year ended
December 31, 1998 is herein incorporated by reference.
 
  Year 2000 Issue
 
     Many existing computer programs use only two digits to identify a year in
the date field. These programs were designed and developed without considering
the impact of the upcoming change in the century. If not corrected, many
computer applications could fail or create erroneous results by the Year 2000.
The Year 2000 issue affects virtually all companies and organizations. If a
company or organization does not successfully address its Year 2000 issues, it
may face material adverse consequences.
 
     As the Trust does not directly maintain any systems, the Trust will not
incur any direct costs related to the Year 2000 issue.
 
     The Trustee has identified those vendors it believes could have an impact
on its day-to-day operations if their operations were interrupted as a result of
Year 2000 problems. The Trust has made formal inquiries to these vendors
requesting information on their state of readiness for the Year 2000. Through
responses received and other literature reviewed by the Trustee with respect to
its vendors, the Trustee believes that all significant vendors are currently
addressing the Year 2000 issue and plan to be compliant prior to the Year 2000.
 
     The Trustee has no reason to believe that its vendors will not be Year 2000
compliant. In the event the Trustee learns that a vendor's system will not be
Year 2000 compliant, the Trustee will assess the potential risk and develop
contingency plans at that time.
 
                                       12
<PAGE>   14
 
     The Trust is a passive entity with no business operations and the
information technology systems ("IT") employed by the Trustee in connection with
its duties on behalf of the Trust are less extensive than the systems employed
by many business entities. The Trust has no formal IT budget and the Trustee
does not anticipate making any expenditures relating to the Trustee's IT systems
used in connection with the Trust during 1999.
 
     Because the royalty interests held by the Trust are fixed, the Trustee is
dependent upon the third parties that hold operating interests with respect
thereto for the receipt of royalty income. Thus, if any such third party failed
to deliver royalty income, the Trustee would have no alternative source for such
income. The Trustee believes that the worst case scenario would be the failure
by one or more of the third parties who pay royalties to the Trust or who make
distributions to Unit holders for the Trust to identify and remediate Year 2000
problems on a timely basis, which could cause the Trustee to be unable to make
required distributions to Unit holders. With respect to a failure by a third
party to deliver royalty income or make distributions to Unit holders on a
timely basis, the Trustee believes that it would have no control over the
efforts of such third party to correct the problems, and significant delays in
the receipt of royalty income and distributions to Unit holders could result.
 
     There can be no guarantee that the Trustee will be able to identify all
potential Year 2000 problems or fully remediate all Year 2000 problems
identified on a timely basis. There can be no assurance that the systems of the
Trustee or third party vendors on which the Trust relies will be timely
remediated. The failure by the Trustee or any such third party to fully
remediate its Year 2000 problems on a timely basis could have a material adverse
affect on the Trustee's ability to receive revenue, account for and make timely
distribution of the Trust's distributable income.
 
     Certain of the statements made above regarding the Trustee's Year 2000
program are forward-looking statements, and there can be no assurance that the
Trustee will be able to achieve Year 2000 compliance in the manner and by the
dates indicated above.
 
ITEM 7A. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK
 
     Not Applicable.
 
ITEM 8. FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA
 
     The Financial Statements of the Trust and the notes thereto at page 8 et
seq. of the Trust's Annual Report to security holders for the year ended
December 31, 1998, are herein incorporated by reference.
 
ITEM 9.CHANGES IN AND DISAGREEMENTS WITH ACCOUNTANTS ON ACCOUNTING AND FINANCIAL
       DISCLOSURE
 
     There have been no changes in accountants and no disagreements with
accountants on any matter of accounting principles or practices or financial
statement disclosures during the twenty-four months ended December 31, 1998.
 
                                    PART III
 
ITEM 10. DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT
 
     The Trust has no directors or executive officers. The Trustee is a
corporate trustee which may be removed, with or without cause, at a meeting of
the Unit holders, by the affirmative vote of the holders of a majority of all
the Units then outstanding.
 
                                       13
<PAGE>   15
 
ITEM 11. EXECUTIVE COMPENSATION
 
     During the years ended December 31, 1998, 1997 and 1996, the Trustee
received total remuneration as follows:
 
<TABLE>
<CAPTION>
                 NAME OF INDIVIDUAL                    CAPACITIES
                    OR NUMBER OF                        IN WHICH         CASH
                  PERSONS IN GROUP                       SERVED      COMPENSATION    YEAR
                 ------------------                    ----------    ------------    ----
<S>                                                    <C>           <C>             <C>
NationsBank, N.A.....................................   Trustee       $65,338(1)     1996
                                                                      $44,735(1)     1997
                                                                      $54,761(1)     1998
</TABLE>
 
---------------
 
(1) Under the Trust Indenture, the Trustee is entitled to an administrative fee
    for its administrative services, preparation of quarterly and annual
    statements with attention to tax and legal matters of: (i) 1/20 of 1% of the
    first $100 million of annual gross revenue of the Trust and 1/30 of 1% in
    excess of $100 million and (ii) Trustee's standard hourly rate in excess of
    300 hours annually. The administrative fee is subject to reduction by a
    credit for funds provision.
 
ITEM 12. SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT
 
     (a) Security Ownership of Certain Beneficial Owners. The following table
sets forth as of December 31, 1998, information with respect to each person
known to own beneficially more than 5% of the outstanding Units of the Trust:
 
<TABLE>
<CAPTION>
                                             AMOUNT AND NATURE OF     PERCENT
             NAME AND ADDRESS               BENEFICIAL OWNERSHIP(1)   OF CLASS
             ----------------               -----------------------   --------
<S>                                         <C>                       <C>
Burlington Resources Oil & Gas Company(1)      27,577,741 Units       59.17%
  5051 Westheimer
  Suite 1400
  Houston, Texas 77056-2124
</TABLE>
 
---------------
 
(1) This information was provided to the Securities and Exchange Commission and
    to the Trust in a Form 4 dated January 6, 1994, filed with the Securities
    and Exchange Commission by Southland Royalty, a wholly-owned subsidiary of
    BRI, and in Amendment 5 to Schedule 13D and Schedule 13E-3 dated December
    28, 1993, filed with the Securities and Exchange Commission by Southland
    Royalty and BRI. Such Units were reported to be owned directly by Southland
    Royalty, now BROG.
 
    The Form 4 filed by Southland Royalty and the Schedule 13D and Schedule
    13E-3 filed by Southland Royalty and BRI with the Securities and Exchange
    Commission may be reviewed for more detailed information concerning the
    matters summarized herein.
 
     (b) Security Ownership of Management. The Trustee owns beneficially no
securities of the Trust. In various fiduciary capacities, NationsBank, N.A.
owned as of March 2, 1999, an aggregate of 352,089 Units with no right to vote
145,196 of these Units, shared right to vote 4,000 of these Units and sole right
to vote 202,893 of these Units. Such Bank disclaims any beneficial interests in
these Units. The number of Units reflected in this paragraph includes Units held
by all branches of NationsBank, N.A.
 
     (c) Change In Control. The Trustee knows of no arrangements which may
subsequently result in a change in control of the Trust.
 
ITEM 13. CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS
 
     The Trust has no directors or executive officers. See Item 11 for the
remuneration received by the Trustee during the years ended December 31, 1998,
1997 and 1996 and Item 12(b) for information concerning Units owned by
NationsBank, N.A. in various fiduciary capacities.
 
                                       14
<PAGE>   16
 
                                    PART IV
 
ITEM 14. EXHIBITS, FINANCIAL STATEMENT SCHEDULES AND REPORTS ON FORM 8-K
 
     The following documents are filed as a part of this Report:
 
FINANCIAL STATEMENTS
 
     Included in Part II of this Report by reference to the Annual Report of the
Trust for the year ended December 31, 1998:
 
          Independent Auditors' Report
 
          Statements of Assets, Liabilities and Trust Corpus
 
          Statements of Distributable Income
 
          Statements of Changes in Trust Corpus
 
          Notes to Financial Statements
 
FINANCIAL STATEMENT SCHEDULES
 
     Financial statement schedules are omitted because of the absence of
conditions under which they are required or because the required information is
given in the financial statements or notes thereto.
 
EXHIBITS
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
         (4)(a)          -- Permian Basin Royalty Trust Indenture dated November 3,
                            1980, between Southland Royalty Company and The First
                            National Bank of Fort Worth (now NationsBank, N.A.), as
                            Trustee, heretofore filed as Exhibit (4)(a) to the
                            Trust's Annual Report on Form 10-K to the Securities and
                            Exchange Commission for the fiscal year ended December
                            31, 1980, is incorporated herein by reference.*

            (b)          -- Net Overriding Royalty Conveyance (Permian Basin Royalty
                            Trust) from Southland Royalty Company to The First
                            National Bank of Fort Worth (now NationsBank, N.A.), as
                            Trustee, dated November 3, 1980 (without Schedules),
                            heretofore filed as Exhibit (4)(b) to the Trust's Annual
                            Report on Form 10-K to the Securities and Exchange
                            Commission for the fiscal year ended December 31, 1980,
                            is incorporated herein by reference.*

            (c)          -- Net Overriding Royalty Conveyance (Permian Basin Royalty
                            Trust -- Waddell Ranch) from Southland Royalty Company to
                            The First National Bank of Fort Worth (now NationsBank,
                            N.A.), as Trustee, dated November 3, 1980 (without
                            Schedules), heretofore filed as Exhibit (4)(c) to the
                            Trust's Annual Report on Form 10-K to the Securities and
                            Exchange Commission for the fiscal year ended December
                            31, 1980, is incorporated herein by reference.*

        (13)             -- Registrant's Annual Report to security holders for fiscal
                            year ended December 31, 1998.**

        (23)             -- Consent of Cawley, Gillespie & Associates, Inc.,
                            reservoir engineer.**

        (27)             -- Financial Data Schedule.**
</TABLE>
 
---------------
 
 * A copy of this Exhibit is available to any Unit holder, at the actual cost of
   reproduction, upon written request to the Trustee, NationsBank, N.A., P.O.
   Box 1317, Fort Worth, Texas 76101.
 
** Filed herewith.
 
                                       15
<PAGE>   17
 
REPORTS ON FORM 8-K
 
     During the last quarter of the Trust's fiscal year ended December 31, 1998,
there was one report on Form 8-K filed by the Trust. In such Form 8-K, the
Trustee reported receipt of the settlement proceeds from the Class Action
lawsuit discussed in Item 3 hereof totalling $766,050.89 and that such proceeds
would be distributed as part of the regular monthly distribution on November 16,
1998 to Unit holders of record on October 31, 1998.
 
                                       16
<PAGE>   18
 
                                   SIGNATURE
 
     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.
 
                                            NATIONSBANK, N.A.
                                              TRUSTEE OF THE PERMIAN BASIN
                                              ROYALTY TRUST
 
                                            By      /s/ ERIC F. HYDEN
                                             -----------------------------------
                                                       (Eric F. Hyden)
                                                       Vice President
 
Date: March 30, 1999
 
              (The Trust has no directors or executive officers.)
 
                                       17
<PAGE>   19
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
                                                                                         SEQUENTIALLY
        EXHIBIT                                                                            NUMBERED
         NUMBER                                      EXHIBIT                                 PAGE
        -------                                      -------                             ------------
<C>                        <S>                                                           <C>
           (4)(a)          -- Permian Basin Royalty Trust Indenture dated November 3,
                              1980, between Southland Royalty Company and The First
                              National Bank of Fort Worth (now NationsBank, N.A.), as
                              Trustee, heretofore filed as Exhibit (4)(a) to the
                              Trust's Annual Report on Form 10-K to the Securities and
                              Exchange Commission for the fiscal year ended December
                              31, 1980, is incorporated herein by reference.*

              (b)          -- Net Overriding Royalty Conveyance (Permian Basin Royalty
                              Trust) from Southland Royalty Company to The First
                              National Bank of Fort Worth (now NationsBank, N.A.), as
                              Trustee, dated November 3, 1980 (without Schedules),
                              heretofore filed as Exhibit (4)(b) to the Trust's Annual
                              Report on Form 10-K to the Securities and Exchange
                              Commission for the fiscal year ended December 31, 1980,
                              is incorporated herein by reference.*

              (c)          -- Net Overriding Royalty Conveyance (Permian Basin Royalty
                              Trust -- Waddell Ranch) from Southland Royalty Company to
                              The First National Bank of Fort Worth (now NationsBank,
                              N.A.), as Trustee, dated November 3, 1980 (without
                              Schedules), heretofore filed as Exhibit (4)(c) to the
                              Trust's Annual Report on Form 10-K to the Securities and
                              Exchange Commission for the fiscal year ended December
                              31, 1980, is incorporated herein by reference.*

          (13)             -- Registrant's Annual Report to security holders for fiscal
                              year ended December 31, 1998.**

          (23)             -- Consent of Cawley, Gillespie & Associates, Inc.,
                              reservoir engineer.**

          (27)             -- Financial Data Schedule.**
</TABLE>
 
---------------
 
 * A copy of this Exhibit is available to any Unit holder, at the actual cost of
   reproduction, upon written request to the Trustee, NationsBank, N.A., P.O.
   Box 1317, Fort Worth, Texas 76101.
 
** Filed herewith.