<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549



                                    Form 10-Q



                Quarterly Report Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934



                  For the Quarterly Period Ended June 30, 2000


                           Commission File No. 1-8033



                           PERMIAN BASIN ROYALTY TRUST


Texas                                                      I.R.S. No. 75-6280532


                    Bank of America, N.A., Trust Department
                                P.O. Box 830650
                              Dallas, Texas 75283

                          Telephone Number 214.209.2400



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 and (2) has been subject to such filing requirements for
the past 90 days. Yes X No
                     ---   ---

Number of Units of beneficial interest of the Trust outstanding at August 1,
2000: 46,608,796

<PAGE>   2


                           PERMIAN BASIN ROYALTY TRUST

                          PART I - FINANCIAL STATEMENTS


Item 1.  Financial Statements

The condensed financial statements included herein have been prepared by Bank of
America, N.A. as Trustee for the Permian Basin Royalty Trust, without audit,
pursuant to the rules and regulations of the Securities and Exchange Commission.
Certain information and footnote disclosures normally included in annual
financial statements have been condensed or omitted pursuant to such rules and
regulations, although the Trustee believes that the disclosures are adequate to
make the information presented not misleading. It is suggested that these
condensed financial statements be read in conjunction with the financial
statements and the notes thereto included in the Trust's latest annual report on
Form 10-K. In the opinion of the Trustee, all adjustments, consisting only of
normal recurring adjustments, necessary to present fairly the assets,
liabilities and trust corpus of the Permian Basin Royalty Trust at March
31,2000, and the distributable income and changes in trust corpus for the
three-month and six-month periods ended June 30, 2000 and 1999 have been
included. The distributable income for such interim periods is not necessarily
indicative of the distributable income for the full year.

Deloitte & Touche LLP, independent certified public accountants, has made a
limited review of the condensed financial statements as of June 30, 2000 and for
the three-month and six-month periods ended June 30, 2000 and 1999 included
herein.


                                      -2-
<PAGE>   3

BANK OF AMERICA, N.A. AS TRUSTEE
FOR THE PERMIAN BASIN ROYALTY TRUST:

We have reviewed the accompanying condensed statement of assets, liabilities and
trust corpus of the Permian Basin Royalty Trust as of June 30, 2000 and the
related condensed statements of distributable income and changes in trust corpus
for the three-month and six-month periods ended June 30, 2000 and 1999. These
financial statements are the responsibility of the Trustee.

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 procedures to
financial data and making inquiries of persons responsible for financial and
accounting matters. It is substantially less in scope than an audit conducted in
accordance with auditing standards generally accepted in the United States of
America, 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.

The accompanying condensed financial statements are prepared on a modified cash
basis as described in Note 1, which is a comprehensive basis of accounting other
than accounting principles generally accepted in the United States of America.

Based on our reviews, we are not aware of any material modifications that should
be made to such condensed financial statements for them to be in conformity with
the basis of accounting described in Note 1.

We have previously audited, in accordance with auditing standards generally
accepted in the United States of America, the statement of assets, liabilities
and trust corpus of the Permian Basin Royalty Trust as of December 31, 1999, and
the related statements of distributable income and changes in trust corpus for
the year then ended (not presented herein); and in our report dated March 25,
2000, we expressed an unqualified opinion on those financial statements. In our
opinion, the information set forth in the accompanying condensed statement of
assets, liabilities and trust corpus as of December 31, 1999 is fairly stated,
in all material respects, in relation to the statement of assets, liabilities
and trust corpus from which it has been derived.




/s/ DELOITTE & TOUCHE LLP
Dallas, Texas
August 1, 2000


                                      -3-
<PAGE>   4


PERMIAN BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                                      June 30    December 31,
ASSETS                                                                 2000         1999
                                                                    (Unaudited)
<S>                                                                 <C>          <C>
Cash and short-term investments                                     $2,939,151   $  2,415,245
Net overriding royalty interests in producing
  oil and gas properties (net of accumulated
  amortization of $8,232,065 and $8,085,238 at
  June 30, 2000 and December 31, 1999, respectively)                 2,743,151      2,889,978
                                                                    ----------   ------------

                                                                    $5,682,302   $  5,305,223
                                                                    ==========   ============

LIABILITIES AND TRUST CORPUS

Distribution payable to Unit holders                                $2,939,151   $  2,415,245
Commitments and contingencies
Trust corpus - 46,608,796 Units of beneficial
  interest authorized and outstanding                                2,743,151      2,889,978
                                                                    ----------   ------------

                                                                    $5,682,302   $  5,305,223
                                                                    ==========   ============
</TABLE>


CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)

<TABLE>
<CAPTION>
                                        Three Months Ended             Six Months Ended
                                             June 30                        June 30
                                        2000           1999            2000           1999
                                     -----------   -----------      -----------   -----------
<S>                                  <C>           <C>              <C>           <C>
Royalty income                       $ 9,037,360   $ 3,957,301      $15,410,417   $ 5,733,261
Interest income                           16,475         4,988           33,304         7,001
                                     -----------   -----------      -----------   -----------
                                       9,053,835     3,962,289       15,443,721     5,740,262

General and administrative
   expenditures                          158,847       116,677          282,668       260,340
                                     -----------   -----------      -----------   -----------

Distributable income                 $ 8,894,989   $ 3,845,612      $15,161,053   $ 5,479,922
                                     ===========   ===========      ===========   ===========

Distributable income per Unit
   (46,608,796 Units)                $   .190844   $   .082509      $   .325283   $   .117573
                                     ===========   ===========      ===========   ===========
</TABLE>


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


                                      -4-
<PAGE>   5


PERMIAN BASIN ROYALTY TRUST

CONDENSED STATEMENTS OF CHANGES IN TRUST CORPUS (UNAUDITED)
--------------------------------------------------------------------------------


<TABLE>
<CAPTION>
                                             THREE MONTHS ENDED            SIX MONTHS ENDED
                                                  JUNE 30                      JUNE 30
                                         --------------------------   ---------------------------
                                             2000           1999          2000           1999
<S>                                      <C>            <C>           <C>            <C>
Trust corpus, beginning of period        $ 2,811,453    $ 3,281,601   $  2,889,978    $ 3,336,583
Amortization of net overriding
  royalty interests                          (68,302)      (143,686)      (146,827)      (198,668)
Distributable income                       8,894,989      3,845,612     15,161,054      5,479,922
Distributions declared                    (8,894,989)    (3,845,612)   (15,161,054)    (5,479,922)
                                         -----------    -----------   ------------    -----------
Total Trust Corpus                       $ 2,743,151    $ 3,137,915   $  2,743,151    $ 3,137,915
                                         ===========    ===========   ============    ===========
</TABLE>

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


                                      -5-
<PAGE>   6


PERMIAN BASIN ROYALTY TRUST

NOTES TO CONDENSED FINANCIAL STATEMENTS (UNAUDITED)
--------------------------------------------------------------------------------


1.    BASIS OF ACCOUNTING

      The Permian Basin Royalty Trust ("Trust") was established as of November
      1, 1980. The net overriding royalties conveyed to the Trust include: (1) a
      75% net overriding royalty carved out of Southland Royalty Company'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 Company'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. The financial
      statements of the Trust are prepared on the following basis:

      o  Royalty income recorded for a month is the amount computed and paid to
         Bank of America, N.A. ("Trustee") as Trustee for the Trust by the
         interest owners: Burlington Resources Oil & Gas Company ("BROG") for
         the Waddell Ranch properties and Riverhill Energy Corporation
         ("Riverhill Energy"), formerly a wholly owned subsidiary of Riverhill
         Capital Corporation ("Riverhill Capital") and formerly an affiliate of
         Coastal Management Corporation ("CMC"), for the Texas Royalty
         properties. CMC currently conducts all field, technical and accounting
         operations on behalf of BROG with regard to the Waddell Ranch
         properties. CMC also conducts the accounting operations for the Texas
         Royalty properties on behalf of Riverhill Energy. Royalty income
         consists of the amounts received by the owners of the interest burdened
         by the net overriding royalty interests ("Royalties") from the sale of
         production less accrued production costs, development and drilling
         costs, applicable taxes, operating charges, and other costs and
         deductions multiplied by 75% in the case of the Waddell Ranch
         properties and 95% in the case of the Texas Royalty properties.

         As was previously reported, in February 1997, BROG sold its interest in
         the Texas Royalty properties to Riverhill Energy.

         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.

      o  Trust expenses recorded are based on liabilities paid and cash reserves
         established out of cash received or borrowed funds for liabilities and
         contingencies.

      o  Distributions to Unit holders are recorded when declared by the
         Trustee.

      o  Royalty income is computed separately for each of the conveyances under
         which the Royalties were conveyed to the Trust. If monthly costs exceed
         revenues for any conveyance ("excess costs"), such excess cannot reduce
         royalty income from other conveyances, but is carried forward with
         accrued interest to be recovered from future net proceeds of that
         conveyance (see Note 3).

     The financial statements of the Trust differ from financial statements
     prepared in accordance with accounting principles generally accepted in the
     United States of America ("GAAP") because revenues are not accrued in the
     month of production and certain cash reserves may be established for
     contingencies which would not be accrued


                                      -6-
<PAGE>   7
      in financial statements. Amortization of the Royalties calculated on a
      unit-of-production basis is charged directly to trust corpus.

      On July 5, 1999, NationsBank, N.A., Trustee of the Permian Basin Royalty
      Trust, legally changed its name to Bank of America, N.A. On July 23, 1999,
      Bank of America, N.A. (formerly known as NationsBank, N.A.) was merged
      with and into Bank of America NT&SA, with the resulting entity being
      called Bank of America, N.A. As a result, immediately following the close
      of business on July 23, 1999, the remaining legal entity was Bank of
      America, N.A. As a result of such merger, the Trustee of the Trust is Bank
      of America, N.A., successor by merger to NationsBank, N.A.

2.    FEDERAL INCOME TAXES

      For Federal income tax purposes, the Trust constitutes a fixed investment
      trust which is taxed as a grantor trust. A grantor trust is not subject to
      tax at the trust level. The Unit holders are considered to own the Trust's
      income and principal as though no trust were in existence. The income of
      the Trust is deemed to have been received or accrued by each Unit holder
      at the time such income is received or accrued by the Trust and not when
      distributed by the Trust.

      The Royalties constitute "economic interests" in oil and gas properties
      for Federal income tax purposes. Unit holders must report their share of
      the revenues from the Royalties as ordinary income from oil and gas
      royalties and are entitled to claim depletion with respect to such income.

      The Trust has on file technical advice memoranda confirming the tax
      treatment described above.

      The classification of the Trust's income for purposes of the passive loss
      rules may be important to a Unit holder. As a result of the Tax Reform Act
      of 1986, royalty income will generally be treated as portfolio income and
      will not offset passive losses.

3.    EXCESS COSTS

      In the calculation of royalty income for the months of June through
      December 1998, costs exceeded revenues for the Waddell Ranch properties
      underlying the Waddell Ranch Net Overriding Royalty Conveyance by
      $1,218,732. Such excess costs were recovered from net proceeds of the
      underlying Waddell Ranch properties during the first quarter of 1999 and
      these properties are again contributing Trust royalty income.

                                     ******


                                      -7-
<PAGE>   8


ITEM 2.  TRUSTEE'S DISCUSSION AND ANALYSIS

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," "predict,"
"anticipate," "goal," "should," "assume," "believe," or other words that convey
the uncertainty of future events or outcomes.

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
Trustee has no reason to believe that there was any effect of the Year 2000
significant to the Trust or its vendors. In the event the Trustee learns that a
vendor's system was affected, the Trustee will assess the potential risk and
develop contingency plans at that time.


                                      -8-
<PAGE>   9
THREE MONTHS ENDED JUNE 30, 2000 AND 1999

For the quarter ended June 30, 2000 royalty income received by the Trust
amounted to $9,037,360 compared to royalty income of $3,957,301 during the
second quarter of 1999. The increase in royalty income is primarily attributable
to an increase in average oil and gas prices and production offset by a
increase in allocated capital expenditures compared to the second quarter of
1999.

Interest income for the quarter ended June 30, 2000, was $16,475 compared to
$4,988 during the second quarter of 1999. The increase in interest income is
primarily attributable to an increase in funds available for investment. General
and administrative expenses during the second quarter of 2000 amounted to
$158,847 compared to $116,677 during the first quarter of 1999. The increase in
general and administrative expenses can be primarily attributed to timing
differences in the receipt and payment of these expenses.

These transactions resulted in distributable income for the quarter ended June
30, 2000 of $8,894,989 or $.190844 per Unit of beneficial interest.
Distributions of $.063643, $.064140 and $.063060 per Unit were made to Unit
holders of record as of April 28, May 31 and June 30, 2000, respectively. For
the second quarter of 1999, distributable income was $3,845,612 or $.082509 per
Unit of beneficial interest.

Royalty income for the Trust for the second quarter of the calendar year is
associated with actual oil and gas production for the period of February,
March and April 2000 from the properties from which the Trust's net
overriding royalty interests ("Royalties") were carved. Oil and gas sales
attributable to the Royalties and the properties from which the Royalties were
carved are as follows:

<TABLE>
<CAPTION>
                                                            Second Quarter
                                                       -----------------------
                                                          2000         1999
<S>                                                    <C>          <C>
ROYALTIES:
Oil sales (Bbls)                                          231,731      230,223
Gas sales (Mcf)                                           858,916      820,461

PROPERTIES FROM WHICH THE ROYALTIES WERE CARVED:
Oil:
   Total oil sales (Bbls)                                 366,546      430,636
   Average per day (Bbls)                                   4,073        4,839
   Average price per Bbl                               $    28.94   $    11.88
Gas:
   Total gas sales (Mcf)                                1,481,134    1,706,705
   Average per day (Mcf)                                   16,457       19,176
   Average price per Mcf                               $     3.31   $     1.70
</TABLE>

The posted price of oil increased to an average price per barrel of $28.94 in
the second quarter of 2000, compared to $11.88 in the second quarter of 1999.
The Trustee has been advised by BROG that for the period August 1, 1993, through
March 31, 2000, the oil from the Waddell Ranch properties was being sold under a
competitive bid to a third party. The increase in the average price of gas from
$1.70 in the second quarter of 1999 to $3.31 in the second quarter of 2000 is
primarily attributable to an increase in the spot prices of natural gas.

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 in the Royalties


                                      -9-
<PAGE>   10
section of the above table do not provide a meaningful comparison. The oil and
gas sales from the properties from which the Royalties are carved decreased
for the applicable period in 2000 compared to 1999.

Capital expenditures for drilling, remedial and maintenance activities on the
Waddell Ranch properties during the second quarter of 2000 totaled $1,669,000 as
compared to $57,000 for the second quarter of 1999. BROG has informed the
Trustee that the 2000 capital expenditures budget has been revised to $14.2
million for the Waddell Ranch. The total amount of capital expenditures for 1999
was $1.1 million. Through the second quarter of 2000, capital expenditures of
$3.4 million have been expended.

The Trustee has been advised that there were no wells completed or in progress
during the three months ended June 30, 2000 on the Waddell Ranch properties.
For the three months ended June 30, 1999, there were no gross wells completed
and there were no wells in progress.

Lease operating expense and property taxes totaled $1.9 million for the second
quarter of 2000, compared to $2.6 million in the second quarter of 1999 on the
Waddell Ranch properties. This decrease is primarily attributable to more
efficient field operations on the Waddell Ranch properties.


                                      -10-
<PAGE>   11
SIX MONTHS ENDED JUNE 30, 2000 AND 1999

For the six months ended June 30, 2000, royalty income received by the Trust
amounted to $15,410,417 compared to royalty income of $5,733,261 for the six
months ended June 30, 1999. The increase in royalty income is primarily due to a
increase in oil and gas prices in the first six months of 2000, compared to the
first six months in 1999, offsetting an increase in allocated capital
expenditures in the first six months of 2000. In the calculation of royalty
income for the month of June 1998, costs exceeded revenues for the Waddell Ranch
properties underlying the Waddell Ranch Net Overriding Royalty Conveyance by
$396,012. Such excess costs were recovered from net proceeds of the underlying
Waddell Ranch properties during the first quarter of 1999 and these properties
are again contributing trust royalty income. Interest income for the six months
ended June 30, 2000 was $33,304 compared to $7,001 during the six months ended
June 30, 1999. The increase in interest income is attributable primarily to a
increase in funds available for investment. General and administrative expenses
for the six months ended June 30, 2000 were $282,668. During the six months
ended June 30, 1999, general and administrative expenses were $260,340. The
increase in general and administrative expenses is primarily due to timing
differences in the receipt and payment of these expenses.

These transactions resulted in distributable income for the six months ended
June 30, 2000 of $15,161,053 or $.325283 per Unit. For the six months ended
June 30, 1999, distributable income was $5,479,922 or $.117573 per Unit.

Royalty income for the Trust for the period ended June 30, 2000 is associated
with actual oil and gas production for the period November 1999 through April
2000 from the properties from which the Royalties were carved. Oil and gas
production attributable to the Royalties and the properties from which the
Royalties were carved are as follows:

<TABLE>
<CAPTION>
                                                         FIRST SIX MONTHS
                                                      ----------------------
                                                          2000       1999
<S>                                                   <C>         <C>
ROYALTIES:
Oil sales (Bbls)                                         426,579     353,921
Gas sales (Mcf)                                        1,579,159   1,255,623

PROPERTIES FROM WHICH THE ROYALTIES WERE CARVED:
Oil:
  Total oil sales (Bbls)                                 741,935     885,262
  Average per day (Bbls)                                   4,077       4,891
  Average price per Bbl                               $    26.26  $    10.78
Gas:
  Total gas sales (Mcf)                                3,000,946   3,534,007
  Average per day (Mcf)                                   16,489      19,525
  Average price per Mcf                               $     3.10  $     1.76
</TABLE>

The average price of oil increased during the six months ended June 30, 2000,
compared to the same period in 1999 was $26.26 per barrel as compared to $10.78
per barrel. The increase in the average price of oil is primarily due to
increases in the posted price for oil. The increase in the average price of gas
from $1.76 per Mcf for the six months ended June 30, 1999 to $3.10 per Mcf for
the six months ended June 30, 2000 is primarily the result of a increase in the
spot prices of natural gas.

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 in the Royalties


                                      -11-
<PAGE>   12
section of the above table do not provide a meaningful comparison. The oil and
gas sales from the properties from which the Royalties are carved decreased for
the applicable period of 2000 compared to 1999.

The Trust has been advised that no gross and no net productive oil wells on the
Waddell Ranch properties were drilled and completed during the six months ended
June 30, 2000, and that 6 gross 2.63 net productive oil wells on the Waddell
Ranch properties were drilled and com pleted during the six months ended June
30, 1999. Capital expenditures for the Waddell Ranch properties for the six
months ended June 30, 2000 totaled $3,386,000 compared to $517,000 for the same
period in 1999. BROG has previously advised the Trust that the remaining 2000
capital expenditures budget for the Waddell Ranch properties is $10.8 million.

Lease operating expense and property taxes totaled $5.0 million in 2000 compared
to $5.7 million in 1999. The decrease in lease operating expense is primarily
attributable to more efficient field operations on the Waddell Ranch properties.



                                      -12-
<PAGE>   13


CALCULATION OF ROYALTY INCOME

         The Trust's royalty income is computed as a percentage of the net
         profit from the operation of the properties in which the Trust owns net
         overriding royalty interests. These percentages of net profits are 75%
         and 95% in the case of the Waddell Ranch properties and the Texas
         Royalty properties, respectively. Royalty income received by the Trust
         for the three months ended June 30, 2000 and 1999 respectively, were
         computed as shown in the table below:


<TABLE>
<CAPTION>
                                                          THREE MONTHS ENDED JUNE 30,
                                            ----------------------------------------------------
                                                       2000                      1999
                                            -------------------------   ------------------------
                                             WADDELL        TEXAS        WADDELL        TEXAS
                                              RANCH        ROYALTY        RANCH        ROYALTY
                                            PROPERTIES    PROPERTIES    PROPERTIES    PROPERTIES
<S>                                         <C>           <C>           <C>           <C>
Gross proceeds of sales from
 properties from which the net
 overriding royalties were carved:
 Oil proceeds                               $ 8,168,047   $ 2,438,493   $ 3,966,511   $ 1,149,530
 Gas proceeds                                 4,262,742       637,223     2,558,968       345,283
 Other revenues
                                            -----------   -----------   -----------   -----------
           Total                             12,430,789     3,075,716     6,525,479     1,494,813
                                            -----------   -----------   -----------   -----------

Less:
 Severance tax:
   Oil                                          334,369        87,207       161,681        37,416
   Gas                                          275,865        32,390       190,947         8,708
 Lease operating expense and
   property tax:
   Oil and gas                                1,860,217       (11,377)    2,464,194       149,765
 Capital expenditures                         1,669,353                      57,292
 Other expense                                                                             16,000
                                            -----------   -----------   -----------   -----------

           Total                              4,139,804       108,220     2,874,114       211,889
                                            -----------   -----------   -----------   -----------

Net profits                                   8,290,985     2,967,496     3,651,365     1,282,924
Net overriding royalty interests                     75%           95%           75%           95%
                                            -----------   -----------   -----------   -----------

Royalty income                              $ 6,218,239   $ 2,819,121   $ 2,738,523   $ 1,218,778
                                            ===========   ===========   ===========   ===========
</TABLE>


                                      -13-
<PAGE>   14



ITEM 3.  QUALITATIVE AND QUANTITATIVE DISCLOSURES ABOUT MARKET RISK

Not applicable.


                                      -14-
<PAGE>   15


                           PART II - OTHER INFORMATION


Items 1 through 5.

Not applicable.


Item 6.        Exhibits and Reports on Form 8-K

                (a)  Exhibits

                     (4)(a)  Permian Basin Royalty Trust Indenture dated
                             November 3, 1980, between Southland Royalty Company
                             (now Burlington Resources Oil & Gas Company) and
                             The First National Bank of Fort Worth (now Bank of
                             America, 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.

                     (4)(b)  Net Overriding Royalty Conveyance (Permian Basin
                             Royalty Trust) from Southland Royalty Company (now
                             Burlington Resources Oil & Gas Company) to The
                             First National Bank of Fort Worth (now Bank of
                             America, 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.

                     (4)(c)  Net Overriding Royalty Conveyance (Permian Basin
                             Royalty Trust - Waddell Ranch) from Southland
                             Royalty Company (now Burlington Resources Oil & Gas
                             Company) to The First National Bank of Fort Worth
                             (now Bank of America, 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.

                     (27)    Financial Data Schedule

                (b)  Reports on Form 8-K

                     No reports were filed during the quarter ended June 30,
                2000.


                                      -15-
<PAGE>   16


                                   SIGNATURES


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.

                                           BANK OF AMERICA, N.A.,
                                            TRUSTEE FOR THE
                                            PERMIAN BASIN ROYALTY TRUST




                                           By    /s/ RON E. HOOPER
                                              --------------------------------
                                                      Ron E. Hooper
                                                      Vice President

Date:  August 10, 2000


              (The Trust has no directors or executive officers.)


                                      -16-
<PAGE>   17


                               INDEX TO EXHIBITS


<TABLE>
<CAPTION>
                                                                                                  Sequentially
               Exhibit                                                                              Numbered
               Number                                Exhibit                                          Page
<S>                       <C>                                                                     <C>
               (4)(a)     Permian Basin Royalty Trust Indenture dated November
                          3, 1980, between Southland Royalty Company (now
                          Burlington Resources Oil & Gas Company) and The First
                          National Bank of Fort Worth (now Bank of America,
                          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 (now
                          Burlington Resources Oil & Gas Company) to The First
                          National Bank of Fort Worth (now Bank of America,
                          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 (now Burlington Resources Oil & Gas Company)
                          to The First National Bank of Fort Worth (now Bank of
                          America, 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.*



               (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, Bank of America, N.A.,
    P. O. Box 830650, Dallas, Texas 75202.

**  Filed herewith.