<PAGE>   1
 
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                                   FORM 10-K
 
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
[X]   FOR THE FISCAL YEAR ENDED DECEMBER 31, 1998
 
                                       OR
 
[ ]   FOR THE TRANSITION PERIOD FROM ________________ TO ________________ .
 
COMMISSION FILE NO. 0-8677
 
                          TIDELANDS ROYALTY TRUST "B"
             (Exact name of registrant as specified in its charter)
 
                                     TEXAS
                        (State or other jurisdiction of
                         incorporation or organization)
                                   75-6007863
                                (I.R.S. Employer
                              Identification No.)
 
                           C/O THE CORPORATE TRUSTEE:
                           NATIONSBANK OF TEXAS, N.A.
                   P.O. BOX 830241, DALLAS, TEXAS 75283-0241
              (Address of principal executive offices) (Zip Code)
 
               Registrant's telephone number, including area code
            (at the office of the Corporate Trustee): (800) 985-0794
 
          Securities registered pursuant to Section 12(b) of the Act:
 
                                      NONE
 
          Securities registered pursuant to Section 12(g) of the Act:
 
                          UNITS OF BENEFICIAL INTEREST
 
     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 __
 
     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]
 
     Aggregate market value of the Units of Beneficial Interest held by
non-affiliates of the Registrant at February 19, 1999: $4,611,669.
 
     Number of Units of Beneficial Interest outstanding as of the close of the
period covered by this report: December 31, 1998 -- 1,386,375 Units.
 
                      Documents incorporated by reference:
 
                                      NONE
 
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<PAGE>   2
 
                             CROSS REFERENCE SHEET
 
     This Form 10-K for the year ended December 31, 1998, of Tidelands Royalty
Trust "B" is not organized by conventional item numbers and headings
contemplated by Securities and Exchange Commission rules. This cross-reference
page is intended to indicate to the reader where (or under which headings)
information required under Form 10-K may be found herein.
 
<TABLE>
<CAPTION>
 FORM 10-K
ITEM NUMBERS
------------                                                               HEADINGS HEREIN
<S>          <C>                                               <C>
PART I ......................................................  General
 
Item  1.     Business........................................  The Trust, Properties
 
Item  2.     Properties......................................  Properties
 
Item  3.     Legal Proceedings...............................  Legal Matters
 
Item  4.     Submission of Matters to a Vote
             of Security Holders.............................  Unitholder Voting Matters
 
PART II .....................................................  Financial
 
Item  5.     Market for Registrant's Common Equity and
             Related Stockholder Matters.....................  Market and Investor Information
 
Item  6.     Selected Financial Data.........................  Selected Financial Data
 
Item  7.     Management's Discussion and Analysis of
               Financial Condition and Results of
               Operations....................................  Management's Discussion and Analysis of
                                                                 Financial Condition and Results of
                                                                 Operations
 
Item  7A.    Quantitative and Qualitative Disclosures About
               Market Risk...................................  Management's Discussion and Analysis of
                                                                 Financial Condition and Results of
                                                                 Operations
 
Item  8.     Financial Statements and Supplementary Data.....  Financial Statements and Supplementary
                                                                 Data
 
Item  9.     Disagreements on Accounting and Financial
             Disclosure......................................  Accounting Matters
 
PART III ....................................................  Management and Principal Unitholders
 
Item 10.     Directors and Executive Officers of the
             Registrant......................................  Administrators
 
Item 11.     Executive Compensation..........................  Management Compensation
 
Item 12.     Security Ownership of Certain Beneficial Owners
               and Management................................  Principal Unitholders
 
Item 13.     Certain Relationships and Related
               Transactions..................................  Management Compensation
 
PART IV .....................................................  Miscellaneous
 
Item 14.     Exhibits, Financial Statement Schedules, and
             Reports on Form 8-K.............................  Exhibits, Financial Statement
                                                                 Schedules, and Reports on
                                                                 Form 8-K
</TABLE>
<PAGE>   3
 
                                    GENERAL
 
                                   THE TRUST
 
     Organization. Tidelands Royalty Trust "B" ("Tidelands") is a royalty trust
created on June 1, 1954, under the laws of the State of Texas. Tidelands is not
permitted to engage in any business activity inasmuch as it was organized for
the sole purpose of providing an efficient, orderly, and practical means for the
administration and liquidation of rights to interests in any oil, gas or other
mineral leases obtained by Gulf Oil Corporation ("Gulf") in a designated area of
the Gulf of Mexico. These rights are evidenced by a contract between Tidelands'
predecessors and Gulf dated April 30, 1951 (the "1951 Contract"), which is
binding upon the assignees of Gulf. As a result of various transactions that
have occurred since 1951, the Gulf interests that were subject to the 1951
Contract now are held by Chevron Corporation ("Chevron"), Elf Acquitane, Inc.
("Elf"), and their assignees.
 
     The Tidelands Royalty Trust "B" Indenture, effective June 1, 1954, as
amended (the "Indenture"), provides that the corporate trustee is to distribute
all cash in Tidelands, less an amount reserved for the payment of accrued
liabilities and estimated future expenses, to unitholders of record on the last
business day of March, June, September, and December of each year. NationsBank
of Texas, N.A. serves as corporate trustee and Mr. Chas. G. McBurney serves as
individual trustee.
 
     The Indenture also provides that the term of the royalty trust created to
hold the rights under the 1951 Contract will expire on April 30, 2001 unless
extended by the vote of the holders of a majority of the outstanding units of
beneficial interest. See "Unitholder Voting Matters" and "Management's
Discussion and Analysis of Financial Condition and Results of
Operations -- General."
 
     Tidelands' wholly-owned subsidiary, Tidelands Royalty "B" Corporation
("Tidelands Corporation"), holds title to interests in properties subject to the
1951 Contract that are situated offshore of Louisiana. Ninety-five percent of
all oil, gas, and other mineral royalties collected by this subsidiary are paid
to Tidelands. Tidelands Corporation, like Tidelands, is prohibited from engaging
in a trade or business and does only those things necessary for the
administration and liquidation of its properties.
 
     Tidelands' only industry segment or purpose is the administration and
collection of royalties.
 
     The Contract. The 1951 Contract identifies 60 specific tracts in the Gulf
of Mexico. These tracts are not all the same size and collectively contain
approximately 1,370,000 acres (sometimes referred to herein as the "Royalty
Area"). If Chevron or Elf acquires a lease or leases on one of the 60 tracts
before April 30, 2001, and if oil or gas is produced and sold from any such
tract, then Chevron or Elf, as the case may be, will make production payments to
Tidelands in an amount equal to approximately 12.5% of the value of the oil and
gas sold from such tract until the sum of $1,500,000 has been paid on such
tract. Thereafter, Tidelands' interest in such tract will be converted to an
overriding royalty and Tidelands will receive payments equal to approximately
4.17% of the value of the oil and gas sold as long as the lease on such tract
exists. This interest applies to each of the 60 tracts that constitute the
Royalty Area. See "Management's Discussion and Analysis of Financial Condition
and Results of Operations."
 
     As of December 31, 1998, Chevron and others held interests in seven leases
subject to Tidelands' interests in six of the 60 tracts in the Royalty Area.
Leases on all six of such tracts contain currently-producing or shut-in wells
subject to Tidelands' interests.
 
     The 1951 Contract provides that any assignment by Gulf (currently Chevron
and Elf) of any leases acquired by it in the Royalty Area and any assignment of
the information, data or records acquired under the 1951 Contract shall be made
subject to the production payments and the overriding royalty interests provided
therein. Chevron has assigned to other operators Chevron's interest in six
leases covering 27,011 acres in the Royalty Area. Chevron has retained an
interest in one lease covering 4,364 acres in the Royalty Area. See Note 1 of
Notes to Consolidated Financial Statements.
<PAGE>   4
 
     The terms of the 1951 Contract also apply to the sale of minerals other
than oil and natural gas. However, there is no production payment due with
respect to these other minerals: the interest in other minerals is limited to an
approximately 4.17% overriding royalty.
 
     In 1998, approximately 7% of Tidelands' royalty revenues were attributable
to oil and approximately 93% were attributable to natural gas. The production
payments and royalty revenues received by the Trust in respect of natural gas
production are affected by seasonal fluctuations in demand for natural gas.
During 1998 Tidelands received royalty payments from five working interest
owners. The following table shows the percentage received each year for the past
3 years for those working interest owners accounting for over 10% of the Trust's
royalty receipts during any of the last three years:
 
<TABLE>
<CAPTION>
                        COMPANY                           1998    1997    1996
                        -------                           ----    ----    ----
<S>                                                       <C>     <C>     <C>
American Explorer.......................................   18%     --      --
Burlington Resources....................................   42%     34%     --
Chevron, USA............................................    8%     13%     30%
Pennzoil Exploration and Production Company.............   30%     41%     62%
</TABLE>
 
     Tidelands derives no revenues from foreign sources and has no export sales.
 
     Tidelands and Tidelands Corporation have no direct employees, although
Tidelands pays a portion of certain administrative expenses (including a portion
of the salary and expense of one individual). See "Management and Principal
Unitholders."
 
                                   PROPERTIES
 
     General. Tidelands is not engaged in oil and gas operations, even though
its income is based on oil and gas operations of others. Tidelands' only
income-producing property is the 1951 Contract, including the property interests
granted thereunder, which provides that payments in the nature of production
payments and overriding royalties will be made to Tidelands based on oil and gas
sales from certain leases in the Royalty Area in the Gulf of Mexico. Tidelands
does not own or directly lease any physical properties.
 
     Reserves. Tidelands' production payments and overriding royalties are
carved out of working interests in certain oil and gas leases in the Gulf of
Mexico. Tidelands does not have engineering data necessary to make an estimate
of the proved oil and gas reserves attributable thereto and is not entitled to
receive such data from the operators and/or owners of the working interests from
which Tidelands' interests are derived.
 
     Since Tidelands does not have access to this reserve information, Tidelands
is unable to compute the standardized measure of discounted future net cash
flows therefrom.
 
     No reports on oil and gas reserves were filed with any federal authority or
agency during 1998 by Tidelands.
 
     Production. Information concerning net quantities of oil and gas produced
for each of the last three fiscal years, as well as the average sales price per
unit of oil and gas produced upon which payments to Tidelands are based, is set
forth below in the following table:
 
<TABLE>
<CAPTION>
                                                         1998       1997       1996
                                                        -------    -------    -------
<S>                                                     <C>        <C>        <C>
Quantity of royalty oil and gas sold
  Oil (in barrels ("bbls")).........................      9,935     10,348      7,958
  Gas (in thousand cubic feet ("mcf"))..............    405,336    495,734    416,999
Weighted average sales price
  for royalty oil and gas sold
  Oil (per bbl)(1)..................................      $8.90     $14.04     $15.92
  Gas (per mcf).....................................      $2.81     $ 2.25     $ 2.34
</TABLE>
 
---------------
 
(1) These amounts are net of the cost of transportation from offshore leases to
     onshore receiving points.
 
                                        2
<PAGE>   5
 
     Information about average production cost (lifting cost) per unit of
production has been omitted due to its unavailability and inapplicability to
Tidelands. For more recent information regarding crude oil sales prices, see
"Management's Discussion and Analysis of Financial Condition and Results of
Operations" below.
 
     Interests in Properties. Tidelands' properties consist of production
payments and overriding royalty interests in 7 oil and gas leases covering
31,375 gross acres in the 1,370,000 acre Royalty Area. These leases are located
in the Gulf of Mexico in the Galveston, High Island, Sabine Pass and West
Cameron areas. In addition to interests in these existing leases, Tidelands is
entitled to receive an interest in any lease obtained before April 30, 2001, by
Chevron or Elf in the Royalty Area.
 
     Set forth in the table below is certain information concerning gross
productive oil and gas wells and gross leased acres in which Tidelands owns its
interests:
 
<TABLE>
<S>                                                   <C>
Gross Productive Wells --
  Oil...............................................       3
                                                          --
                                                          --
  Gas...............................................      12
                                                          --
                                                          --
Gross Leased Acres --
  Productive........................................  31,375
                                                      ======
</TABLE>
 
     Information regarding net wells or acres is not included since Tidelands
does not own any working interests.
 
     Productive Properties. Productive properties cover 31,375 gross acres under
7 different leases. These 7 leases contain 15 wells, two of which are
dual-completion wells. Three of these wells produce oil, and 12 wells have been
completed to produce natural gas and condensate. See "Present Activities."
 
     The following table contains information about the average daily production
attributable to Tidelands' interest, by field, for the six month period, from
January through June 1998, 1997 and 1996. Only fields that were producing at the
end of the six-month period are listed. Production from these fields accounted
for substantially all of Tidelands' distributable income in 1998. The
information in the table is based upon data obtained from the Petroleum
Information Corporation. The information for the period ended June 1998 is the
most recent production information available to Tidelands from the Petroleum
Information Corporation. Information for the periods ended June 1997 and 1996 is
included for comparison purposes.
 
<TABLE>
<CAPTION>
                                                         NET MCF GAS & OIL
                                            YEAR       EQUIVALENT PER DAY(1)
                                           FIRST      -----------------------
                 FIELD                    PRODUCED    1998     1997     1996
                 -----                    --------    -----    -----    -----
<S>                                       <C>         <C>      <C>      <C>
Offshore Texas
  Galveston Block 303...................    1987       713      450      108
  High Island Block 128.................    1989        37      130      416
Offshore Louisiana
  Sabine Pass Block 13..................    1981       222      177      112
  West Cameron Block 165................    1969        97      372      802
  West Cameron Block 225................    1969        33        4        1
  West Cameron Block 333................    1978        10       47       26
</TABLE>
 
---------------
 
(1) Net oil production is reflected in the amount of its mcf equivalent of
    natural gas on a btu basis.
 
     Royalty Area. The State of Texas and the United States own all the mineral
rights in the Royalty Area and possess the exclusive right to lease their
respective areas for oil, gas and other mineral development. Leases are granted
on the basis of sealed competitive bids at sales held on specified dates.
Companies other than Chevron and Elf have acquired leases in the Royalty Area
and it is estimated that approximately 1,000,000 of the 1,370,000 acres are
leased. This leaves approximately 370,000 acres available for leasing in the
Royalty Area. The bulk of the unleased acreage is located in an area about 50
miles southeast of Galveston, Texas.
 
                                        3
<PAGE>   6
 
     Present Activities. Tidelands currently receives royalties from oil and
natural gas sold from all of the leases in the Royalty Area, although delivery
quantities are subject to seasonal demand.
 
     Published reports indicate that during 1998, Chevron and Elf did not bid on
any lease located in the Royalty Area in the two federal lease sales held during
that year.
 
     The Minerals Management Service of the United States Department of the
Interior will receive bids in a lease sale in the Central Gulf area on March 17,
1999. The sale covers a portion of the Royalty Area that lies in the West
Cameron area.
 
     Tidelands is not obligated to provide any fixed and determinable quantities
of oil or gas in the future under any existing contracts or agreements.
 
     Difficulty in Obtaining Certain Data. Tidelands' only activities are the
collection and distribution of revenues from production payments and overriding
royalties on certain oil and gas leases in the Gulf of Mexico, pursuant to
agreements between Tidelands' predecessors and Gulf and its transferees and
assignees. The leases that are subject to the interests held by Tidelands are
owned by Chevron or other oil and gas production and development companies.
Certain information as to reserves, availability of oil and gas, development
plans for undeveloped acreage, and other matters, with respect to the particular
leases subject to Tidelands' interests lies solely within the knowledge of these
other companies. Engineering data, if any, regarding these leaseholds would have
been compiled principally by or for the operators of these leaseholds and
Tidelands believes that it would not be provided access to such information.
Because of this, it appears that unreasonable effort and expense would be
involved in seeking to obtain all the information set forth under applicable
Securities and Exchange Commission rules and guides.
 
     Furthermore, certain information concerning net acreage and net wells has
been omitted due to the nature of Tidelands' interests (i.e., production
payments and overriding royalties) in such leaseholds. Also, certain information
concerning drilling results specified in Guide 2 of the Securities Exchange Act
of 1934 Industry Guides has been omitted since Tidelands has no control over
exploration decisions and such information is thus deemed irrelevant in
discussing operations within the control of Tidelands' administrators.
 
                                 LEGAL MATTERS
 
     Neither Tidelands nor Tidelands Corporation, nor any of their respective
properties, is a party to or subject to any material pending litigation as of
the date hereof.
 
                                        4
<PAGE>   7
 
                           UNITHOLDER VOTING MATTERS
 
     During 1998, no matter was submitted by Tidelands to a vote of its
unitholders.
 
     Under the terms of the Indenture, the unitholders are limited solely to the
following rights and powers with respect to their units: (1) to elect a
replacement Trustee by vote of the holders of a majority of the outstanding
units of beneficial interest for any Trustee vacancy occurring; (2) to inspect
the books and records of Tidelands at reasonable intervals and during reasonable
business hours; (3) by vote of the holders of a majority of the outstanding
units of beneficial interest, to extend the term of Tidelands for consecutive
twenty (20) year intervals; (4) by vote of the holders of a majority of the
outstanding units of beneficial interest, to create one or more corporations to
receive and hold title to Tidelands' assets, provided that there is no objecting
unitholder; (5) to terminate Tidelands so long as the holders of eighty percent
(80%) of the outstanding units of beneficial ownership consent; (6) to remove
the Trustees or their successors by vote of the holders of a majority of the
outstanding units of beneficial interest; (7) with the consent of the holders of
ten percent (10%) of the outstanding units of beneficial ownership, to call a
meeting of the unitholders in order to take any action that may be validly taken
by the unitholders; and (8) to amend the Indenture, so long as the holders of
eighty percent (80%) of the outstanding units of beneficial ownership consent,
provided that (a) no amendment shall change the nature of Tidelands from that of
a purely ministerial trust, (b) there shall be no change in the rights, duties,
or responsibilities of either Trustee without the consent of such Trustee, and
(c) there shall be no change in the purpose of Tidelands or in the substantive
rights of unitholders if one unitholder objects. Under the Indenture, the
unitholders are not permitted to exercise any additional powers with respect to
the management or operation of Tidelands.
 
     The Indenture provides that the sole interest of each unitholder during the
existence of Tidelands shall be his right to receive his proportionate part of
the net proceeds in the form of money in the hands of the corporate trustee that
such unitholder is entitled to receive, and upon termination of Tidelands, to
receive conveyances or assignments of his share of the property then
constituting the trust estate. No unitholder has the right to call for or demand
or secure any partition during the existence of Tidelands.
 
                                        5
<PAGE>   8
 
                                   FINANCIAL
 
                        MARKET AND INVESTOR INFORMATION
 
     Tidelands is authorized to issue 1,386,525 units of beneficial interest;
1,386,375 units were held by 436 unitholders of record as of March 11, 1999. The
remaining 150 units are reserved to be issued to specific parties if and when
they decide to transfer their rights under the 1951 Contract to Tidelands. There
were no changes in the number of outstanding units of beneficial interest during
1998.
 
     The units of beneficial interest in Tidelands trade in the over-the-counter
market and are listed in the NASD's Bulletin Board under the symbol "TIRTZ". The
following table presents information obtained from the National Quotation
Bureau, Inc. as to the high and low bid prices and includes distributions to
unitholders, by quarter, for the past two years:
 
<TABLE>
<CAPTION>
                                          BID QUOTATION
                CALENDAR                  --------------      DISTRIBUTIONS
                  YEAR                    HIGH      LOW        (PER UNIT)
                --------                  -----    -----      -------------
<S>                                       <C>      <C>        <C>
1998
  First quarter.........................  $7.00    $6.00          $.19
  Second quarter........................   6.13     5.75           .24
  Third quarter.........................   5.88     4.88           .29
  Fourth quarter........................   6.00     4.88           .08
1997
  First quarter.........................  $5.75    $5.00          $.17
  Second quarter........................   7.00     5.14           .13
  Third quarter.........................   8.50     5.88           .09
  Fourth quarter........................   7.88     7.00           .45
</TABLE>
 
     Such over-the-counter market quotations reflect interdealer prices without
retail mark-up, mark-down or commission and may not necessarily represent actual
transactions.
 
     Tidelands must distribute to its unitholders all cash accumulated each
quarter, less an amount reserved for accrued liabilities and estimated future
expenses. Such distributions have been made since the third quarter of 1977 and
will continue so long as the income from oil and gas royalties exceeds
administrative costs.
 
     The Securities and Exchange Commission has neither approved nor disapproved
Tidelands' Annual Report for its year ended December 31, 1998, nor has it passed
upon its accuracy or adequacy. While Tidelands' complete Form 10-K (excluding
exhibits) for the year ended December 31, 1998, is included in Tidelands' 1998
Annual Report, a copy of such Form 10-K (without exhibits) is available without
charge to interested parties. There will be copying and mailing charges for
copies of any exhibits requested. Written requests should be directed to Ms.
Jane J. Shea, NationsBank, N.A., P.O. Box 830241, Dallas, Texas 75283-0241.
 
                            SELECTED FINANCIAL DATA
 
<TABLE>
<CAPTION>
                                          1998         1997         1996         1995         1994
                                       ----------   ----------   ----------   ----------   ----------
<S>                                    <C>          <C>          <C>          <C>          <C>
Income -- oil and gas royalties......  $1,228,313   $1,262,876   $1,103,926   $  978,172   $1,555,352
Net income...........................  $1,192,688   $1,234,986   $1,076,335   $  965,004   $1,499,244
Net income per unit..................        $.86         $.89         $.78         $.70        $1.08
Distributions to unitholders.........  $1,103,637   $1,165,924   $1,029,524   $  960,169   $2,142,298
Distributions per unit...............        $.80         $.84         $.74         $.69        $1.55
Total assets.........................  $1,645,925   $2,421,226   $1,945,260   $1,905,164   $1,909,605
</TABLE>
 
                                        6
<PAGE>   9
 
               MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                      CONDITION AND RESULTS OF OPERATIONS
 
     Liquidity and Capital Resources. Tidelands' only business purpose is to
collect revenues from its royalty-type interests in oil and gas leases, pay
administrative expenses, and distribute the remaining revenues to its
unitholders. Tidelands can neither purchase additional properties nor dispose of
its existing properties. Because of these limitations Tidelands does not require
long term or short term capital. Furthermore, because all Tidelands' revenues
are invested in liquid funds pending distribution, Tidelands does not face
liquidity problems.
 
     Results of Operations. Tidelands' income consists primarily of oil and gas
royalties and is based on the value at the wellhead of Tidelands' percentage
interest in oil and gas sold without reduction for production expenses. Value at
the wellhead for oil is the purchasers' posted price at its receiving point
onshore, less the cost of transportation from the offshore lease to the onshore
receiving point. Value at the wellhead for natural gas is based upon the
proceeds from sales under arms-length agreements. In the event an agreement is
not arms-length in nature, the value is based upon current market prices.
 
  General
 
     Distributions to unitholders amounted to $.80 per unit in 1998, a decrease
of $.04 over the $.84 distributed in 1997.
 
     The average daily production of oil and gas (stated in mcf equivalents) to
Tidelands' interest was 1,693 mcf per day in the first quarter of 1998, and
increased to 1,772 mcf per day in the fourth quarter, primarily due to increased
production of oil and condensate.
 
     Natural gas prices for gas produced and sold decreased 12% in 1998 over the
prices of 1997. In 1997 the average price received for gas produced and sold was
$2.25 per mcf and in 1998 the price decreased to $1.97.
 
     Royalties on oil and condensate amounted to 7% of Tidelands' revenue in
1998. The average price received by Tidelands for oil in 1997 amounted to $14.04
per barrel and decreased to $8.90 per barrel in 1998. Three oil wells on Sabine
Pass Block 13 account for most of the revenue from oil. The posted price for oil
delivered onshore from this block averaged $13.55 in 1998, but Tidelands'
average price was less because of the high cost of transporting the oil from the
production platform to the onshore market.
 
     Each of Tidelands' producing properties has paid out its $1,500,000
production payment and, therefore, Tidelands' present royalty interests
(4.17%)in such properties will not be further reduced.
 
     Tidelands has retained a funded reserve for possible royalty overpayments
received by Tidelands in various years from 1988 through 1993. During the year
ended December 31, 1998 Tidelands restored to income $340,485 of its contingency
reserve that management determined was no longer needed to cover refunds that
may be required upon redetermination of gas prices for royalty payments in prior
periods. Net income per unit was increased $.25 by this decision.
 
     Tidelands' revenues are derived from the oil and gas production activities
of unrelated parties. Tidelands' revenues and distributions fluctuate from
period to period based upon factors beyond Tidelands' control, including without
limitation the number of leases bid on and obtained by parties subject to the
1951 Contract, the number of productive wells drilled on leases subject to
Tidelands' interest, the level of production over time from such wells and the
prices at which the oil and gas from such wells is sold. Tidelands believes that
it will continue to have revenues sufficient to permit distributions to be made
to unitholders for the foreseeable future, although no assurance can be made
regarding the amounts thereof. The foregoing sentence is a forward-looking
statement. Factors that might cause actual results to differ from expected
results include reductions in prices or demand for oil and gas, which might then
lead to decreased production; reductions in production due to depletion of
existing wells or disruptions in service, including as the result of storm
damage, blowouts or other production accidents, and geological changes such as
cratering of productive formations; expiration or release of leases subject to
Tidelands' interests; and the discontinuation by parties subject to the 1951
Contract of their efforts to obtain leases in the Royalty Area.
 
                                        7
<PAGE>   10
 
     Important aspects of the Trust's operations are conducted by third parties.
These include the production and sale of oil and gas and the calculation and
payment of royalty payments to the Trust, which are conducted by oil and gas
companies that lease tracts subject to the Trust's interests. Similarly, the
Trust's distributions are processed and paid by The Bank of New York as the
agent for the trustee of the Trust. Any disruption of the Trust's operations
that results from Year 2000 problems of these third parties could have a
material adverse effect on the Trust. The Trust does not have access to
information that would permit the Trust to determine the status of these third
parties' efforts to analyze and address Year 2000 issues. The Trust intends to
monitor these parties' public announcements and disclosure regarding Year 2000
issues, and to seek direct assurances where appropriate, in an effort to ensure
that these parties address Year 2000 issues that could adversely affect the
Trust.
 
     Tidelands does not have any reportable quantitative or qualitative market
risk disclosure.
 
OIL AND GAS ROYALTIES -- 1998 AND 1997
 
     Income from oil and gas royalties decreased 3% in 1998 as compared to 1997.
Gas royalties increased 2% and accounted for 93% of income for 1998. These
increases primarily were caused by the increase in revenue from the reduction of
the reserve for gas price adjustments. See "-- General." Average oil prices
decreased 37% and average gas prices decreased 12%.
 
     The following table presents comparative operating data which reflects
these underlying circumstances.
 
                           COMPARATIVE OPERATING DATA
 
<TABLE>
<CAPTION>
                                                                                CHANGE FROM
                                                                                1997 TO 1998
                                                                             ------------------
                                                      1998         1997       AMOUNT    PERCENT
                                                   ----------   ----------   --------   -------
<S>                                                <C>          <C>          <C>        <C>
Income:
  Oil royalties(1)...............................  $   88,389   $  145,259   $(56,870)    (39)%
  Gas royalties..................................   1,139,924    1,117,617     22,307       2%
                                                   ----------   ----------   --------
                                                   $1,228,313   $1,262,876   $(34,563)     (3)%
                                                   ==========   ==========   ========
Net production quantities
  Oil (bbls).....................................       9,935       10,348   $   (413)     (4)%
  Gas (mcf)......................................     405,336      495,734    (90,398)    (18)%
Average net prices
  Oil(1).........................................  $     8.90   $    14.04   $  (5.14)    (37)%
  Gas(2).........................................  $     2.81   $     2.25   $    .56      25%
</TABLE>
 
---------------
 
(1) These amounts are net of the cost of transportation from offshore leases to
    onshore receiving points.
 
(2) The average price in 1998 includes $.84 per mcf attributable to the $340,485
    reserve reduction. The average price for gas produced and sold in 1998 was
    $1.97.
 
OIL AND GAS ROYALTIES -- 1997 AND 1996
 
     Income from oil and gas royalties increased 14% in 1997 as compared to
1996. Gas royalties accounted for 88% of income from royalties in 1997. The
price received for gas during 1997 decreased 4% from 1996 to $2.25 per mcf.
 
                                        8
<PAGE>   11
 
     The following table presents comparative operating data which reflects
these underlying circumstances.
 
                           COMPARATIVE OPERATING DATA
 
<TABLE>
<CAPTION>
                                                                       CHANGE FROM
                                                                       1996 TO 1997
                                                                    ------------------
                                             1997         1996       AMOUNT    PERCENT
                                          ----------   ----------   --------   -------
<S>                                       <C>          <C>          <C>        <C>
Income:
  Oil royalties(1)......................  $  145,259   $  126,680   $ 18,579      15%
  Gas royalties.........................   1,117,617      977,246    140,371      14%
                                          ----------   ----------   --------
                                          $1,262,876   $1,103,926   $158,950      14%
                                          ==========   ==========   ========
Net production quantities
  Oil (bbls)............................      10,348        7,958      2,390      30%
  Gas (mcf).............................     495,734      416,999     78,735      19%
Average net prices
  Oil(1)................................  $    14.04   $    15.92   $  (1.88)   (12)%
  Gas...................................  $     2.25   $     2.34   $   (.09)    (4)%
</TABLE>
 
---------------
 
(1) These amounts are net of the cost of transportation from offshore leases to
    onshore receiving points.
 
                  FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA
 
     Tidelands' consolidated financial statements listed in the following index,
together with the related notes and the report of KPMG LLP, independent
certified public accountants, are presented on pages 11-17 hereof:
 
<TABLE>
<CAPTION>
                                                                     PAGE
                                                                    ------
<S> <C>                                                             <C>
--  Independent Auditors' Report................................     F-1
 
--  Consolidated Balance Sheets as of December 31, 1998 and
      1997......................................................     F-2
 
--  Consolidated Statements of Income and Undistributed Income
      for the Three Years Ended December 31, 1998...............     F-3
 
--  Consolidated Statements of Cash Flows for the Three Years
      Ended December 31, 1998...................................     F-4
 
--  Notes to Consolidated Financial Statements..................     F-5
</TABLE>
 
     All schedules have been omitted because they are not required or because
the required information is shown in the consolidated financial statements or
notes thereto.
 
                               ACCOUNTING MATTERS
 
     During 1998 and 1997 there were no disagreements by Tidelands with its
principal accountants on any matter of accounting principles or practices or
financial statement disclosure.
 
                                        9
<PAGE>   12
 
                      MANAGEMENT AND PRINCIPAL UNITHOLDERS
 
                                 ADMINISTRATORS
 
     Tidelands was created by a trust agreement effective June 1, 1954 and there
is no provision for the election of directors and officers. However, the
agreement does provide for the appointment of an individual trustee and a
corporate trustee.
 
     NationsBank, N.A. is the corporate trustee.
 
     During 1998, Chas. G. McBurney, the individual trustee, resigned for
personal reasons. Although the instruments pursuant to which the Trust were
created provide for an individual trustee, none of the individuals identified
therein as possible individual trustees currently are available to serve as the
individual trustee. Management of the Trust believes that the duties of the
individual trustee can be administered by Mr. R. Ray Bell, the principal
accounting officer of the Trust. Management of the Trust also believes that the
Trust likely would incur substantial expenses in recruiting and electing a new
individual trustee. The indenture (the "Indenture") pursuant to which the Trust
was created will expire on April 30, 2001 unless extended by vote of the holders
of a majority of the outstanding units of beneficial interest in the Trust. In
order to reduce the expenses to be incurred in electing a new individual
trustee, the Trust may elect to submit such matter to a vote of the holders of
units of beneficial interest in conjunction with the submission to such holders
of the question where to extend the term of the Indenture. Management of the
Trust has not determined when, or if, either such matter will be presented to
the holders of units of beneficial interest.
 
     The trustees have entered into an arrangement with Marine Petroleum
Corporation (a wholly-owned subsidiary of Marine Petroleum Trust, parent of
Tidelands) to share certain administrative expenses. Mr. R. Ray Bell may be
considered a significant employee of Tidelands even though he is not directly
employed by Tidelands or Tidelands Corporation. Mr. Bell has been involved in
the administration of Tidelands since its inception. He is 71 years old, and
since July 1, 1977, Mr. Bell has been employed by Marine Petroleum Corporation,
a subsidiary of Marine Petroleum Trust, as vice president and director. Mr. Bell
will serve in such capacities until the next annual meeting of directors of
Marine Petroleum Corporation or until his successor is elected and qualified.
 
                            MANAGEMENT COMPENSATION
 
     During Tidelands' fiscal year ended December 31, 1998, Tidelands paid or
accrued fees of $24,135 to NationsBank, N.A., as corporate trustee. The
individual trustee served without compensation.
 
     During Tidelands' fiscal year ended December 31, 1998, Tidelands paid
$35,610 to Marine Petroleum Corporation as its share of certain administrative
expenses. These expenses are shared in the ratio of each of the trusts' gross
receipts to the total gross receipts of both trusts.
 
                                       10
<PAGE>   13
 
                             PRINCIPAL UNITHOLDERS
 
     The following table sets forth the persons known to Tidelands who own
beneficially more than five percent of its outstanding units of beneficial
interest:
 
<TABLE>
<CAPTION>
                                                                                   AMOUNT
                                                                                BENEFICIALLY
                                                                                OWNED AS OF
                                                    NAME AND ADDRESS            DECEMBER 31,    PERCENT
             TITLE OF CLASS                        OF BENEFICIAL OWNER              1998        OF CLASS
             --------------                        -------------------          ------------    --------
<S>                                          <C>                                <C>             <C>
Units of Beneficial Interest.............    Marine Petroleum Trust               452,366        32.6%
                                             P.O. Box 830241
                                             Dallas, Texas 75283-0241
</TABLE>
 
                                 MISCELLANEOUS
 
                  EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND
                              REPORTS ON FORM 8-K
 
(a) Financial Statements -- See "Financial Statements and Supplementary Data"
    above.
 
(b) Reports on Form 8-K -- None.
 
(c) Exhibits
 
     (3)   Indenture of Trust dated June 1, 1954, as amended (filed as Exhibit
           (3) to the Annual Report on Form 10-K of Tidelands Royalty Trust "B"
           for the year ended December 31, 1994, filed with the Securities and
           Exchange Commission on March 30, 1995, and incorporated herein by
           reference).
 
    (22)   Subsidiaries.
 
                                       11
<PAGE>   14
 
[KPMG LLP LETTERHEAD]
 
                          INDEPENDENT AUDITORS' REPORT
 
The Trustees
Tidelands Royalty Trust "B":
 
     We have audited the accompanying consolidated balance sheets of Tidelands
Royalty Trust "B" and subsidiary as of December 31, 1998 and 1997, and the
related consolidated statements of income and undistributed income and cash
flows for each of the years in the three-year period ended December 31, 1998.
These consolidated financial statements are the responsibility of the Trust's
management. Our responsibility is to express an opinion on these consolidated
financial statements based on our audits.
 
     We conducted our audits in accordance with generally accepted auditing
standards. Those standards require that we plan and perform the audit to obtain
reasonable assurance about whether the financial statements are free of material
misstatement. An audit includes examining, on a test basis, evidence supporting
the amounts and disclosures in the financial statements. An audit also includes
assessing the accounting principles used and significant estimates made by
management, as well as evaluating the overall financial statement presentation.
We believe that our audits provide a reasonable basis for our opinion.
 
     In our opinion, the consolidated financial statements referred to above
present fairly, in all material respects, the financial position of Tidelands
Royalty Trust "B" and subsidiary as of December 31, 1998 and 1997 and the
results of their operations and their cash flows for each of the years in the
three-year period ended December 31, 1998, in conformity with generally accepted
accounting principles.
 
                                            KPMG LLP
 
Dallas, Texas
March 3, 1999
 
                                      F-1
<PAGE>   15
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
                          CONSOLIDATED BALANCE SHEETS
                           DECEMBER 31, 1998 AND 1997
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                 1998              1997
                                                              ----------        ----------
<S>                                                           <C>               <C>
Current assets:
  Cash and cash equivalents.................................  $1,525,131        $2,257,909
  Oil and gas royalties receivable..........................     113,214           159,737
  Federal income taxes receivable...........................       7,578             3,578
                                                              ----------        ----------
            Total current assets............................   1,645,923         2,421,224
 
Oil, gas and other mineral properties.......................           2                 2
                                                              ----------        ----------
                                                              $1,645,925        $2,421,226
                                                              ==========        ==========
                               LIABILITIES AND TRUST EQUITY
Current liabilities:
  Accounts payable (note 3).................................     645,567           987,641
  Income distributable to unitholders.......................     107,334           629,612
                                                              ----------        ----------
            Total current liabilities.......................     752,901         1,617,253
                                                              ----------        ----------
 
Trust equity:
  Corpus -- authorized 1,386,525 units of beneficial
     interest,
     issued 1,386,375 units at nominal value................           2                 2
  Undistributed income (note 2).............................     893,022           803,971
                                                              ----------        ----------
            Total trust equity..............................     893,024           803,973
                                                              ----------        ----------
                                                               1,645,925        $2,421,226
                                                              ==========        ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       F-2
<PAGE>   16
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
           CONSOLIDATED STATEMENTS OF INCOME AND UNDISTRIBUTED INCOME
                      THREE YEARS ENDED DECEMBER 31, 1998
 
<TABLE>
<CAPTION>
                                                            1998          1997          1996
                                                         ----------    ----------    ----------
<S>                                                      <C>           <C>           <C>
Income:
  Oil and gas royalties................................  $1,228,313    $1,262,876    $1,103,926
  Interest and other...................................      76,569        77,861        72,843
                                                         ----------    ----------    ----------
            Total income...............................   1,304,882     1,340,737     1,176,769
                                                         ----------    ----------    ----------
Expenses:
  Production and other taxes...........................         620           620           620
  General and administrative...........................      98,574        89,131        82,514
                                                         ----------    ----------    ----------
            Total expenses.............................      99,194        89,751        83,134
                                                         ----------    ----------    ----------
            Income before federal income taxes.........   1,205,688     1,250,986     1,093,635
Federal income taxes of subsidiary (note 1(d)).........      13,000        16,000        17,300
                                                         ----------    ----------    ----------
            Net income.................................   1,192,688     1,234,986     1,076,335
Undistributed income at beginning of year..............     803,971       734,909       688,098
                                                         ----------    ----------    ----------
                                                          1,996,659     1,969,895     1,764,433
Distributions to unitholders...........................   1,103,637     1,165,924     1,029,524
                                                         ----------    ----------    ----------
Undistributed income at end of year....................  $  893,022    $  803,971    $  734,909
                                                         ==========    ==========    ==========
Net income per unit....................................        $.86          $.89          $.78
Distributions per unit.................................        $.80          $.84          $.74
Weighted average units outstanding.....................   1,386,375     1,386,375     1,386,375
                                                         ==========    ==========    ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       F-3
<PAGE>   17
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                      THREE YEARS ENDED DECEMBER 31, 1998
 
<TABLE>
<CAPTION>
                                                          1998           1997          1996
                                                       -----------    ----------    -----------
<S>                                                    <C>            <C>           <C>
Cash flows from operating activities:
  Net income.........................................  $ 1,192,688    $1,234,986    $ 1,076,335
  Adjustments to reconcile net income to net cash
     provided by operating activities:
     Change in assets and liabilities:
       Oil and gas royalties receivable..............       46,523        15,275         23,383
       Federal income taxes receivable...............       (4,000)        3,648         (7,600)
       Accounts payable..............................     (342,074)        4,208         (1,508)
                                                       -----------    ----------    -----------
          Net cash provided by operating
            activities...............................      893,137     1,258,117      1,090,610
                                                       -----------    ----------    -----------
Cash flows from financing activities -- distributions
  to unitholders.....................................   (1,625,915)     (763,228)    (1,034,357)
                                                       -----------    ----------    -----------
          Net increase (decrease) in cash and cash
            equivalents..............................     (732,778)      494,889         56,253
Cash and cash equivalents at beginning of year.......    2,257,909     1,763,020      1,706,767
                                                       -----------    ----------    -----------
Cash and cash equivalents at end of year.............  $ 1,525,131    $2,257,909    $ 1,763,020
                                                       ===========    ==========    ===========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       F-4
<PAGE>   18
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                           DECEMBER 31, 1998 AND 1997
 
(1) SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES AND GENERAL
 
  (a) General
 
     The Trust was established on June 1, 1954 with a transfer of contract
rights to certain properties to the Trust in exchange for units of beneficial
interest. The contract rights enable the Trust to receive an interest in any
oil, gas or other mineral leases obtained by Gulf Oil Corporation, now Chevron
U.S.A., Inc. (Chevron) which is a subsidiary of Chevron Corporation, and its
assignees in a designated area of the Gulf of Mexico during a 50-year period
beginning April 30, 1951. Royalty revenue received from Chevron accounted for
approximately 8%, 13% and 30% of total royalty revenue for the years ended
December 31, 1998, 1997 and 1996, respectively. Royalty revenue received from
Pennzoil Exploration and Production Company totaled approximately 30%, 41% and
62% for the years ended December 31, 1998, 1997 and 1996, respectively. In
addition, royalty revenue received from Burlington Resources Oil and Gas Company
accounted for approximately 42% and 34% of total royalty revenue for the years
ended December 31, 1998 and 1997. Royalty revenue from American Explorer, a new
payor, amounted to 18% in 1998. No other companies accounted for more than 10%
of the Trust's royalty revenues during the year ended December 31, 1998.
 
     The Trust is required under its indenture to distribute all income, after
paying its liabilities and obligations, to the unitholders quarterly. The Trust
cannot invest any of the money of the Trust for any purpose and cannot engage in
a trade or business.
 
     A Louisiana trust can only exist for a short period of time; therefore the
unitholders assigned their off-shore Louisiana contract rights to Tidelands
Royalty "B" Corporation, a wholly owned subsidiary of the Trust, reserving a 95%
net profits interest to themselves. The net profits interest contract was
transferred to the Trust along with the other properties. The Trust is
authorized to pay expenses of the Corporation should it be necessary.
 
     The Trust has entered into an arrangement with Marine Petroleum Corporation
(a wholly-owned subsidiary of Marine Petroleum Trust, an affiliate of Tidelands)
to share certain administrative expenses. The sole purpose of this operation is
to assist the trustees in the administration of the trusts. General and
administrative expenses totaled $98,574, $89,131 and $82,514 for the years ended
December 31, 1998, 1997 and 1996, respectively.
 
     At December 31, 1998 and 1997, Marine Petroleum Trust owned 32.6% of the
Trust's outstanding units of beneficial interest.
 
  (b) Principles of Consolidation
 
     The consolidated financial statements include the Trust and its
wholly-owned subsidiary. All intercompany accounts and transactions have been
eliminated in consolidation.
 
  (c) Oil, Gas and Other Mineral Properties
 
     At the time the Trust was established, no determinable market value was
available for the assets transferred to the Trust; consequently, nominal values
were assigned. Accordingly, no allowance for depletion has been computed.
 
     The Trust's revenues are derived from production payments and overriding
royalty interests related to properties located in the Gulf of Mexico.
 
     Net revenues from oil and gas royalties related to proved developed oil and
gas reserves were $1,228,313, $1,262,876 and $1,103,926 in 1998, 1997 and 1996,
respectively.
 
                                       F-5
<PAGE>   19
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  (d) Federal Income Taxes
 
     No provision has been made for Federal income taxes on the Trust's income
since such taxes are the liability of the unitholders. Federal income taxes have
been provided on the income of the subsidiary corporation, excluding the 95% of
oil and gas royalties to be distributed to the Trust and after deducting
statutory depletion.
 
  (e) Credit Risk Concentration and Cash Equivalents
 
     Financial instruments which potentially subject the Trust and its
wholly-owned subsidiary to concentrations of credit risk are primarily
investments in cash equivalents and unsecured oil and gas royalties receivable.
The Trust and its wholly-owned subsidiary place their cash investments with
financial institutions that management considers creditworthy and limit the
amount of credit exposure from any one financial institution. Royalties
receivable are from large creditworthy companies and the Trust historically has
not encountered collection problems. The estimated fair values of cash
equivalents and oil and gas royalties receivable approximate the carrying values
due to the short term nature of these financial instruments.
 
     Cash equivalents of $1,454,865 and $1,483,495 at December 31, 1998 and
1997, respectively, consist of cash held in money market and overnight
government backed securities accounts. For purposes of the statements of cash
flows, the Trust considers all highly liquid debt instruments with original
maturities of three months or less to be cash equivalents.
 
  (f) Statements of Cash Flows
 
     The Trust paid $17,000, $12,352 and $24,900 in Federal income taxes in
1998, 1997 and 1996, respectively. No payments of interest were made in 1998,
1997 and 1996.
 
  (g) Use of Estimates
 
     The preparation of financial statements in conformity with generally
accepted accounting principles requires management to make estimates and
assumptions that affect the reported amounts of assets and liabilities and
disclosure of contingent assets and liabilities at the date of the financial
statements and the reported amounts of revenues and expenses during the
reporting period. Actual results could differ from those estimates.
 
(2) UNDISTRIBUTED INCOME
 
     Undistributed income includes $607,516 and $545,449 applicable to the
subsidiary corporation at December 31, 1998 and 1997, respectively.
 
(3) OVERPAID ROYALTIES
 
     The Trust has recorded a liability for possible royalty overpayments
received by the Trust in various years from 1988 through 1993. A potential
liability for the estimated amount of the overpayments is reflected in accounts
payable in the accompanying consolidated balance sheets. During 1998, Tidelands
determined that $340,485 was no longer required to be reserved, because the
likelihood had been reduced that repayment of such amount actually would be
required. Accordingly, accounts payable was reduced and oil and gas royalties
was increased by such amount.
 
(4) SUPPLEMENTAL INFORMATION RELATING TO OIL AND GAS RESERVES (UNAUDITED)
 
     Oil and gas reserve information relating to the Trust's royalty interests
is not presented because such information is not available to the Trust. The
Trust's share of oil and gas produced for its royalty interests was
 
                                       F-6
<PAGE>   20
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
as follows: oil (barrels) -- 9,935 in 1998, 10,348 in 1997 and 7,958 in 1996;
and gas (mcf) -- 405,336 in 1998, 495,734 in 1997 and 416,999 in 1996.
 
(5) SUMMARY OF QUARTERLY FINANCIAL DATA (UNAUDITED)
 
     The following quarterly financial information for the years ended December
31, 1998 and 1997 is unaudited; however, in the opinion of management, all
adjustments necessary to present a fair statement of the results of operations
for the interim periods have been included.
 
<TABLE>
<CAPTION>
                                                 OIL AND GAS       NET        NET INCOME
                                                  ROYALTIES       INCOME       PER UNIT
                                                 -----------    ----------    ----------
<S>                                              <C>            <C>           <C>
Quarter ended:
  March 31, 1998...............................  $  467,245     $  460,550      $ .33
  June 30, 1998................................     251,970        234,165        .17
  September 30, 1998...........................     191,244        187,013        .13
  December 31, 1998............................     317,854        310,960        .23
                                                 ----------     ----------      -----
                                                 $1,228,313     $1,192,688      $ .86
                                                 ==========     ==========      =====
Quarter ended:
  March 31, 1997...............................  $  232,313     $  227,161      $ .16
  June 30, 1997................................     291,695        289,413        .21
  September 30, 1997...........................     373,876        358,410        .26
  December 31, 1997............................     364,992        360,002        .26
                                                 ----------     ----------      -----
                                                 $1,262,876     $1,234,986      $ .89
                                                 ==========     ==========      =====
</TABLE>
 
                                       F-7
<PAGE>   21
 
                                   SIGNATURES
 
     Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the Registrant has duly caused this Annual Report on Form
10-K to be signed by the undersigned thereunto duly authorized.
 
                                            Tidelands Royalty Trust "B"
                                            (Registrant)
 
                                            By: NationsBank, N.A.
                                              (in its capacity as Corporate
                                                Trustee
                                              of Tidelands Royalty Trust "B"
                                              and not in its individual capacity
                                              or otherwise)
 
Date: March 17, 1999                        By:      /s/ JANE J. SHEA
                                              ----------------------------------
                                                         Jane J. Shea
                                                        Vice President
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, this
Annual Report on Form 10-K has been signed below by the following persons on
behalf of the Registrant and in the capacities and on the dates indicated.
 
<TABLE>
<CAPTION>
                        NAME                                         CAPACITIES                       DATE
                        ----                                         ----------                       ----
<C>                                                      <S>                                <C>
NationsBank, N.A.                                        Corporate Trustee                            March 17, 1999
 
                By: /s/ JANE J. SHEA
  -------------------------------------------------
                    Jane J. Shea
                   Vice President
 
                   /s/ R. RAY BELL                       Principal Accounting Officer                 March 17, 1999
-----------------------------------------------------
                     R. Ray Bell
</TABLE>
<PAGE>   22
                                EXHIBIT INDEX


EXHIBIT
NUMBER                          DESCRIPTION
-------                         -----------

22              Subsidiaries of Tideland Royalty Trust "B"

27              Financial Data Schedule