<PAGE>   1
 
================================================================================
 
                                   FORM 10-K
 
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
[X]   FOR THE FISCAL YEAR ENDED DECEMBER 31, 1996
 
                                       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 March 7, 1997: $4,903,547.
 
     Number of Units of Beneficial Interest outstanding as of the close of the
period covered by this report: December 31, 1996 -- 1,386,375 Units.
 
                      Documents incorporated by reference:
 
                                      NONE
 
================================================================================
<PAGE>   2
 
                             CROSS REFERENCE SHEET
 
     This Form 10-K for the year ended December 31, 1996, 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  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 -- Review and Outlook."
 
     As of December 31, 1996, Chevron and others held interests in eight 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 seven
leases covering 32,011 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 1996, approximately 12% of Tidelands' production payment and royalty
revenues were attributable to oil and approximately 88% 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. Royalty revenue received from Chevron accounted for
approximately 30%, 19% and 24% of total royalty revenue for the years ended
December 31, 1996, 1995 and 1994, respectively. Royalty revenue received from
Pennzoil Exploration and Production Company totaled approximately 62%, 63% and
59% for the years ended December 31, 1996, 1995 and 1994, respectively.
 
     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 1996 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>
                                                         1996       1995       1994
                                                        -------    -------    -------
<S>                                                     <C>        <C>        <C>
Quantity of royalty oil and gas sold
  Oil (in barrels ("bbls")).........................      7,958      7,804      7,899
  Gas (in thousand cubic feet ("mcf"))..............    416,999    540,597    778,517
Weighted average sales price
  for royalty oil and gas sold
  Oil (per bbl)(1)..................................     $15.92     $12.61     $11.14
  Gas (per mcf).....................................     $ 2.34     $ 1.63     $ 1.88
</TABLE>
 
---------------
 
(1) These amounts are net of the cost of transportation from offshore leases to
     onshore receiving points.
 
     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.
 
                                        2
<PAGE>   5
 
     Interests in Properties. Tidelands' properties consist of production
payments and overriding royalty interests in 8 oil and gas leases covering
36,375 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...............................................       2
                                                         ===
  Gas...............................................      11
                                                         ===
Gross Leased Acres --
  Productive........................................  36,375
                                                      ======
</TABLE>
 
     Information regarding net wells or acres is not included since Tidelands
does not own any working interests.
 
     Productive Properties. Productive properties cover 36,375 gross acres under
8 different leases. These 8 leases contain 13 single completion wells. Two of
these completions produce oil, and 11 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 1994, 1995 and 1996. Only fields that were producing at the
end of the year are listed. The information in the table is based upon data
obtained from the Petroleum Information Corporation. Production from these
fields accounted for substantially all of Tidelands' distributable income in
1996.
 
<TABLE>
<CAPTION>
                                                       NET MCF GAS & OIL
                                                           EQUIVALENT
                                            YEAR           PER DAY(1)
                                           FIRST      --------------------
                 FIELD                    PRODUCED    1996    1995    1994
                 -----                    --------    ----    ----    ----
<S>                                       <C>         <C>     <C>     <C>
Offshore Texas
  Galveston Block 303...................    1987      108     143     222
  High Island Block 128.................    1989      416     190     579
Offshore Louisiana
  Sabine Pass Block 13..................    1981      112      80     119
  West Cameron Block 165................    1969      802     946     916
  West Cameron Block 333................    1978       26      84     170
</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 these other operators have under lease approximately
430,000 of the 1,370,000 acres therein. This leaves approximately 630,000 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.
 
     Drilling Results. Three wells were drilled during 1996 on leases in which
Tidelands owns an overriding royalty interest. Burlington Resources drilled Well
No. 4 on Galveston Block 303; the well was completed as a gas well and
production commenced in February 1997. The other two wells were drilled in the
West Cameron Area. Well No. A-2(st) was sidetracked out of an existing well on
West Cameron Block 229 and Well No. 5 was drilled on West Cameron Block 225.
Both wells are gas wells. There were no wells drilled in 1995 or 1994 on any
lease in which Tidelands has an interest.
 
                                        3
<PAGE>   6
 
     Present Activities. Tidelands currently receives royalties from oil and
natural gas sold from 6 of the 8 producing leases in the Royalty Area, although
delivery quantities are subject to seasonal demand.
 
     Published reports indicate that during 1996, Chevron and Elf did not bid on
any lease located in the Royalty Area in the two federal lease sales held that
year.
 
     The Minerals Management Service of the United States Department of the
Interior received bids in a lease sale in the Central Gulf area on March 6,
1997. The sale covered a portion of the Royalty Area that lies in the West
Cameron area. Published reports indicate that neither Chevron nor Elf made a bid
on any block located in the Royalty 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 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 1996, 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 451 unitholders of record as of March 19, 1997. 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
1996.
 
     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>
1996
  First quarter.........................  $6.75    $5.75            $.17
  Second quarter........................   6.75     5.00             .21
  Third quarter.........................   5.75     4.75             .20
  Fourth quarter........................   6.38     4.75             .16
1995
  First quarter.........................  $8.50    $6.50            $.18
  Second quarter........................   7.75     6.50             .18
  Third quarter.........................   7.50     6.00             .16
  Fourth quarter........................   7.00     6.00             .17
</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.
 
     Prior to February 27, 1997, the units of beneficial interest in the Trust
traded on the Nasdaq's Small Cap Market. The Trust's units were delisted because
the Trust did not meet the Nasdaq's minimum assets and equity criteria.
Management of the Trust believes that Nasdaq's action was not based on any
deterioration of the Trust's financial condition or prospects. Since 1993, the
Trust was listed pursuant to an exception from Nasdaq's continued listing
criteria. Nasdaq notified the Trust that its determination not to continue this
exception was based in part on "the emergence of the [Over the Counter Bulletin
Board] as a viable option for companies not qualifying for continued inclusion
on Nasdaq."
 
     Management of the Trust believes that the Over the Counter Market will
prove to be a satisfactory market mechanism for trading in the units. Actual
results, of course, may vary and will depend on the number of market makers who
are active in the units, the number of buyers and sellers of units, the prices
at which such buyers and sellers are willing to sell, and the future results of
the Trust's operation.
 
     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, 1996, nor has it passed
upon its accuracy or adequacy. While Tidelands' Form 10-K (excluding exhibits)
for the year ended December 31, 1996, is included in toto in Tidelands' 1996
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.
Patricia Cox, NationsBank of Texas, N.A., P.O. Box 830241, Dallas, Texas
75283-0241.
 
                                        6
<PAGE>   9
 
                            SELECTED FINANCIAL DATA
 
<TABLE>
<CAPTION>
                                          1996         1995         1994         1993         1992
                                       ----------   ----------   ----------   ----------   ----------
<S>                                    <C>          <C>          <C>          <C>          <C>
Income -- oil and gas royalties......  $1,103,926   $  978,172   $1,555,352   $4,022,181   $  957,900
Net income...........................  $1,076,335   $  965,004   $1,499,244   $3,924,078   $  915,636
Net income per unit..................        $.78         $.70        $1.08        $2.83         $.66
Distributions to unitholders.........  $1,029,524   $  960,169   $2,142,298   $3,318,978   $  905,177
Distributions per unit...............        $.74         $.69        $1.55        $2.39         $.65
Total assets.........................  $1,945,260   $1,905,164   $1,909,605   $3,928,046   $1,795,028
</TABLE>
 
                                        7
<PAGE>   10
 
               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
administration 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 $.74 per unit in 1996, an increase
of $.05 over the $.69 distributed in 1995. Distributions in 1994 and 1993
included royalties on 3 gas wells that are no longer producing and that did not
contribute substantially to the Trust's income in 1996 and 1995.
 
     The average daily production of oil and gas (stated in mcf equivalents) to
Tidelands' interest was 1,508 mcf per day in the first quarter of 1996, but
declined to 1,006 mcf per day in the fourth quarter.
 
     Natural gas prices increased 44% in 1996 over the prices of 1995. In 1995
the average price received for natural gas by Tidelands was $1.63 per mcf and in
1996 the price increased to $2.34. However, gas prices weakened in the first
months of 1997. Spot market prices for gas in the Gulf of Mexico were quoted as
low as $1.70 for February 1997 deliveries.
 
     Tidelands is due to commence receiving royalties in 1997 from a new gas
well completed by Burlington Resources on Galveston Block 303. Tidelands has an
overriding royalty interest of approximately 4% in the lease on this block.
 
     Royalties on oil and condensate amounted to 12% of Tidelands' revenue in
1996. The average price received by Tidelands for oil in 1995 amounted to $12.61
per barrel and increased to $15.92 per barrel in 1996. Two 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 $21.54 in 1996, 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' 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.
 
                                        8
<PAGE>   11
 
OIL AND GAS ROYALTIES -- 1995 AND 1996
 
     Income from oil and gas royalties increased 13% in 1996 as compared to
1995. Gas royalties accounted for 88% of income from royalties in 1996. The
price received for gas during 1996 increased 44% from 1995 to $2.34 per mcf.
 
     The following table presents comparative operating data which reflects
these underlying circumstances.
 
                           COMPARATIVE OPERATING DATA
 
<TABLE>
<CAPTION>
                                                                      CHANGE FROM
                                                                     1995 TO 1996
                                                                  -------------------
                                             1996        1995      AMOUNT     PERCENT
                                          ----------   --------   ---------   -------
<S>                                       <C>          <C>        <C>         <C>
Income:
  Oil royalties(1)......................  $  126,680   $ 98,423   $  28,257      28%
  Gas royalties.........................     977,246    879,749      97,497      11%
                                          ----------   --------   ---------
                                          $1,103,926   $978,172   $ 125,754      13%
                                          ==========   ========   =========
Net production quantities
  Oil (bbls)............................       7,958      7,804         154       2%
  Gas (mcf).............................     416,999    540,597    (123,598)    (23)%
Average net prices
  Oil(1)................................  $    15.92   $  12.61   $    3.31      26%
  Gas...................................  $     2.34   $   1.63   $     .71      44%
</TABLE>
 
---------------
 
(1) These amounts are net of the cost of transportation from offshore leases to
     onshore receiving points.
 
OIL AND GAS ROYALTIES -- 1995 AND 1994
 
     Income from oil and gas royalties decreased 37% in 1995 as compared to
1994. Gas royalties decreased 40% and accounted for 90% of income for 1995.
These decreases primarily were caused by a decrease in the volume of gas
produced and a decrease in its average price. See "-- General." Average oil
prices increased 13% while average gas prices decreased 13%.
 
     The following table presents comparative operating data which reflects
these underlying circumstances.
 
                           COMPARATIVE OPERATING DATA
 
<TABLE>
<CAPTION>
                                                                              CHANGE FROM
                                                                             1994 TO 1995
                                                                          -------------------
                                                    1995        1994       AMOUNT     PERCENT
                                                  --------   ----------   ---------   -------
<S>                                               <C>        <C>          <C>         <C>
Income:
  Oil royalties(1)..............................  $ 98,423   $   87,998   $  10,425      12%
  Gas royalties.................................   879,749    1,467,354    (587,605)    (40)%
                                                  --------   ----------   ---------
                                                  $978,172   $1,555,352   $(577,180)    (37)%
                                                  ========   ==========   =========
Net production quantities
  Oil (bbls)....................................     7,804        7,899         (95)     (1)%
  Gas (mcf).....................................   540,597      778,517    (237,920)    (31)%
Average net prices
  Oil(1)........................................  $  12.61   $    11.14   $    1.47      13%
  Gas...........................................  $   1.63   $     1.88   $    (.25)    (13)%
</TABLE>
 
---------------
 
(1) These amounts are net of the cost of transportation from offshore leases to
     onshore receiving points.
 
                                        9
<PAGE>   12
 
                  FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA
 
     Tidelands' consolidated financial statements listed in the following index,
together with the related notes and the report of KPMG Peat Marwick LLP,
independent certified public accountants, are presented on pages 11-17 hereof:
 
<TABLE>
<CAPTION>
                                                                     PAGE
                                                                    ------
<S> <C>                                                             <C>
--  Independent Auditors' Report................................      11
 
--  Consolidated Balance Sheets as of December 31, 1996 and
      1995......................................................      12
 
--  Consolidated Statements of Income and Undistributed Income
      for the Three Years Ended December 31, 1996...............      13
 
--  Consolidated Statements of Cash Flows for the Three Years
      Ended
      December 31, 1996.........................................      14
 
--  Notes to Consolidated Financial Statements..................      15
</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 1996 and 1995 there were no disagreements by Tidelands with its
principal accountants on any matter of accounting principles or practices or
financial statement disclosure.
 
                      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 of Texas, N.A. is the corporate trustee and Mr. Chas. G.
McBurney of Dallas, Texas is the individual trustee.
 
     Mr. McBurney is 87 years old and for at least the past five years has been
engaged in the management of his investments.
 
     Prior to October 21, 1996, Mr. L.C. Paslay served as the Individual Trustee
of the Trust. In October 1996, Mr. Paslay notified the Trust that he was
resigning his position as Individual Trustee. Management of the Trust
understands that Mr. Paslay resigned for personal reasons. Pursuant to Section 5
of Article VI of the Indenture under which the Trust was created, Mr. Chas. G.
McBurney became the Individual Trustee of the Trust, effective on October 21,
1996.
 
     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 a certified public
accountant, 69 years old, and a graduate of Midwestern State University in
Wichita Falls, Texas, with a Bachelor of Science degree in business
administration and economics. 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.
 
                                       10
<PAGE>   13
 
                            MANAGEMENT COMPENSATION
 
     During Tidelands' fiscal year ended December 31, 1996, Tidelands paid or
accrued fees of $14,210 to NationsBank of Texas, N.A., as corporate trustee. The
individual trustee served without compensation.
 
     During Tidelands' fiscal year ended December 31, 1996, Tidelands paid
$23,752 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.
 
                             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              1996        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>
 
     In addition, as of December 31, 1996, Cede & Company held of record 592,703
units of beneficial interest of Tidelands, or approximately 41% of the total
units outstanding.
 
     The following table sets forth the number of units of beneficial interest
of Marine Petroleum Trust, a parent of Tidelands, beneficially owned by Mr. L.
C. Paslay and by Mr. Chas. G. McBurney (Mr. Paslay and Mr. McBurney did not
directly own any units in Tidelands as of December 31, 1996):
 
<TABLE>
<CAPTION>
                                                                      AMOUNT AND NATURE
                                                                   OF BENEFICIAL OWNERSHIP   PERCENT OF
     BENEFICIAL OWNER                    TITLE OF CLASS            AS OF DECEMBER 31, 1996     CLASS
     ----------------                    --------------            -----------------------   ----------
<S>                            <C>                                 <C>                       <C>
L.C. Paslay................    Units of Beneficial Interest in
                               Marine Petroleum Trust                      286,469            4.67%(1)
Chas. G. McBurney..........    Units of Beneficial Interest in
                               Marine Petroleum Trust                       81,966            1.34%(2)
</TABLE>
 
---------------
 
(1) Represents percentage of units owned by Mr. Paslay in Marine Petroleum Trust
    (14.32%) multiplied by the percentage of units in Tidelands owned by Marine
    Petroleum Trust (32.6%), a "parent" of Tidelands.
 
(2) Represents percentage ownership of units by Mr. McBurney in Marine Petroleum
    Trust (4.10%) multiplied by the percentage of units in Tidelands owned by
    Marine Petroleum Trust (32.6%), a "parent" of Tidelands.
 
                                 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
 
                          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, 1996 and 1995, 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, 1996.
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, 1996 and 1995 and the
results of their operations and their cash flows for each of the years in the
three-year period ended December 31, 1996, in conformity with generally accepted
accounting principles.
 
                                            KPMG PEAT MARWICK LLP
 
Dallas, Texas
March 7, 1997
 
                                       12
<PAGE>   15
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
                          CONSOLIDATED BALANCE SHEETS
                           DECEMBER 31, 1996 AND 1995
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                                 1996              1995
                                                              ----------        ----------
<S>                                                           <C>               <C>
Current assets:
  Cash and cash equivalents.................................  $1,763,020        $1,706,767
  Oil and gas royalties receivable..........................     175,012           198,395
  Federal income taxes receivable...........................       7,226                --
                                                              ----------        ----------
            Total current assets............................   1,945,258         1,905,162
Oil, gas and other mineral properties.......................           2                 2
                                                              ----------        ----------
                                                              $1,945,260        $1,905,164
                                                              ==========        ==========
                               LIABILITIES AND TRUST EQUITY
Current liabilities:
  Accounts payable (note 3).................................  $  983,433        $  984,941
  Income distributable to unitholders.......................     226,916           231,749
  Federal income taxes payable..............................          --               374
                                                              ----------        ----------
            Total current liabilities.......................   1,210,349         1,217,064
                                                              ----------        ----------
 
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).............................     734,909           688,098
                                                              ----------        ----------
            Total trust equity..............................     734,911           688,100
                                                              ----------        ----------
                                                              $1,945,260        $1,905,164
                                                              ==========        ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       12
<PAGE>   16
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
           CONSOLIDATED STATEMENTS OF INCOME AND UNDISTRIBUTED INCOME
                      THREE YEARS ENDED DECEMBER 31, 1996
 
<TABLE>
<CAPTION>
                                                            1996          1995          1994
                                                         ----------    ----------    ----------
<S>                                                      <C>           <C>           <C>
Income:
  Oil and gas royalties................................  $1,103,926    $  978,172    $1,555,352
  Interest and other...................................      72,843        79,451        55,572
                                                         ----------    ----------    ----------
            Total income...............................   1,176,769     1,057,623     1,610,924
                                                         ----------    ----------    ----------
Expenses:
  Production and other taxes...........................         620           620           620
  General and administrative...........................      82,514        75,347       100,460
                                                         ----------    ----------    ----------
            Total expenses.............................      83,134        75,967       101,080
                                                         ----------    ----------    ----------
            Income before Federal income taxes.........   1,093,635       981,656     1,509,844
Federal income taxes of subsidiary (note 1(d)).........      17,300        16,652        10,600
                                                         ----------    ----------    ----------
            Net income.................................   1,076,335       965,004     1,499,244
Undistributed income at beginning of year..............     688,098       683,263     1,326,317
                                                         ----------    ----------    ----------
                                                          1,764,433     1,648,267     2,825,561
Distributions to unitholders...........................   1,029,524       960,169     2,142,298
                                                         ----------    ----------    ----------
Undistributed income at end of year....................  $  734,909    $  688,098    $  683,263
                                                         ==========    ==========    ==========
Net income per unit....................................        $.78          $.70         $1.08
Distributions per unit.................................        $.74          $.69         $1.55
Weighted average units outstanding.....................   1,386,375     1,386,375     1,386,375
                                                         ==========    ==========    ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       13
<PAGE>   17
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
                     CONSOLIDATED STATEMENTS OF CASH FLOWS
                      THREE YEARS ENDED DECEMBER 31, 1996
 
<TABLE>
<CAPTION>
                                                           1996          1995           1994
                                                        ----------    -----------    ----------
<S>                                                     <C>           <C>            <C>
Cash flows from operating activities:
  Net income..........................................  $1,076,335    $   965,004    $1,499,244
  Adjustments to reconcile net income to net cash
     provided by operating activities:
     Change in assets and liabilities:
       Accounts receivable............................      23,383        (46,935)        3,631
       Federal income taxes...........................      (7,600)        (3,619)       18,593
       Accounts payable...............................      (1,508)        (2,384)     (168,746)
                                                        ----------    -----------    ----------
          Net cash provided by operating activities...   1,090,610        912,066     1,352,722
                                                        ----------    -----------    ----------
Cash flows from financing activities -- distributions
  to unitholders......................................  (1,034,357)      (963,442)   (3,352,932)
                                                        ----------    -----------    ----------
          Net increase (decrease) in cash and cash
            equivalents...............................      56,253        (51,376)   (2,000,210)
Cash and cash equivalents at beginning of year........   1,706,767      1,758,143     3,758,353
                                                        ----------    -----------    ----------
Cash and cash equivalents at end of year..............  $1,763,020    $ 1,706,767    $1,758,143
                                                        ==========    ===========    ==========
</TABLE>
 
          See accompanying notes to consolidated financial statements.
 
                                       14
<PAGE>   18
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                           DECEMBER 31, 1996 AND 1995
 
(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 30%, 19% and 24% of total royalty revenue for the years ended
December 31, 1996, 1995 and 1994, respectively. Royalty revenue received from
Pennzoil Exploration and Production Company totaled approximately 62%, 63% and
59% for the years ended December 31, 1996, 1995 and 1994, respectively.
 
     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.
 
     At December 31, 1996 and 1995, 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 $1,103,926, $978,172 and $1,555,352 in 1996, 1995 and 1994,
respectively.
 
  (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% to
be distributed to the Trust and after deducting statutory depletion.
 
                                       15
<PAGE>   19
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
  (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 $1,406,325 and $1,339,089 at December 31, 1996 and
1995, 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 $24,900 and $20,271 in Federal income taxes in 1996 and
1995, respectively. The Trust received a $7,993 refund of Federal income taxes
in 1994. No payments of interest were made in 1996, 1995 and 1994.
 
  (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 $477,907 and $403,506 applicable to the
subsidiary corporation at December 31, 1996 and 1995, respectively.
 
(3) OVERPAID ROYALTIES
 
     The Trust has recorded estimated royalty overpayments which may have been
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.
 
(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 as follows:
oil (barrels) -- 7,958 in 1996, 7,804 in 1995 and 7,899 in 1994; and gas
(mcf) -- 416,999 in 1996, 540,597 in 1995 and 778,517 in 1994.
 
                                       16
<PAGE>   20
 
                   TIDELANDS ROYALTY TRUST "B" AND SUBSIDIARY
 
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
 
(5) SUMMARY OF QUARTERLY FINANCIAL DATA (UNAUDITED)
 
     The following quarterly financial information for the years ended December
31, 1996 and 1995 is unaudited; however, in the opinion of management, all
adjustments necessary to a fair statement of the results of operations for the
interim periods have been included.
 
<TABLE>
<CAPTION>
                                      OIL AND GAS     TOTAL         NET        NET INCOME
                                       ROYALTIES     EXPENSES      INCOME       PER UNIT
                                      -----------    --------    ----------    ----------
<S>                                   <C>            <C>         <C>           <C>
Quarter ended:
  March 31, 1996....................  $  292,949     $ 20,296    $  286,663      $ .21
  June 30, 1996.....................     345,358       30,397       327,830        .24
  September 30, 1996................     217,433       12,909       218,859        .16
  December 31, 1996.................     248,186       19,532       242,983        .17
                                      ----------     --------    ----------      -----
                                      $1,103,926     $ 83,134    $1,076,335      $ .78
                                      ==========     ========    ==========      =====
Quarter ended:
  March 31, 1995....................  $  261,326     $ 22,421    $  254,268      $ .18
  June 30, 1995.....................     156,819       27,977       146,070        .11
  September 30, 1995................     278,542        9,478       283,883        .21
  December 31, 1995.................     281,485       16,091       280,783        .20
                                      ----------     --------    ----------      -----
                                      $  978,172     $ 75,967    $  965,004      $ .70
                                      ==========     ========    ==========      =====
</TABLE>
 
                                       17
<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 of Texas, N.A.
                                              (in its capacity as Corporate
                                                Trustee of Tidelands Royalty 
                                                Trust "B" and not in its 
                                                individual capacity or 
                                                otherwise)
                                              
 
Date: March 27, 1997                        By:      /s/  PATRICIA COX
                                                         Patricia Cox
                                                        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 of Texas, N.A.                               Corporate Trustee                            March 27, 1997
 
           By:          /s/  PATRICIA COX
                    Patricia Cox
                   Vice President
 
                   /s/  CHAS. G. McBURNEY                Individual Trustee                           March 27, 1997
                  Chas. G. McBurney
 
                        /s/  R. RAY BELL                 Principal Accounting Officer                 March 27, 1997
                     R. Ray Bell
</TABLE>
<PAGE>   22
 
                               INDEX TO EXHIBITS
 
<TABLE>
<CAPTION>
                                                                          SEQUENTIALLY
  EXHIBIT                                                                   NUMBERED
    NO.                              DESCRIPTION                              PAGE
------------                         -----------                          ------------
<S>          <C>                                                          <C>
   (22)      -- Subsidiaries.
     27      -- Financial Data Schedule.
</TABLE>