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

                                    Form 10-Q

              [X] Quarterly Report Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934
                  For the quarterly period ended March 31, 1998

                                       or

              [ ] Transition Report Pursuant to Section 13 or 15(d)
                     of the Securities Exchange Act of 1934
                   For the transition period from           to
                                                 -----------  -----------

                         Commission File Number: 1-11608

                      WILLIAMS COAL SEAM GAS ROYALTY TRUST
             (Exact name of registrant as specified in its charter)


          Delaware                                             75-6437433
(State or other jurisdiction                                (I.R.S. Employer
     of incorporation or                                   Identification No.)
       organization)

                                 Trust Division
                           NationsBank of Texas, N.A.
                                NationsBank Plaza
                                 901 Main Street
                                   12th Floor
                               Dallas, Texas 75202
                    (Address of principal executive offices)
                                   (Zip code)

                                 (214) 508-2400
              (Registrant's telephone number, including area code)

         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports) and (2) has been subject to such
filing requirements for the past 90 days. Yes [x] No [ ]

         Number of units of beneficial interest outstanding at May 11, 1998:
9,700,000.


<PAGE>   2

                         PART I - FINANCIAL INFORMATION

Item 1.  Financial Statements.

         The financial statements included herein have been prepared by
NationsBank of Texas, N.A., as Trustee (the "Trustee") of Williams Coal Seam Gas
Royalty Trust (the "Trust"), pursuant to the rules and regulations of the
Securities and Exchange Commission. Certain information and footnote disclosures
normally included in annual financial statements have been condensed or omitted
pursuant to such rules and regulations, although the Trustee believes that the
disclosures are adequate to make the information presented not misleading. It is
suggested that these condensed financial statements be read in conjunction with
the financial statements and notes thereto incorporated by reference in the
Trust's Annual Report on Form 10-K for the year ended December 31, 1997. The
December 31, 1997 balance sheet is derived from the audited balance sheet of
that date. In the opinion of the Trustee, all adjustments, consisting only of
normal recurring adjustments, necessary to present fairly the assets,
liabilities and trust corpus of the Trust as of March 31, 1998, and the
distributable income and the changes in trust corpus for the three-month periods
ended March 31, 1998 and 1997, have been included. The distributable income for
such interim periods is not necessarily indicative of the distributable income
for the full year.

         The financial statements as of March 31, 1998 and for the three-month
periods ended March 31, 1998 and 1997 included herein have been reviewed by
Ernst & Young LLP, independent public accountants, as stated in their report
appearing herein.



                                        2
<PAGE>   3

                     Independent Accountants' Review Report

NationsBank of Texas, N.A.
  Trustee of Williams Coal Seam Gas Royalty Trust

We have reviewed the accompanying condensed statement of assets, liabilities and
trust corpus of the Williams Coal Seam Gas Royalty Trust as of March 31, 1998,
and the related condensed statements of distributable income and the statements
of changes in trust corpus for the three-month periods ended March 31, 1998 and
1997. These financial statements are the responsibility of the Trustee.

We conducted our reviews in accordance with standards established by the
American Institute of Certified Public Accountants. A review of interim
financial information consists principally of applying analytical procedures to
financial data, and making inquiries of persons responsible for financial and
accounting matters. It is substantially less in scope than an audit conducted in
accordance with generally accepted auditing standards, which will be performed
for the full year with the objective of expressing an opinion regarding the
financial statements taken as a whole. Accordingly, we do not express such an
opinion.

As described in Note 2 to the financial statements, these financial statements
have been prepared on a modified cash basis of accounting, which is a
comprehensive basis of accounting other than generally accepted accounting
principles.

Based on our reviews, we are not aware of any material modifications that should
be made to the accompanying condensed financial statements referred to above for
them to be in conformity with the basis of accounting described in Note 2.

We have previously audited, in accordance with generally accepted auditing
standards, the statement of assets, liabilities and trust corpus of the Williams
Coal Seam Gas Royalty Trust as of December 31, 1997, and the related statements
of distributable income and changes in trust corpus for the year then ended (not
presented herein) and in our report dated March 27, 1998, we expressed an
unqualified opinion on those financial statements. In our opinion, the
information set forth in the accompanying condensed statement of assets,
liabilities and trust corpus as of December 31, 1997, is fairly stated, in all
material respects, in relation to the statement of assets, liabilities and trust
corpus from which it has been derived.


                                                               Ernst & Young LLP


Tulsa, Oklahoma
May 11, 1998

                                        3
<PAGE>   4

WILLIAMS COAL SEAM GAS ROYALTY TRUST

CONDENSED STATEMENTS OF ASSETS, LIABILITIES AND TRUST CORPUS
(UNAUDITED)

--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                    March 31,     December 31,
ASSETS                                                1998            1997
                                                  -----------     -----------
<S>                                               <C>             <C>        
Current Assets -
        cash and cash equivalents                 $    30,234     $    30,636
Royalty interests in oil
        and gas properties
        (less accumulated
        amortization of
        $79,153,654 at
        March 31, 1998
        and $77,150,886 at
        December 31, 1997)                         59,413,009      61,415,777
                                                  -----------     -----------

TOTAL ASSETS                                      $59,443,243     $61,446,413
                                                  ===========     ===========


LIABILITIES AND TRUST CORPUS

Current Liabilities -
        trust expenses payable                    $   178,255     $   174,713

Trust corpus -
        9,700,000 units of
        beneficial interest
        authorized and
        outstanding                                59,264,988      61,271,700
                                                  -----------     -----------

TOTAL LIABILITIES
        AND TRUST CORPUS                          $59,443,243     $61,446,413
                                                  ===========     ===========
</TABLE>

The accompanying notes are an integral part of these financial statements. See
accountants' review report.




                                        4
<PAGE>   5

--------------------------------------------------------------------------------

WILLIAMS COAL SEAM GAS ROYALTY TRUST

CONDENSED STATEMENTS OF DISTRIBUTABLE INCOME (UNAUDITED)

--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                        THREE MONTHS      THREE MONTHS
                                           ENDED             ENDED
                                       March 31, 1998    March 31, 1997
                                      ----------------  ----------------
<S>                                     <C>              <C>        
Royalty income                          $ 3,048,296      $ 4,103,814
Interest income                               9,566           12,186
                                        -----------      -----------
                                          3,057,862        4,116,000

General and administrative
        expenses                           (123,944)        (187,134)
                                        -----------      -----------
Distributable income                    $ 2,933,918      $ 3,928,866
                                        ===========      ===========

Distributable income
        per unit
        (9,700,000 units)               $       .30      $       .41
                                        ===========      ===========
</TABLE>


The accompanying notes are an integral part of these financial statements. See
accountants' review report.




                                        5
<PAGE>   6

WILLIAMS COAL SEAM GAS ROYALTY TRUST

CONDENSED STATEMENTS OF CHANGES IN TRUST CORPUS (UNAUDITED)

--------------------------------------------------------------------------------

<TABLE>
<CAPTION>
                                                    THREE MONTHS     THREE MONTHS
                                                       ENDED            ENDED
                                                  March 31, 1998     March 31, 1997
                                                 ----------------  -----------------
<S>                                               <C>               <C>         
Trust corpus,
        beginning of period                       $ 61,271,700      $ 70,021,574
Amortization of royalty
        interests                                   (2,002,768)       (2,063,015)
Distributable income                                 2,933,918         3,928,866
Distributions to unitholders                        (2,937,862)       (3,966,000)
                                                  ------------      ------------


Trust corpus, end
        of period                                 $ 59,264,988      $ 67,921,424
                                                  ============      ============

Distributions per unit
        (9,700,000 units)                         $        .30      $        .41
                                                  ============      ============
</TABLE>


The accompanying notes are an integral part of these financial statements. See
accountants' review report.




                                        6
<PAGE>   7

WILLIAMS COAL SEAM GAS ROYALTY TRUST

NOTES TO FINANCIAL STATEMENTS (UNAUDITED)

--------------------------------------------------------------------------------
1.      TRUST ORGANIZATION AND PROVISIONS

        Williams Coal Seam Gas Royalty Trust (the "Trust") was formed as a
Delaware business trust pursuant to the terms of the Trust Agreement of Williams
Coal Seam Gas Royalty Trust (as amended, the "Trust Agreement") entered into
effective as of December 1, 1992 by and among Williams Production Company, a
Delaware corporation ("WPC"), as trustor, The Williams Companies, Inc., a
Delaware corporation ("Williams"), and NationsBank of Texas, N.A., a national
banking association (the "Trustee"), and Chemical Bank Delaware, a Delaware
banking corporation (the "Delaware Trustee"), as trustees. The trustees are
independent financial institutions.

        The Trust was formed to acquire and hold certain net profits interests
(the "Royalty Interests") in proved natural gas properties located in the San
Juan Basin of New Mexico and Colorado (the "Underlying Properties") owned by
WPC. The Trust was initially created effective as of December 1, 1992 with a
$100 contribution by WPC. On January 21, 1993, the Royalty Interests were
conveyed to the Trust by WPC pursuant to the Net Profits Conveyance (the
"Conveyance") dated effective as of October 1, 1992 by and among WPC, Williams,
the Trustee and the Delaware Trustee, in consideration for all the 9,700,000
authorized units of beneficial interest in the Trust ("Units"). WPC transferred
its Units by dividend to its parent, Williams, which sold an aggregate of
5,980,000 Units to the public through various underwriters in January and
February 1993 (the "Public Offering"). During the second quarter of 1995
Williams transferred its Units to Williams Holdings of Delaware, Inc. (WHD), a
separate holding company for Williams' non regulated businesses. Substantially
all of the production attributable to the Underlying Properties is from the
Fruitland coal formation and constitutes "coal seam" gas that entitles the
owners of such production, provided certain requirements are met, to tax credits
for Federal income tax purposes pursuant to Section 29 of the Internal Revenue
Code of 1986, as amended.

        On May 7, 1997, effective as of May 1, 1997, WPC transferred the
Underlying Properties to an unaffiliated third party ("Buyer") pursuant to the
terms of the Purchase and Sale Agreement dated as of May 1, 1997 (herein so
called) between WPC and Buyer (the "Transaction"). Prior to the Transaction, WPC
had owned the Underlying Properties, subject to and burdened by the Royalty
Interests owned by the Trust, since the inception of the Trust. Neither the
Trustee nor the Delaware Trustee has any control over or responsibility relating
to the operation of the Underlying Properties. The Transaction was previously
reported in the Trust's Form 10-Q for the quarter ended March 31, 1997, and
thereafter described in more detail in the Current Report on Form 8-K filed with
the Securities and Exchange Commission on June 23, 1997 (the "Transaction Form
8-K").


                                        7
<PAGE>   8

        Concurrently with the Transaction, WPC and Buyer entered into a
Management Services Agreement dated May 1, 1997 (the "Management Services
Agreement") whereby WPC agreed, among other things, to continue to manage and
operate the Underlying Properties and to handle the receipt and payment of funds
with respect thereto. Prior to the Transaction, WPC received all payments
relating to the Underlying Properties and, pursuant to the Conveyance, paid to
the Trust the portion thereof attributable to the Royalty Interests. Following
the Transaction, under the Management Services Agreement, WPC continues to
collect all revenues on behalf of Buyer and remains obligated to pay to the
Trust on behalf of Buyer the amounts payable with respect to the Royalty
Interests.

        Concurrently with the Transaction, WPC, Williams, the Trust and Buyer
entered into an Agreement dated May 7, 1997 (the "Supplemental Agreement")
pursuant to which (i) the parties acknowledged that WPC was selling the
Underlying Properties to Buyer, but retaining all of its duties and obligations
under the Trust Agreement, Conveyance and related documents (the "Trust
Documents"), subject to the terms and conditions set forth in the Purchase and
Sale Agreement and the agreements entered into pursuant to the Purchase and sale
Agreement, (ii) Williams and WPC each confirmed and agreed that, notwithstanding
the sale of the Underlying Properties to Buyer, Williams and WPC would continue
to perform their respective obligations to the Trust pursuant to the Trust
Documents, including without limitation the performance assurances of Williams
set forth in the Conveyance, and (iii) Buyer acknowledged and agreed that it was
purchasing the Underlying Properties burdened by the Royalty Interests owned by
the Trust.

        As a result of these assurances and the Trustee's belief that the
Transaction will have no adverse effect on Unitholders, the information and
descriptions set forth herein give no effect to the Transaction. Consequently,
with regard to ownership of the Underlying Properties, references herein to
"WPC" with respect to those periods after the effective date of the Transaction
are to Buyer. The Transaction Form 8-K should be consulted for further
information on the Transaction.

        The Trustee has the power to collect and distribute the proceeds
received by the Trust and to pay Trust liabilities and expenses. The Delaware
Trustee has only such powers as are set forth in the Trust Agreement and is not
empowered to otherwise manage or take part in the business of the Trust. The
Royalty Interests are passive in nature and neither the Delaware Trustee nor the
Trustee has any control over or any responsibility relating to the operation of
the Underlying Properties.

        The Trust will terminate no later than December 31, 2012, subject to
earlier termination under certain circumstances described in the Trust Agreement
(the "Termination Date"). Cancellation of the Trust will occur on or following
the Termination Date when all Trust assets have been sold and the net proceeds
thereof distributed to Unitholders.

        The only assets of the Trust, other than cash and cash equivalents being
held for the payment of expenses and liabilities and for distribution to
Unitholders, are the Royalty Interests. The Royalty Interests consist primarily
of a net profits interest (the "NPI") in the Underlying Properties. The NPI
generally entitles the Trust to receive 81 percent of the NPI Net Proceeds,



                                        8
<PAGE>   9

as defined below, attributable to (i) gas produced and sold from WPC's net
revenue interests (working interests less lease burdens) in the properties in
which WPC has a working interest (the "WI Properties") and (ii) the revenue
stream received by WPC attributable to its 35 percent net profits interest in
5,348 gross acres in La Plata County, Colorado (the "Farmout Properties"). The
Royalty Interests also include a 20 percent interest in WPC's Infill Net
Proceeds, as defined below, from the sale of production if well spacing rules
are effectively modified and additional wells are drilled on producing drilling
blocks on the WI Properties (the "Infill Wells") during the term of the Trust.
No Infill Wells have been drilled on the WI Properties to date. "NPI Net
Proceeds" consists generally of the revenue stream received by WPC from its 35
percent net profits interest in the Farmout Properties, plus the aggregate
proceeds attributable to WPC's net revenue interest, based on the price paid at
or in the vicinity of the wellhead (the "Wellhead"), of gas produced from the WI
Properties, less WPC's share of certain taxes and costs. "Infill Net Proceeds"
consists generally of the aggregate proceeds, based on the price at the
Wellhead, of gas produced from WPC's net revenue interest in any Infill Wells
less certain taxes and costs. The NPI percentage is subject to certain future
downward adjustments based on a rate of return computation once cumulative
aggregate production targets are met (see Note 7). The complete definitions of
NPI Net Proceeds and Infill Net Proceeds are set forth in the Conveyance.

2.      BASIS OF ACCOUNTING

        The financial statements of the Trust are prepared on a modified cash
basis and are not intended to present financial position and results of
operations in conformity with generally accepted accounting principles ("GAAP").
Preparation of the Trust's financial statements on such basis includes the
following:

        Revenues are recognized in the period in which amounts are received by
        the Trust. General and administrative expenses are recognized on an
        accrual basis.

        Amortization of the Royalty Interests is calculated on a
        unit-of-production basis and charged directly to trust corpus.

        Distributions to Unitholders are recorded when declared by the Trustee
        (see Note 4).

        The financial statements of the Trust differ from financial statements
prepared in accordance with GAAP because royalty income is not accrued in the
period of production and amortization of the Royalty Interests is not charged
against operating results.

        Williams sold an aggregate of 5,980,000 Units of the Trust's authorized
9,700,000 Units in the Public Offering at the offering price of $20 per Unit,
retaining 3,720,000 Units. Subsequently, Williams sold an additional 151,209
Units for $23.50 per Unit. Accordingly, the condensed statements of assets,
liabilities and trust corpus reflect the sale of these Units at the respective
sale prices thereof, as well as the remaining 3,568,791 Units at Williams'
historical cost. During the second quarter of 1995 Williams transferred its
Units to WHD, a separate holding company for Williams' non regulated businesses.
If WHD, in the future, should sell all or a portion of its retained Units, at
that time, the carrying value on the Trust's statements of



                                        9
<PAGE>   10

assets, liabilities and trust corpus may again be adjusted from WHD's historical
cost to the subsequent sale price with respect to the Units sold.

3.      FEDERAL INCOME TAXES

        The Trust is a grantor trust for Federal income tax purposes. As a
grantor trust, the Trust will not be required to pay Federal or state income
taxes. Accordingly, no provision for income taxes has been made in these
financial statements.

        Because the Trust will be treated as a grantor trust, and because a
Unitholder will be treated as directly owning an interest in the Royalty
Interests, each Unitholder will be taxed directly on his per Unit pro rata share
of income attributable to the Royalty Interests consistent with the Unitholder's
method of accounting and without regard to the taxable year or accounting method
employed by the Trust.

        Production from coal seam gas wells drilled after December 31, 1979 and
prior to January 1, 1993, qualifies for the Federal income tax credit for
producing nonconventional fuels under Section 29 of the Internal Revenue Code.
This tax credit is calculated annually based on each year's qualified production
through the year 2002. Such credit, based on the Unitholder's pro rata share of
qualifying production, may not reduce his regular tax liability (after the
foreign tax credit and certain other non-refundable credits) below his
alternative minimum tax. Any part of the Section 29 credit not allowed for the
tax year solely because of this limitation is subject to certain carryover
provisions. Each Unitholder should consult his tax advisor regarding Trust tax
compliance matters.

4.      DISTRIBUTIONS TO UNITHOLDERS

        The Trustee determines for each quarter the amount of cash available for
distribution to Unitholders. Such amount (the "Quarterly Distribution Amount")
is an amount equal to the excess, if any, of the cash received by the Trust, on
or prior to the last day of the month following the end of each calendar quarter
from the Royalty Interests, plus, with certain exceptions, any other cash
receipts of the Trust during such quarter, over the liabilities of the Trust
paid during such quarter, subject to adjustments for changes made by the Trustee
during such quarter in any cash reserves established for the payment of
contingent or future obligations of the Trust.

        The Quarterly Distribution Amount for each quarter is payable to
Unitholders of record on the 45th day following the end of such calendar quarter
unless such day is not a business day in which case the record date is the next
business day thereafter. The Trustee distributes the Quarterly Distribution
Amount within 60 days after the end of each calendar quarter to each person who
was a Unitholder of record on the associated record date, together with interest
estimated to be earned on such amount from the date of receipt thereof by the
Trustee to the payment date.

        In addition to the regular quarterly distributions, under certain
circumstances specified in the Trust Agreement (such as upon a purchase price
adjustment, if any, or pursuant to the sale of




                                       10
<PAGE>   11

a Royalty Interest), the Trust would make a special distribution (a "Special
Distribution Amount"). A Special Distribution Amount would be made when amounts
received by the Trust under such circumstances aggregated in excess of
$9,000,000. The record date for a Special Distribution Amount will be the 15th
day following receipt of amounts aggregating a Special Distribution Amount by
the Trust (unless such day is not a business day in which case the record date
will be the next business day thereafter) unless such day is within 10 days of
the record date for a Quarterly Distribution Amount in which case the record
date will be the date as is established for the next Quarterly Distribution
Amount. Distribution to Unitholders of a Special Distribution Amount will be
made no later than 15 days after the Special Distribution Amount record date.

5.      SUBSEQUENT EVENTS

        Subsequent to March 31, 1998, the Trust declared the following
distribution:

<TABLE>
<CAPTION>
      Quarterly
       Record         Payment             Distribution
        Date           Date                 per Unit
      ---------      ---------            ------------
<S>                  <C>                  <C>
       May 15         May 30                $.533202
</TABLE>

        The distribution per unit increased from $.302872 in the first quarter
of 1998 to $.533202 in the second quarter of 1998. The increase in distributions
was mainly the result of adjustments to the Trust's percentage ownership of
particular wells as a result of federal unit expansions as well as a decrease in
expenses related to royalties, taxes and operating costs. This increase in the
distribution was partially offset by an increase in capital expenditures.

6.      CONTINGENCIES

        Under the terms of the gas purchase contract entered into by WPC and WFS
Gas Resources Company ("WFS Gas Resources"), an affiliate of WPC, as amended
(the "Gas Purchase Contract"), additional revenues may be paid to the Trust to
meet the minimum gas price provision of 97 percent of $1.75 per MMBtu (the
"Minimum Purchase Price"). This additional revenue is subject to recoupment by
the purchaser from future revenues received from production commencing January
1, 1994 when the applicable index price exceeds the Minimum Purchase Price as
long as the Minimum Purchase Price commitment is in effect. The primary term of
the Gas Purchase Contract expired on December 31, 1997, however for calendar
year 1998, WFS Gas Resources did not elect to exercise its annual option to
discontinue paying under the Gas Purchase Contract by giving notice of its
election to pay solely on an index price. Consequently, WFS Gas Resources will
continue to purchase gas pursuant to the Gas Purchase Contract through December
31, 1998 and for additional years until such time as WFS Gas Resources exercises
its annual option to discontinue paying under the Gas Purchase Contract.

        During the first quarter of 1998, the applicable index price was above
the Minimum Purchase Price resulting in recoupments against the price credit
account established pursuant to the terms of the Gas Purchase Contract. WPC
estimates that, as of March 31, 1998, WFS Gas




                                       11
<PAGE>   12

Resources had aggregate price credits in the price credit account of
approximately $11.9 million of which the Trust's 81 percent interest was
approximately $9.6 million. The applicable index price was above the Minimum
Purchase Price in April 1998.

        The entitlement of WFS Gas Resources to recoup the price credits means
that if and when the applicable Blanco Hub Spot Price rises above $1.75 per
MMBtu, future royalty income paid to the Trust would be reduced until such time
as such price credits have been fully recouped. Corresponding cash distributions
to Unitholders would also be reduced.

7.      POSSIBLE NPI PERCENTAGE CHANGE

        The NPI generally entitles the Trust to receive 81 percent of the NPI
Net Proceeds. However, at the point that cumulative production from the
Underlying Properties exceeds 178.5 Bcf of gas and the internal rate of return
of the "after tax cash flow per Trust Unit" (as defined in the Conveyance) is
equal to or greater than 12 percent but not more than 14 percent, the percentage
of NPI Net Proceeds payable in respect of the NPI would be reduced to 60
percent. If such level of production is exceeded and such internal rate of
return of the after tax cash flow per Trust Unit exceeds 14 percent, the
percentage of NPI Net Proceeds payable in respect of the NPI would be reduced to
40 percent. WPC has advised the Trustee that the cumulative production from the
Underlying Properties to date has been approximately 152.3 Bcf. Based upon
projections by Miller and Lents, Ltd., the Trust's independent petroleum
engineers, the internal rate of return is not currently expected to be 12
percent or higher until the third quarter of 2000, although no assurance can be
made that it will not occur sooner than projected.

Item 2.         Trustee's Discussion and Analysis of Financial Condition
                and Results of Operations.

        On May 7, 1997, effective as of May 1, 1997, WPC transferred the
Underlying Properties to an unaffiliated third party ("Buyer") pursuant to the
terms of the Purchase and Sale Agreement dated as of May 1, 1997 (herein so
called) between WPC and Buyer (the "Transaction"). Prior to the Transaction, WPC
had owned the Underlying Properties, subject to and burdened by the Royalty
Interests owned by the Trust, since the inception of the Trust. Neither the
Trustee nor the Delaware Trustee has any control over or responsibility relating
to the operation of the Underlying Properties. The Transaction was previously
reported as a subsequent event by the Trust in its Form 10-Q for the quarter
ended March 31, 1997, and thereafter described in more detail in the Current
Report on Form 8-K filed with the Securities and Exchange Commission on June 23,
1997 (the "Transaction Form 8-K").

        Concurrently with the Transaction, WPC and Buyer entered into a
Management Services Agreement dated May 1, 1997 (the "Management Services
Agreement") whereby WPC agreed, among other things, to continue to manage and
operate the Underlying Properties and to handle the receipt and payment of funds
with respect thereto. Prior to the Transaction, WPC received all payments
relating to the Underlying Properties and, pursuant to the Conveyance, paid to
the Trust the portion thereof attributable to the Royalty Interests. Following
the Transaction, under the Management Services Agreement, WPC continues to
collect all revenues on behalf of Buyer



                                       12
<PAGE>   13

and remains obligated to pay to the Trust on behalf of Buyer the amounts payable
with respect to the Royalty Interests.

        Concurrently with the Transaction, WPC, Williams, the Trust and Buyer
entered into an Agreement dated May 7, 1997 (the "Supplemental Agreement")
pursuant to which (i) the parties acknowledged that WPC was selling the
Underlying Properties to Buyer, but retaining all of its duties and obligations
under the Trust Agreement, Conveyance and related documents (the "Trust
Documents"), subject to the terms and conditions set forth in the Purchase and
Sale Agreement and the agreements entered into pursuant to the Purchase and sale
Agreement, (ii) Williams and WPC each confirmed and agreed that, notwithstanding
the sale of the Underlying Properties to Buyer, Williams and WPC would continue
to perform their respective obligations to the Trust pursuant to the Trust
Documents, including without limitation the performance assurances of Williams
set forth in the Conveyance, and (iii) Buyer acknowledged and agreed that it was
purchasing the Underlying Properties burdened by the Royalty Interests owned by
the Trust.

        As a result of these assurances and the Trustee's belief that the
Transaction will have no adverse effect on Unitholders, the information and
descriptions set forth herein give no effect to the Transaction. Consequently,
with regard to ownership of the Underlying Properties, references herein to
"WPC" with respect to those periods after the effective date of the Transaction
are to Buyer. The Transaction Form 8-K should be consulted for further
information on the Transaction.

         The Trust makes quarterly cash distributions to holders of units of
beneficial interest ("Units") in the Trust ("Unitholders"). The only assets of
the Trust, other than cash and cash equivalents being held for the payment of
expenses and liabilities and for distribution to Unitholders, are net profits
interests (the "Royalty Interests") in certain proved coal seam gas properties
located in the San Juan Basin of New Mexico and Colorado (the "Underlying
Properties"). The Royalty Interests owned by the Trust burden the Underlying
Properties, which are owned by WPC and not the Trust.

         Distributable income of the Trust consists of the excess of royalty
income plus interest income over the general and administrative expenses of the
Trust. Upon receipt by the Trust, royalty income is invested in short-term
investments in accordance with the Trust Agreement (as defined in Note 1 to the
financial statements of the Trust appearing elsewhere in this Form 10-Q ("Note
1")) until its subsequent distribution to Unitholders.

         The amount of distributable income of the Trust for any quarter may
differ from the amount of cash available for distribution to Unitholders in such
quarter due to differences in the treatment of the expenses of the Trust in the
determination of those amounts. The financial statements of the Trust are
prepared on a modified cash basis pursuant to which the expenses of the Trust
are recognized when incurred. Consequently, the reported distributable income of
the Trust for any quarter is determined by deducting from the income received by
the Trust the amount of expenses incurred by the Trust during such quarter. The
amount of cash available for distribution to Unitholders, however, is determined
in accordance with the provisions of the Trust Agreement and reflects the
deduction from the income actually received by the Trust of the




                                       13
<PAGE>   14

amount of expenses actually paid by the Trust and adjustments for changes in
reserves for unpaid liabilities. See Note 4 to the financial statements of the
Trust appearing elsewhere in this Form 10-Q for additional information regarding
the determination of the amount of cash available for distribution to
Unitholders.

Three Months Ended March 31, 1998 Compared to Three Months Ended March 31, 1997

         For the quarter ended March 31, 1998, royalty income received by the
Trust amounted to $3,048,296 as compared to $4,103,814 received for the same
quarter in 1997. The decrease in royalty income is primarily due to a decline in
production and an increase in expenses related to royalties, taxes, operating
costs and capital expenditures. Production related to the royalty income
received by the Trust in the first quarter of 1998 was 2,404,077 MMBtu as
compared to 3,915,754 MMBtu for the same quarter in 1997. Interest income for
the quarter ended March 31, 1998 was $9,566 compared to $12,186 for the same
quarter in 1997. General and administrative expenses during the first quarter of
1998 amounted to $123,944 compared to $187,134 for the same quarter in 1997.
This decrease was the result of the timing of payments of certain annual
expenses such as NYSE listing fees and engineering costs paid in the first
quarter of 1997.

         Distributable income for the quarter ended March 31, 1998 was
$2,933,918 or $.30 per Unit compared to $3,928,866 or $.41 per Unit for the
first quarter of 1997. This decrease was the result of the production decrease
and an increase in expenses related to royalties, taxes, operating costs and
capital expenditures. A distribution of $.302872 per Unit was made on February
27, 1998 to Unitholders of record on February 17, 1998.

         Because the Trust incurs administrative expenses throughout a quarter
but receives its royalty income only once in a quarter, the Trustee established
in the first quarter of 1993 a cash reserve for the payment of expenses and
liabilities of the Trust. The Trustee thereafter has adjusted the amount of such
reserve in certain quarters as required for the payment of the Trust's expenses
and liabilities, in accordance with the provisions of the Trust Agreement. The
Trustee anticipates that it will maintain for the foreseeable future a cash
reserve which will fluctuate as expenses are paid and royalty income is
received.

         Royalty income to the Trust is attributable to the sale of depleting
assets. All of the Underlying Properties burdened by the Royalty Interests
consist of producing properties. Accordingly, the proved reserves attributable
to WPC's interest in the Underlying Properties are expected to decline
substantially during the term of the Trust and a portion of each cash
distribution made by the Trust will, therefore, be analogous to a return of
capital. Accordingly, cash yields attributable to the Units are expected to
decline over the term of the Trust.

         Royalty income received by the Trust in a given calendar quarter will
generally reflect the sum of (i) proceeds from the sale of gas produced from the
WI Properties during the preceding calendar quarter, plus (ii) cash received by
WPC with respect to the Farmout Properties either (a) during the preceding
calendar quarter or (b) if received in sufficient time to be paid to the Trust,
in the month immediately following such calendar quarter. Accordingly, the
royalty income included in distributable income for the quarter ended March 31,
1998 was based on production




                                       14
<PAGE>   15

volumes and natural gas prices for the period October 1997 through December
1997, as shown in the table below. Due to delays associated with the receipt of
income related to the Farmout Properties, the Trust's royalty income for the
first quarter of 1998 reflects estimated production volumes from the Farmout
Properties for the months of September 1997 through November 1997, as shown in
the table below. The production volumes included in the table below are for
production attributable to the Underlying Properties, and not for production
attributable to the Trust's Royalty Interests and are net of the amount of
production attributable to WPC's royalty obligations to third parties, which is
determined by contractual arrangement with such parties.

<TABLE>
<CAPTION>
                                                              Three Months                     Three Months
                                                                  Ended                            Ended
                                                            December 31, 1997                December 31, 1996
                                                            -----------------                -----------------
<S>                                                             <C>                          <C>        
Production (MMBtu) (1)
     WI Properties                                              1,798,800 (2)                   3,065,212  (4)
     Farmout Properties                                         1,169,196 (3)                   1,769,052  (5)

Blanco Hub Spot Price
     ($/MMBtu)  (6)                                                 $2.70                           $2.53
Net Wellhead Price
     WI Properties ($/MMBtu) (6)                                    $ .92                           $1.03
</TABLE>

-----------------------

(1)      Million British Thermal Units.

(2)      Includes prior period adjustments of 48,423 MMBtu.

(3)      Reflects estimated volumes for September 1997 through November 1997.

(4)      Includes prior period adjustments of 761,849 MMBtu.

(5)      Reflects actual volumes for September 1996 through November 1996.

(6)      Simple average of the months included in the period presented.

         Production from the WI Properties is generally sold pursuant to a gas
purchase contract between WPC and WFS Gas Resources Company ("WFS Gas
Resources") (as successor in interest to Williams Gas Marketing Company) (as
amended, the "Gas Purchase Contract"). The Gas Purchase Contract provides
certain protections for WFS Gas Resources in the form of price credits (for
production purchased by WFS Gas Resources on or after January 1, 1994) and for
Unitholders when the applicable Blanco Hub Spot Price falls below $1.75 per
MMBtu and provides certain benefits for WFS Gas Resources when the Blanco Hub
Spot Price exceeds $2.00 per MMBtu. The Gas Purchase Contract also provides that
the price paid for gas by WFS Gas Resources is reduced by the amount of
gathering, processing and certain other costs paid by WFS Gas Resources.

         The initial five-year term ("Primary Term") of the Gas Purchase
Contract expired on December 31, 1997. Following the expiration of the Primary
Term, the Gas Purchase Contract will continue in effect for one or more
consecutive additional one-year terms (each such term a "Contract Year") unless
and until WFS Gas Resources exercises its annual option, exercisable fifteen
days prior to the end of each Contract Year, to discontinue purchasing gas from
WPC




                                       15
<PAGE>   16

under the terms of the gas purchase contract and instead purchase gas at a
monthly price equal to the index price of 97 percent of the Blanco Hub Spot
Price. For the Contract Year January 1, 1998 through December 31, 1998, WFS Gas
Resources did not exercise this option and the pricing mechanism of the Primary
Term will therefore remain in place through at least December 31, 1998.

         The Blanco Hub Spot Price was above $1.75 per MMBtu during January,
February and March 1998. However, pursuant to the terms of the gas purchase
contract, WFS Gas Resources continued to purchase gas produced from the WI
Properties at the $1.70 minimum purchase price, less certain gathering,
processing and delivery costs paid by WFS Gas Resources, established by the gas
purchase contract; and recouped price credits from for each MMBtu of natural gas
so purchased equal to the difference between the $1.70 minimum purchase price
and the applicable index price (which price is equal to 97 percent of the
applicable Blanco Hub Spot Price). WPC estimates that, as of March 31, 1998, WFS
Gas Resources had aggregate price credits of approximately $11.9 million of
which the Trust's 81 percent interest was approximately $9.6 million. The Blanco
Hub Spot Price was above $1.75 per MMBtu in April 1998.

         The entitlement of WFS Gas Resources to recoup the price credits means
that if and when the applicable Blanco Hub Spot Price rises above $1.75 per
MMBtu, future royalty income paid to the Trust would be reduced until such time
as such price credits have been fully recouped. Corresponding cash distributions
to Unitholders would also be reduced.

         The information in this Form 10-Q concerning production and prices
relating to the Underlying Properties is based on information prepared and
furnished by WPC to the Trustee. The Trustee has no control over and no
responsibility relating to the operation of the Underlying Properties.

Year 2000 Issue

         Many existing computer programs use only two digits to identify a year
in the date field. These programs were designed and developed without
considering the impact of the upcoming change in the century. If not corrected,
many computer applications could fail or create erroneous results by or at the
year 2000. The Year 2000 issue affects virtually all companies and
organizations. If a company or organization does not successfully address its
Year 2000 issues, it may face material adverse consequences.

         The Trust is reliant on the performance of Williams and third party
vendors for the receipt of royalty income, payment of expenses and disbursement
of distributable income. The Trustee can provide no assurance as to whether
Williams and third party vendors will successfully address the Year 2000 issue.
Failing to successfully address the Year 2000 issue by Williams and third party
vendors could have a material adverse impact on the Trust and its Unitholders.




                                       16
<PAGE>   17

Forward-Looking Statements

         This report on Form 10-Q includes "forward-looking statements" within
the meaning of Section 27A of the Securities Act of 1933, as amended, and
Section 21E of the Securities Exchange Act of 1934, as amended. All statements
other than statements of historical fact included in this Form 10-Q, including,
without limitation, statements contained in this "Trustee's Discussion and
Analysis of Financial Condition and Results of Operations" regarding the Trust's
financial position and industry conditions, are forward-looking statements.
Although the Trustee believes that the expectations reflected in such
forward-looking statements are reasonable, it can give no assurance that such
expectations will prove to have been correct.

Item 3.           Quantitative and Qualitative Disclosures About Market Risk.

         Inapplicable.


                                       17
<PAGE>   18

                           PART II - OTHER INFORMATION

Item 6.           Exhibits and Reports on Form 8-K.

         (a)      Exhibit No.                                 Description

                       27                            Financial Data Schedule

         (b)      No reports on Form 8-K were filed during the quarter for which
                  this report is filed.




                                       18
<PAGE>   19

                                   SIGNATURES

         Pursuant to the requirements of the Securities Exchange Act of 1934,
the registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.

                               WILLIAMS COAL SEAM GAS ROYALTY TRUST

                               By: NATIONSBANK OF TEXAS, N.A., Trustee



                               By: /s/ Ron Hooper
                                   ------------------------------------------
                                   Ron Hooper
                                   Vice President and Administrator


               (The Trust has no directors or executive officers.)


Date:  May 14, 1998





                                       19
<PAGE>   20

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
                  Exhibit No.                                 Description
                  -----------                                 -----------
                  <S>                                <C>
                       27                            Financial Data Schedule
</TABLE>