<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, 1999

                                       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, N.A. (d/b/a Bank of America, N.A.)
                                 901 Main Street
                                   17th Floor
                               Dallas, Texas 75202
                    (Address of principal executive offices)
                                   (Zip code)

                                 (214) 209-2400
              (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 15, 1999:
9,700,000.


<PAGE>   2

                         PART I - FINANCIAL INFORMATION

Item 1.  Financial Statements.

         The financial statements included herein have been prepared by
NationsBank, N.A. (d/b/a Bank of America, 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, 1998 (the "1998 Annual Report"). The December 31,
1998 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, 1999, and the distributable income and the
changes in trust corpus for the three-month periods ended March 31, 1999 and
1998, 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, 1999 and for the three-month
periods ended March 31, 1999 and 1998 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

The Trustee
  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, 1999,
and the related condensed statements of distributable income and changes in
trust corpus for the three-month periods ended March 31, 1999 and 1998. 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, 1998, 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 26, 1999, 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, 1998, 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 14, 1999

                                        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                                                1999              1998      
                                                ---------------   ---------------

<S>                                             <C>               <C>
Current Assets -
        cash and cash equivalents               $        83,816   $        80,599
Royalty interests in oil
        and gas properties
        (less accumulated
        amortization of
        $92,009,421 at
        March 31, 1999
        and $88,783,924 at
        December 31, 1998)                           46,557,242        49,782,739
                                                ---------------   ---------------

TOTAL ASSETS                                    $    46,641,058   $    49,863,338
                                                ===============   ===============


LIABILITIES AND TRUST CORPUS

Current Liabilities -
        trust expenses payable                  $       125,039   $        93,986

Trust corpus -
        9,700,000 units of
        beneficial interest
        authorized and
        outstanding                                  46,516,019        49,769,352
                                                ---------------   ---------------

TOTAL LIABILITIES
        AND TRUST CORPUS                        $    46,641,058   $    49,863,338
                                                ===============   ===============
</TABLE>



The accompanying notes are an integral part of these financial statements. See
Independent 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, 1999    March 31, 1998  
                                      ---------------    ---------------

<S>                                   <C>                <C>            
Royalty income                        $     4,110,785    $     3,048,296
Interest income                                13,401              9,566
                                      ---------------    ---------------
                                            4,124,186          3,057,862

General and administrative
        expenses                             (167,835)          (123,944)
                                      ---------------    ---------------
Distributable income                  $     3,956,351    $     2,933,918
                                      ===============    ===============

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


The accompanying notes are an integral part of these financial statements. See
independent 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, 1999    March 31, 1998 
                                      ---------------    ---------------
<S>                                   <C>                <C>            
Trust corpus,
        beginning of period           $    49,769,352    $    61,271,700
Amortization of royalty
        interests                          (3,225,497)        (2,002,768)
Distributable income                        3,956,351          2,933,918
Distributions to unitholders               (3,984,187)        (2,937,862)
                                      ---------------    ---------------


Trust corpus, end
        of period                     $    46,516,019    $    59,264,988
                                      ===============    ===============

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


The accompanying notes are an integral part of these financial statements. See
independent 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, N.A. (d/b/a Bank of America,
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 at the
time of the Trust's formation 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 6,131,209 Units to the public through various underwriters in
January and February 1993 (the "Public Offering"). During the second quarter of
1995 Williams transferred its remaining 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. Effective May 1, 1997, WPC transferred the
Underlying Properties, subject to and burdened by the Royalty Interests, to
Quatro Finale LLC, a non-affiliated Delaware limited liability company ("Quatro
Finale").

        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.


                                        7

<PAGE>   8

        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, as
defined below, attributable to (i) gas produced and sold from Quatro Finale's
net revenue interests (working interests less lease burdens) in the properties
in which Quatro Finale has a working interest (the "WI Properties") and (ii) the
revenue stream received by Quatro Finale 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 Quatro
Finale'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
Quatro Finale from its 35 percent net profits interest in the Farmout
Properties, plus the aggregate proceeds attributable to Quatro Finale'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 Quatro Finale'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
Quatro Finale'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. Based on current estimates, a downward adjustment to the NPI is
expected during the year 2000. 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

                                        8

<PAGE>   9

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 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.


                                        9

<PAGE>   10

        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 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, 1999, the Trust declared the following
distribution:

<TABLE>
<CAPTION>
                     Quarterly
                      Record              Payment         Distribution
                       Date                Date             per Unit  
                     ---------            -------         ------------
                     <S>                  <C>             <C>     
                      May 17              May 28            $.286977
</TABLE>

        The distribution per unit decreased from $.410740 in the first quarter
of 1999 to $.286977 in the second quarter of 1999. The decrease in distributions
was mainly the result of the 15th expansion of the San Juan 31-6 Fruitland
Coal Seam unit. The unit expansion adjustment was partially offset by lower than
normal operating and capital costs.

6.      CONTINGENCIES

        Under the terms of the gas purchase contract entered into by WPC and WFS
Gas Resources Company ("WFS Gas Resources") (as successor to Williams Gas
Marketing Company), as amended (the "Gas Purchase Contract"), additional
revenues may be paid to the Trust to meet the Minimum Purchase Price provision
of 97 percent of $1.75 per MMBtu. This additional revenue is subject to
recoupment by the purchaser from future revenues received from production
commencing after January 1, 1994 when the applicable index price exceeds the
Minimum Purchase Price as long as the Minimum Purchase Price commitment is in
effect. Pursuant to the terms of the Gas Purchase Contract, a price credit
account was established for the purpose of accounting for such recoupments. The
primary term of the Gas Purchase Contract expired on December 31, 1997, at which
time WFS Gas Resources had the option to discontinue paying the Minimum Purchase
Price by giving notice of its election to pay solely on an index price. For each
of the contract years January 1, 1998 through December 31, 1998 and January 1,
1999 through December 31, 1999, WFS Gas Resources did not exercise this option
and the pricing mechanism of the primary term has and will continue to remain in
effect through at least December 31, 1999.

        During the first quarter of 1999, the applicable index price was
below the Minimum Purchase Price resulting in accruals in the price credit

                                       10

<PAGE>   11

account established under the Gas Purchase Contract. WPC estimates that, as of
March 31, 1999, WFS Gas Resources had aggregate price credits in the price
credit account of approximately $11.7 million of which the Trust's 81 percent
interest in Quatro Finale's interest in the WI Properties, represents a
potential offset of $9.5 million against future royalty income otherwise payable
to the Trust. The applicable index price was above the Minimum Purchase Price 
in April 1999.

        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 otherwise payable 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 Trustee has been advised by WPC that the Minerals Management
Service ("MMS"), a subagency of the U.S. Department of the Interior, has from
time to time considered the inclusion of the value of the Section 29 tax
credits attributable to coal seam gas production in the calculation of gross
proceeds for purposes of calculating the royalty that is payable to the MMS. On
August 30, 1993, the U.S. Office of the Inspector General (the "OIG") issued an
audit report stating that Section 29 tax credits should be included in the
calculation of gross proceeds and recommending that the MMS pursue collection
of additional royalties with respect to past and future production. On December
8, 1993, however, the Office of the Solicitor of the U.S. Department of the
Interior gave its opinion to the MMS that the report of the OIG was incorrect
and that Section 29 tax credits are not part of gross proceeds for the purpose
of Federal royalty calculations. WPC believes that any such inclusion of the
value of Section 29 tax credits for the purposes of calculating royalty
payments required to be made on Federal and Indian lands would be inappropriate
since all mineral interest owners, including royalty owners, are entitled to
Section 29 tax credits for their proportionate share of qualifying coal seam
gas production. WPC has advised the Trustee that it would vigorously oppose any
attempt by the MMS to require the inclusion of the value of Section 29 tax
credits in the calculation of gross proceeds. However, if such regulations were
adopted and upheld, royalty payments would be increased which would decrease
NPI Net Proceeds and, therefore, the amounts payable to the Trust. The
reduction in amounts payable to the Trust would cause a corresponding reduction
in associated Section 29 tax credits available to Unitholders.

        The Trustee has also been informed by WPC that the MMS has informed
some San Juan Basin natural gas producers that they have incorrectly deducted
certain costs in the producers' coal bed methane valuations in determining the
amounts due to Federal royalty owners. While WPC believes that their past
computations have been appropriately stated, applying the MMS methodology could
result in an adjustment to amounts previously paid to the Trust of
approximately $3,000,000.
 
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 178.6 Bcf. Based upon
projections, the internal rate of return is not currently expected to be 12 
percent or higher until the fourth 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.

         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 Quatro Finale 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) 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


                                       11

<PAGE>   12

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
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, 1999 Compared to Three Months Ended March 31, 1998

         For the quarter ended March 31, 1999, royalty income received by the
Trust amounted to $4,110,785 as compared to $3,048,296 received for the same
quarter in 1998. The increase in royalty income is primarily due to an increase
in production and a decrease 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 1999 was 4,031,239 MMBtu as
compared to 2,499,902 MMBtu for the same quarter in 1998. Interest income for
the quarter ended March 31, 1999 was $13,401 compared to $9,566 for the same
quarter in 1998. General and administrative expenses during the first quarter of
1999 amounted to $167,835 compared to $123,944 for the same quarter in 1998.

         Distributable income for the quarter ended March 31, 1999 was
$3,956,351 or $.41 per Unit compared to $2,933,918 or $.30 per Unit for the
first quarter of 1998. This increase was the result of the production increase
and a decrease in expenses related to royalties, taxes, operating costs and
capital expenditures. A distribution of $.410740 per Unit was made on March 1,
1999 to Unitholders of record on February 16, 1999.

         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 Quattro Finale'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
Quatro Finale with respect to the Farmout Properties


                                       12

<PAGE>   13

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, 1999 was based on production volumes and
natural gas prices for the period October 1998 through December 1998, 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
1999 reflects estimated production volumes from the Farmout Properties for the
months of September 1998 through November 1998, 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 Quatro
Finale'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, 1998                December 31, 1997
                                                            -----------------                -----------------
<S>                                                         <C>                              <C>
Production (MMBtu) (1)
     WI Properties                                               3,854,235(2)                   1,798,800(4)
     Farmout Properties                                          1,122,603(3)                   1,287,499(5)

Blanco Hub Spot Price
     ($/MMBtu)  (6)                                         $         1.84                   $       2.70
Net Wellhead Price 
     WI Properties ($/MMBtu) (6)                            $          .94                   $        .92
</TABLE>

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

(1)      Million British Thermal Units.
(2)      Includes prior period adjustments of 295,001 MMBtu.
(3)      Reflects estimated volumes for September 1998 through November 1998
         (Includes prior period adjustments of (169,114)).
(4)      Includes prior period adjustments of 48,423 MMBtu.
(5)      Reflects actual volumes for September 1997 through November 1997.
(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

                                       13

<PAGE>   14
prior to the end of each Contract Year, to discontinue purchasing gas 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 each of
the contract years January 1, 1998 through December 31, 1998 and January 1, 1999
through December 31, 1999, WFS Gas Resources did not exercise this option and
the pricing mechanism of the Primary Term therefore has and will continue to
remain in effect through at least December 31, 1999.

         The Blanco Hub Spot Price was below $1.75 per MMBtu during January,
February and March 1999. 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 accrued price credits 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, 1999, WFS Gas
Resources had aggregate price credits in the price credit account of
approximately $11.7 million of which the Trust's 81 percent interest in Quatro
Finale's interest in the WI Properties, represents a potential offset of $9.5
million against future royalty income otherwise payable to the Trust. The
applicable index price was below the Minimum Purchase Price in April 1999.

         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 Trustee has
identified its primary system that is vulnerable to the Year 2000 issue: its
General Ledger/Accounts Payable System. The current system is Year 2000
compliant. The Trust selected a system that has been warranted to be Year 2000
compliant and completed the installation of the new system at the beginning of
1998. The cost of the system was approximately $6,000. To date the Trustee has
incurred no other costs in connection with its efforts to identify, assess,
remediate and test the Trust's systems for Year 2000 compliance.

         The Trustee is in the process of identifying and assessing other
information technology ("IT") systems used in connection with the Trust, as well
as other systems, for Year 2000 compliance.

                                       14

<PAGE>   15
Non-IT systems are generally more difficult to assess because they often contain
embedded technology that may be subject to Year 2000 problems. The total cost of
the Trustee's Year 2000 efforts is expected to be approximately $10,000
(including the $6,000 referred to above), all of which is expected to be
incurred and paid during the last two quarters of 1998 and the first two
quarters of 1999. Of this amount, the Trustee estimates that $4,000 is
attributable to identification and assessment of affected systems and $6,000 is
attributable to remediation (which may include the replacement of certain
noncomplying systems). The Trustee expects all of its Year 2000 compliance
efforts to be completed by the end of the second quarter of 1999.

         The Trustee has additionally identified those vendors it believes could
have an impact on its day-to-day operations if their operations were interrupted
as a result of Year 2000 problems. The Trustee has developed a questionnaire
regarding the vendors' Year 2000 status. These vendors, consisting primarily of
energy companies, have been contacted before January 1, 1999 to determine their
Year 2000 status. WPC, which provides extensive accounting services to the
Trust, has indicated that its IT system will be Year 2000 complaint. The Trustee
is continuing discussions with WPC regarding its certification.

         The Trustee has no reason to believe that its vendors will not be Year
2000 compliant. In the event the Trustee learns that a vendor's system will not
be Year 2000 compliant, the Trustee will assess the potential risk and develop
contingency plans at that time.

         The Trust is a passive entity with no business operations, and the IT
systems employed by the Trustee in connection with its duties on behalf of the
Trust are less extensive than the systems employed by many business entities.
The Trust has no formal IT budget, and the Trustee does not anticipate making
any other significant capital expenditures relating to the Trustee's IT systems
used in connection with Trust during 1998 or 1999. Thus, the expenditures
expected to be made in connection with the Year 2000 efforts described above
will represent substantially all of the Trustee's IT-related capital
expenditures on behalf of the Trust during 1998 and 1999. These expenses will be
paid as expenses of the Trust.

         Because the royalty interests held by the Trust are fixed, the Trustee
is dependent upon the third parties (primarily energy companies) that hold
operating interests with respect thereto for the receipt of royalty income.
Thus, if any such third party failed to deliver royalty income, the Trustee
would have available no alternative source for such income. The Trustee believes
that the worst case scenario would be the failure by the Trustee and one or more
third parties who pay royalties to the Trust to identify or remediate Year 2000
problems on a timely basis, which could cause the Trustee to be unable to make
required distributions to Unitholders. Such inability could result in the
incurrence by the Trust of interest charges or other liabilities to Unitholders.
The Trustee believes that in the event of a failure of any of its internal
systems it would be able to replace such systems in a relatively short period of
time, relying on internal resources of Bank of America, N.A., which serves as
the Trustee, although there can be no assurance that such replacement would not
be costly or that it would be completed without resulting in a significant delay
in the distributions to Unitholders. With respect to a failure by a third party
to deliver royalty income on a timely basis, the Trustee believes that it would
have no control over the efforts of such third party to correct the problems,
and significant delays in the receipt of royalty income could result.


                                       15

<PAGE>   16
         The Trust will utilize both internal and external resources to achieve
Year 2000 compliance. The Trustee estimates that its identification and
assessment activities are approximately 80% complete and that its remediation
and testing efforts are approximately 90% complete. It expects that all of its
Year 2000 efforts related to the Trust's internal systems will be completed by
the end of the second quarter of 1999. However, there can be no guarantee that
the Trustee will be able to identify all potential Year 2000 problems or to
fully remediate all Year 2000 problems identified on a timely basis. There also
can be no assurance that the systems of third party vendors on which the Trust
relies will be timely remediated. The failure by the Trustee or any such third
party to fully remediate its Year 2000 problems on a timely basis could have a
material adverse affect on the Trustee's ability to account for and make timely
distribution of the Trust's distributable income.

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.

         The only assets of and sources of income to the Trust are the Royalty
Interests, which generally entitle the Trust to receive a share of the net
profits from natural gas production from the Underlying Properties.
Consequently, the Trust's financial results can be significantly affected by
fluctuations in natural gas prices and the Trust has commodity price risk
exposure associated with the natural gas markets in the United States. The
Royalty Interests do not entitle the Trust to control or influence the operation
of the Underlying Properties or the sale of gas produced therefrom. Natural gas
produced from the WI Properties, which comprises the majority of production
attributable to the Royalty Interests, is currently sold by Quatro Finale
pursuant to the terms of the Gas Purchase Contract. Although the Trust is not a
party to the Gas Purchase Contract, the Gas Purchase Contract may significantly
impact revenues to the Trust. Although the Gas Purchase Contract mitigates the
risk to the Trust of low gas prices, it also limits the ability of the Trust to
benefit from the effects of higher gas prices, particularly to the extent a
balance exists in the Price Credit Account. See "Item 2 -- The Royalty Interests
-- Gas Purchase Contract" in the 1998 Annual Report for detailed information
about the Gas Purchase Contract and its impact on the Trust and Unitholders.

         The Trust is a passive entity and other than the Trust's ability to
periodically borrow money as necessary to pay expenses, liabilities and
obligations of the Trust that cannot be paid out of cash held by the Trust, the
Trust is prohibited from engaging in borrowing transactions. The amount of any
such borrowings is unlikely to be material to the Trust. The Trust periodically
holds short term investments acquired with funds held by the Trust pending
distribution to Unitholders and funds held in reserve for the payment of Trust
expenses and liabilities. Because of the short-term nature of


                                       16

<PAGE>   17

these borrowings and investments and certain limitations upon the types of such
investments which may be held by the Trust, the Trustee believes that the Trust
is not subject to any material interest rate risk. The Trust does not engage in
transactions in foreign currencies which could expose the Trust or Unitholders
to any foreign currency related market risk.


                                       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, N.A.
                                  (d/b/a BANK OF AMERICA, N.A.), Trustee



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


               (The Trust has no directors or executive officers.)


Date:  May 17, 1999



                                       19

<PAGE>   20

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit 
Number           Description
-------          -----------
<S>              <C>
  27             Financial Data Schedule
</TABLE>