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

                                    FORM 10-Q

                  QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934



FOR THE QUARTER ENDED MARCH 31, 1999  COMMISSION FILE NUMBER 2-22997



                                MILLS MUSIC TRUST
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)



    NEW YORK                                                  13-6183792
(STATE OR OTHER JURISDICTION OF                             (I.R.S. EMPLOYER
 INCORPORATION OR ORGANIZATION)                            IDENTIFICATION NO.)



C/O MARINE MIDLAND BANK,   140 BROADWAY,   NEW YORK, NY          10015
         (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)              (ZIP CODE)



REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE                (212) 658-6014


         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 TRUST UNITS OUTSTANDING AS OF MARCH 4, 1999    277,712
<PAGE>   2
                                                                          Page 2



                          PART I - FINANCIAL STATEMENTS

Item 1.  Financial Information

                                MILLS MUSIC TRUST
                  STATEMENTS OF CASH RECEIPTS AND DISBURSEMENTS
                   THREE MONTHS ENDED MARCH 31, 1999 AND 1998

                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                        Three Months Ended
                                                             March 31
                                                   -----------------------------
                                                     1999                 1998
                                                   --------             --------
<S>                                                <C>                  <C>
Receipts:
 Mills Music, Inc.                                 $274,046             $199,882
                                                   --------             --------

Total Receipts                                      274,046              199,882
Undistributed cash
 at beginning of
 the period                                              39                    8

Disbursements -
administrative expenses                              (7,336)             (12,270)
                                                   --------             --------

Balance available
 for distribution                                   266,749              187,620

Cash distribution
 to unit holders                                    266,714              187,620
                                                   --------             --------

Undistributed cash at
  end of the period                                $     35             $      0
                                                   ========             ========

Cash distribution per
 unit (based on 277,712
   units outstanding)                              $  .9604             $  .6756
                                                   ========             ========
</TABLE>


    See accompanying Notes to Statements of Cash Receipts and Disbursements.
<PAGE>   3
                                                                          Page 3



                                MILLS MUSIC TRUST
             NOTES TO STATEMENTS OF CASH RECEIPTS AND DISBURSEMENTS
                   THREE MONTHS ENDED MARCH 31, 1999 AND 1998

                                   (UNAUDITED)

NOTE 1.  ACCOUNTING POLICIES AND GENERAL INFORMATION

                  Mills Music Trust ("the Trust") was created in 1964 for the
         purpose of acquiring the rights to receive payments of a deferred
         contingent purchase price contract obligation payable by Mills Music,
         Inc. ("Mills"). The contingent payments are determined quarterly, and
         are based on a formula which takes into account gross royalty income
         from certain music copyrights and licenses of Mills, less royalties
         paid and amounts deducted by Mills in accordance with contract terms.

                  Payments from Mills to the Trust are made in March, June,
         September, and December, and include net royalty income of the
         preceding calendar quarter. The payments received are accounted for on
         a cash basis, as are expenses paid. The Declaration of Trust requires
         the distribution of all funds received by the Trust to the Unit holders
         after payment of expenses.

                  The statements of cash receipts and disbursements reflect only
         cash transactions and do not present transactions that would be
         included in financial statements presented on the accrual basis of
         accounting, as contemplated by generally accepted accounting
         principles.

                  There is no book value per unit because cumulative
         distributions are in excess of the initial investment in the Trust.

NOTE 2.  RELATED PARTY TRANSACTIONS

                  The Declaration of Trust provides that each trustee shall
         receive reimbursement for expenses reasonably incurred in the
         performance of his duties and annual compensation of $2,500 per year
         for his services as trustee, provided that such aggregate compensation
         to the trustees as a group may not exceed 3% of the monies received by
         the Trust in any year. The Declaration of Trust further provides for
         reimbursement to the corporate trustee for its clerical and
         administrative services to the Trust. Accordingly, Marine Midland Bank
         receives reimbursement for such services and for services performed as
         Registrar and Transfer Agent. The Declaration of Trust further provides
         that if any trustee performs unusual or extraordinary services,
         reasonable compensation for such services shall be paid, subject to
         certain
<PAGE>   4
                                                                          Page 4



                                MILLS MUSIC TRUST
             NOTES TO STATEMENTS OF CASH RECEIPTS AND DISBURSEMENTS
                   THREE MONTHS ENDED MARCH 31, 1999 AND 1998
                                   (CONTINUED)

                                   (UNAUDITED)

         limitations and to prior confirmation by a majority in interest of
         Trust Certificate holders. Pursuant to these provisions, disbursements
         to related parties were made as follows for the three months ended
         March 31, 1998 and 1997.

<TABLE>
<CAPTION>
                                                          1999              1998
                                                          ----              ----
<S>                                                       <C>               <C>
Trustee Fees:
    Bernard D. Fischman                                   $625              $625
    Marine Midland Bank                                    625               625
</TABLE>



NOTE 3.  ROYALTY EXAMINATION

                  The Trust's claim against Belwin Mills Publishing Corporation,
         the former administrators of the Old Mills Catalogue, in connection
         with a royalty examination is pending. It cannot be determined at this
         time, what, if any, amount may ultimately be received by the Trust.

                  Legal and accounting fees paid from inception (1987) through
         March 31, 1999 by the Trust in connection with this examination
         aggregate $75,438.

                  The Trust has determined that its previously disclosed claim
         against the former administrator of the Old Mills Catalogue in
         connection with the 1987 royalty examination is not cost beneficial
         and, therefore, is not being pursued. No examination of royalty
         information has been performed subsequent to 1987.

NOTE 4.  FEDERAL INCOME TAXES

                  No provision for income taxes has been made since the
         liability is that of the unit holders and not the Trust.
<PAGE>   5
                                                                          Page 5


                          PART I - FINANCIAL STATEMENTS


Item 2.  Management's Discussion and Analysis of Results of Operations

                  The Trust's receipts from Mills Music, Inc. are derived from
         copyrights established prior to 1964 and such receipts fluctuate based
         upon public interest in the "nostalgia" appeal of older songs.



                           PART II - OTHER INFORMATION

                Items 1 through 6, inclusive, are not applicable.
<PAGE>   6
                                                                          Page 6



                                   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.


                                                      MILLS MUSIC TRUST
                                              --------------------------------
                                                        (Registrant)





Date    April 12, 1999                        By:     BERNARD D. FISCHMAN
     ----------------------                       ----------------------------
                                                  Bernard D. Fischman, Trustee




Date    April 12, 1999                        By:      MARCIA MARKOWSKI
     -----------------------                      ----------------------------
                                                  Marine Midland Bank
                                                  Corporate Trustee