<PAGE>

                                                                    Exhibit 10.4

                    FIRST AMENDMENT TO STOCKHOLDERS AGREEMENT

         This First Amendment (this "Amendment") is entered into as of October
13, 1999, by and among Digital Theater Systems, Inc., a Delaware corporation
(the "Company"), Forth Investments, LLC, Universal City Studios, Inc., and the
other stockholders of the Company listed on Annex I hereto, in order to amend
that certain Stockholders Agreement (the "Stockholders Agreement") dated as of
October 24, 1997, among the Company and the stockholders of the Company listed
on Schedule A thereto. Capitalized terms used in this Amendment and not defined
shall have the meanings given such terms in the Stockholders Agreement.

         WHEREAS, pursuant to Section 12(a) of the Stockholders Agreement,
except as otherwise provided therein, any amendment to the Stockholders
Agreement must be approved in writing by (i) the Company; (ii) the Stockholders
holding at least a majority in voting power of the Stockholders Shares subject
to the Stockholders Agreement; (iii) Spielberg (so long as Spielberg continues
to hold 50% or more of the Stockholders Shares held by Spielberg that are
subject to the Stockholders Agreement); (iv) Universal (so long as Universal
continues to hold 50% or more of the Stockholders Shares held by Universal that
are subject to the Stockholders Agreement); and (v) the holders of a majority in
voting power of the shares set forth on Annex I to the Shareholders Agreement
(collectively, the "Approving Parties"); and

         WHEREAS, the Approving Parties desire to amend the Shareholders
Agreement as set forth below.

         NOW THEREFORE, the undersigned, in consideration of the premises,
covenants and agreements contained herein, do hereby agree as follows:

1.       Clause (i) of the definition of "Excluded Securities" contained in the
Stockholders Agreement is hereby amended to read in its entirety as follows:

         "any options issued or issuable pursuant to a Stock Option Plan and any
         shares of Common Stock issuable upon exercise of any options granted
         pursuant to a Stock Option Plan; provided, that any shares of Common
         Stock which are so issued or issuable shall not exceed 2,510,466 shares
         of Common Stock in the aggregate,"

2.       Except as amended hereby, the Stockholders Agreement shall remain in
full force and effect.

<PAGE>

         IN WITNESS WHEREOF, the undersigned have caused this Amendment to be
duly executed as of the date and year first above written.

                                           Mr. Terry Beard

                                           By: ________________________________
                                               Mr. Terry Beard
                                               Management Shareholder &
                                               Chairman of the Board

                                           Digital Theater Systems, Inc.

                                           By: /s/ Dan Slusser
                                               ---------------------------------
                                               Dan Slusser
                                               Vice Chairman & CEO

                                           Forth Investments, LLC

                                           By: /s/ Michael Rutman

                                           Name: Michael Rutman

                                           Title: CFO

                                           Universal City Studios, Inc.

                                           By: /s/ William A. Sutman

                                           Name: William A. Sutman

                                           Title: SVP & CFO

                                           Westin Presidio Capital II

                                           By: /s/ James B. McElwee
                                               ---------------------------------
                                           Name: James B. Elwee

                                           Title: General Partner

                                  Page 2 of 2