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                                                                    EXHIBIT 10.4



                             FIRST AMENDMENT TO THE
                         1996 EQUITY PARTICIPATION PLAN
                                       OF
                         CANDLEWOOD HOTEL COMPANY, INC.

        This First Amendment to The 1996 Equity Participation Plan of Candlewood
Hotel Company, Inc. (the "Plan"), is adopted by Candlewood Hotel Company, Inc.,
a Delaware corporation (the "Company") effective as of May 18, 1998.

                                    RECITALS

        A.      The Plan was adopted by the Board of Directors of the Company on
                September 30, 1996 and was approved by the stockholders of the
                Company on November 7, 1996.

        B.      On January 26, 1998, the Board of Directors of the Company
                approved the following amendment to the Plan:

                                    AMENDMENT

                1.    Section 2.1(a) of the Plan is hereby amended to read in
                      its entirety as follows.


                      "2.1  Shares Subject to Plan

                      (a) The shares of stock subject to Options, awards of
Restricted Stock, Performance Awards, Dividend Equivalents, awards of Deferred
Stock, Stock Payments or Stock Appreciation Rights shall be Common Stock,
initially shares of the Company's Common Stock, par value $.01 per share. The
aggregate number of such shares which may be issued upon exercise of such
options or rights or upon any such awards under the Plan shall not exceed
1,676,710. The shares of Common Stock issuable upon exercise of such options or
rights or upon any such awards may be either previously authorized but unissued
shares or treasury shares."

               The undersigned, Warren D. Fix, Chief Financial Officer,
Executive Vice President and Secretary of the Company, hereby certifies that the
Stockholders of the Company approved the foregoing First Amendment to the Plan
effective as of May 18, 1998.

                                     CANDLEWOOD HOTEL COMPANY, INC.,
                                     a Delaware corporation


                                     By: /S/ WARREN D. FIX
                                         ---------------------------------------
                                         Warren D. Fix, Chief Financial Officer,
                                         Executive Vice President and Secretary