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                                                          Exhibit 99.906CERT

   CERTIFICATION PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002
      (SUBSECTIONS (a) AND (b) OF SECTION 1350, CHAPTER 63 OF TITLE 18,
                              UNITED STATES CODE)


     In connection with the report of Reserve Municipal Money Market Trust
(the "Registrant") on Form N-CSR (the "Report") filed with the Securities and
Exchange Commission on August 9, 2004, each of the undersigned officers of
the Registrant does hereby certify that, to the best of such officer's
knowledge:

1) the Report fully complies with the requirements of Section 13(a) or 15(d),
   as applicable, of the Securities Exchange Act of 1934, as amended;

2) the information contained in the Report fairly presents, in all material
   respects, the financial condition and results of operations of the Registrant
   as of, and for, the periods presented in the Report.

Dated:  January 24, 2005


By: /s/ Bruce R. Bent
    -----------------------
    Name: Bruce R. Bent
    Title: Chairman and CEO


Dated:  January 24, 2005


By: /s/ Arthur T. Bent III
    -----------------------
    Arthur T. Bent III
    Treasurer (Principal Financial Officer)


     A signed original of this written statement required by Section 906, or
other document authenticating, acknowledging, or otherwise adopting the
signature that appears in typed form within the electronic version of this
written statement required by Section 906, has been provided to the
registrant and will be retained by the Registrant and furnished to the
Securities and Exchange Commission or its staff upon request.

     This certification is being furnished solely pursuant to 18 U.S.C. ss.
1350 and is not being filed as part of the Report or as a separate disclosure
document.