DEAN WITTER U S GOVERNMENT MONEY MARKET TRUST, 497J, 1998-03-03

DEAN WITTER U S GOVERNMENT MONEY MARKET TRUST
497J, 1998-03-03

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        DEAN WITTER U. S. GOVERNMENT MONEY MARKET TRUST
                     TWO WORLD TRADE CENTER
                    NEW YORK, NEW YORK 10048




                                   March  2, 1998



Securities and Exchange Commission
450 Fifth Street, N.W.
Washington, D.C.  20549


Re:  Dean Witter U. S. Government Money Market Trust
     File Number 2-74980


Dear Sir or Madam:

      On behalf of the Registrant, the undersigned certifies that
the  form  of  Prospectus and Statement of Additional Information
that  would have been filed under Section 497(c) would  not  have
differed  from  those contained in the text of  the  Registrant's
most  recent registration statement that was filed electronically
via EDGAR with the Securities and Exchange Commission on March 2,
1998.


                                   Very truly yours,
                               /s/ Marilyn K. Cranney
                                   Marilyn K. Cranney
                                   Assistant Secretary



cc: Randolph Koch
    Barry Fink