DEAN WITTER U S GOVERNMENT MONEY MARKET TRUST, 497J, 1996-03-21

DEAN WITTER U S GOVERNMENT MONEY MARKET TRUST
497J, 1996-03-21

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







                                   March 21, 1996


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

Re:  Dean Witter U. S. Government Money Market Trust
     File #2-74980
     Rule 497(j) Filing                         

Dear Sir/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 15, 1996.


                                   Very truly yours,

                                   /s/ Marilyn K. Cranney     
                                       Marilyn K. Cranney
                                       Assistant Secretary
                                   


cc: Randolph Koch
    Sheldon Curtis