DEAN WITTER U S GOVERNMENT MONEY MARKET TRUST
24F-2NT, 1995-03-08
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                             RULE 24f-2 NOTICE

                                    For
              
             Dean Witter U. S. Government Money Market Trust 
                          (File No. 811-3326) 


Fiscal Year for Which Notice is filed             01/31/95

Unsold balance at beginning of fiscal year             
     of shares of beneficial interest previously
     registered under Securities Act of 1933

Number of shares registered during fiscal              
     year

Number of shares sold during fiscal year          1,791,101,896   
     pursuant to indefinite registration

*Calculation of filing fee:

(1)  Sale price of shares sold during            $1,791,101,896   
        fiscal year pursuant to indefinite
     registration
                            
(2)  Purchase price of shares redeemed           $1,825,827,160   
     during fiscal year
 
(3)  Purchase price of shares previously         $0     
     applied pursuant to Section 24e-2(a)

(4)  Item (2) less item (3)                      $1,825,827,160   


(5)  Item (1) less item (4)                      ($34,725,264)    

(6)  Amount of filing fee                        $0


                             
                         By    /s/Sheldon Curtis                
                                  Sheldon Curtis
                              Vice President and General Counsel

Dated:  March 8, 1995



               DEAN WITTER U. S. GOVERNMENT MONEY MARKET TRUST
                     Two World Trade Center
                       New York, NY  10048
                                

                                        March 8, 1995


Dean Witter U. S. Government Money
    Market Trust
Two World Trade Center
72nd Floor
New York, NY  10048

Dear Sirs:

     In connection with the public offering of shares of beneficial
interest, $.01 par value, of Dean Witter U. S. Government Money
Market Trust (the "Trust"), I have examined such corporate records
and documents and have made such further investigation and
examination as I have deemed necessary for the purpose of this
opinion.

     It is my opinion, as Legal Counsel for the Trust, that the
Trust is an unincorporated business trust duly organized and
validly existing under the laws of the State of Massachusetts and
that the shares of beneficial interest covered by the Rule 24f-2 
Notice, March 8, 1995 (File No. 2-74980 and 811-3326), were
issued and paid for in accordance with the terms of the offering,
as set forth in the prospectus filed as part of the Registration
Statement, as amended, of the Trust and were legally issued, fully
paid and non-assessable by the Trust.

     I hereby consent to the filing of this opinion as an exhibit
to the Notice pursuant to Rule 24f-2.   In giving this consent, I
do not thereby admit that I am within the category of persons whose
consent is required under Section 7 of the Securities Act of 1933,
as amended, or the rules and requisitions of the Securities and
Exchange Commission thereunder.


                                        Very truly yours,

                                                                  
                                    /S/Sheldon Curtis
        
                                        Sheldon Curtis
                                        General Counsel

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