NUVEEN TAX FREE MONEY MARKET FUND INC
497J, 1998-06-24
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[MORGAN, LEWIS & BOCKIUS LLP LETTERHEAD]





June 24, 1998



VIA EDGAR
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Securities and Exchange Commission
450 Fifth Street, N.W.
Judiciary Plaza
Washington, D.C. 20549

Re:  Nuveen Tax-Free Money Market, Inc. (File Nos. 33-8371, 811-4822)
     Filing pursuant to Rule 497(j)
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Ladies and Gentlemen:

On behalf of our client, Nuveen Tax-Free Money Market, Inc. (the "Fund"), we are
filing, pursuant to Rule 497(j) under the Securities Act of 1933, as amended, 
this letter certifying that the Prospectus and Statement of Additional 
Information dated June 24, 1998 do not differ from those contained in the Fund's
Post-Effective Amendment No. 13 which was filed via EDGAR on June 16, 1998.

Please contact me at (202) 467-7662 if you have any questions or comments 
concerning this filing.


Sincerely,

/s/Thomas S. Harman

Thomas S. Harman


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