NUVEEN TAX FREE MONEY MARKET FUND INC
24F-2NT, 1995-04-24
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 SECURITIES AND EXCHANGE COMMISSION
 Washington, DC  20549

 RULE 24f-2 NOTICE
 for
 NUVEEN TAX-FREE MONEY MARKET FUND, INC.
 File Number 33-8371

Massachusetts Tax-Free Money Market Fund 

Rule 24f-2(b)(1) under the Investment Company Act of 1940 ("1940 Act").

(i) Fiscal year for which notice is filed:

February 28, 1995 (fiscal year end)

(ii) The amount of shares of the same series, if any, which had been
registered under the Securities Act of 1933 ("1933 Act") other than pursuant
to Rule 24f-2 but which remained unsold at the beginning of such fiscal year:

$       -  0  - 

(iii) The amount of shares, if any, registered during such fiscal year
other than pursuant to Rule 24f-2:

$       4,067,656 

(iv) The amount of shares sold during such fiscal year:

$     165,040,056 

(v) The amount of shares sold during such fiscal year in reliance upon 
registration pursuant to Rule 24f-2*:

$     160,972,400 

  
* Computation of Fee pursuant to Section 6(b) of the 1933 Act
and Rule 24f-2(c) under the 1940 Act:

1. Actual aggregate sale price for which such shares were sold during
the previous fiscal year:

$         160,972,400 

2. Actual aggregate redemption price of such
shares redeemed during such previous fiscal year:      ($   181,790,525  )

3. Actual aggregate redemption price of such
redeemed shares previously applied pursuant to 
Section 24e-2(a) under the 1940 Act:                        ($   -0-   )

4. Net Adjustment to aggregate sale price:
($181,790,525)    

5. Aggregate sale price to be used as basis computation of fee:

($  20,818,125) 

6. Fee of .034483% (.00034483)

$     0.00 

page 1 of 3


New York Tax-Free Money Market Fund 

Rule 24f-2(b)(1) under the Investment Company Act of 1940 ("1940 Act").

(i) Fiscal year for which notice is filed:

February 28, 1995 (fiscal year end)

(ii) The amount of shares of the same series, if any, which had been
registered under the Securities Act of 1933 ("1933 Act") other than pursuant
to Rule 24f-2 but which remained unsold at the beginning of such fiscal year:

$       -  0  - 

(iii) The amount of shares, if any, registered during such fiscal year
other than pursuant to Rule 24f-2:

$       7,203,065 

(iv) The amount of shares sold during such fiscal year:

$        17,521,550 

(v) The amount of shares sold during such fiscal year in reliance upon 
registration pursuant to Rule 24f-2*:

$         10,318,485 

  
* Computation of Fee pursuant to Section 6(b) of the 1933 Act
and Rule 24f-2(c) under the 1940 Act:

1. Actual aggregate sale price for which such shares were sold during
the previous fiscal year:

$         10,318,485 

2. Actual aggregate redemption price of such
shares redeemed during such previous fiscal year:      ($   16,400,855  )

3. Actual aggregate redemption price of such
redeemed shares previously applied pursuant to 
Section 24e-2(a) under the 1940 Act:                        ($0.00)

4. Net Adjustment to aggregate sale price:
($16,400,855)    

5. Aggregate sale price to be used as basis computation of fee:

($6,082,370)

6. Fee of .034483% (.00034483)

$     0.00 

page 2 of 3


 SIGNATURE


The undersigned Registrant has duly caused this Rule 24f-2 Notice to be 
signed on its behalf by the undersigned in the City of Chicago, State 
of Illinois.


Dated:   April 24, 1995 NUVEEN TAX-FREE MONEY MARKET FUND, INC.
                              (name of registrant)


  By:     
        Gifford R. Zimmerman
        Vice President and Assistant Secretary




Exhibit:   Opinion of Counsel




 page 3 of 3




SIGNATURE


The undersigned Registrant has duly caused this Rule 24f-2 Notice to be 
signed on its behalf by the undersigned in the City of Chicago, State of 
Illinois.



Dated:   April 24, 1995 NUVEEN TAX-FREE MONEY MARKET FUND, INC.
                             (name of registrant)


  By:   /s/ Gifford R. Zimmerman   
        Gifford R. Zimmerman
        Vice President and Assistant Secretary


Exhibit:   Opinion of Counsel





page 3 of 3





April 19, 1995

Nuveen Tax-Free Money Market Fund, Inc.
333 West Wacker Drive
Chicago, Illinois  60606

RE:  Rule 24f-2 Notice

Ladies and Gentlemen:

We have acted as counsel to Nuveen Tax-Free Money Market Fund, Inc., 
a Minnesota corporation (the "Fund"), in connection with the Fund's 
registration, pursuant to Rule 24f-2 under the Investment Company Act of 
1940, as amended, of an indefinite number of its Nuveen Massachusetts 
Tax-Free Money Market Fund - Institutional Series Shares; Nuveen
Massachusetts Tax-Free Money Market Fund - Service Plan Series 
Shares; Nuveen Massachusetts Tax-Free Money Market Fund - 
Distribution Plan Series Shares; Nuveen New York Tax-Free 
Money Market Fund - Institutional Series Shares; Nuveen New 
York Tax-Free Money Market Fund - Service Plan Series Shares; and 
Nuveen New York Tax-Free Money Market Fund - Distribution Plan 
Series Shares, par value $.01 (collectively, the "Shares"), under the 
Securities Act of 1933, as amended.  We understand that, pursuant to such 
Rule 24f-2, the Fund proposes to file a notice (the "Notice") with the 
Securities and Exchange Commission with respect to the fiscal year ended 
February 28, 1995, in order to make definite in number the registration 
of Shares in the aggregate amount of $ 171,290,885.  This opinion
is being delivered to you in connection with the Fund's filing of such Notice.

In connection with this opinion, we have reviewed, among other things, 
executed copies of the following documents:

(a) a certificate of the Secretary of State of the State of Minnesota as to the 
existence and good standing of the Fund;

(b) copies, certified by the Secretary of State of the State of Minnesota, 
of the Fund's Articles of Incorporation and of all amendments and all 
supplements thereto (the "Articles of Incorporation");

(c) a certificate executed by Karen L. Healy, the Assistant Secretary of 
the Fund, certifying as to, and attaching copies of, the Fund's Articles 
of Incorporation and By-Laws, as amended (the "By-Laws") and certain 
resolutions adopted by the Board of Directors of the Fund authorizing 
the issuance of the Shares covered by the Notice; and

(d) a certificate executed by H. William Stabenow, the Treasurer of the 
Fund, as to the issuance of the Shares in accordance with the Fund's 
Articles of Incorporation and By-Laws and as to the receipt by the Fund 
of the net asset value of the Shares covered by the Notice.

In our capacity as counsel to the Fund, we have examined the originals, 
or certified, conformed or reproduced copies, of all records, agreements, 
instruments and documents as we have deemed relevant or necessary as 
the basis for the opinion hereinafter expressed.  In all such examinations, 
we have assumed the legal capacity of all natural persons executing
documents, the genuineness of all signatures, the authenticity of all 
original or certified copies, and the conformity to original or certified 
copies of all copies submitted to us as conformed or reproduced copies.  
As to various questions of fact relevant to such opinion, we have relied
upon, and assume the accuracy of, certificates and oral or written statements 
of public officials and officers or representatives of the Fund.

Based upon and subject to, the limitations set forth herein, we are of the 
opinion that the Shares covered by the Notice were legally issued and are 
fully paid and nonassessable.

The opinion expressed herein is limited to the laws of the State of Minnesota.  
As to matters of Minnesota law covered thereby, we have relied solely upon 
the opinion of Dorsey & Whitney, P.L.L.P., addressed to us and dated 
April 19, 1995.

Very truly yours,

FRIED, FRANK, HARRIS, SHRIVER & JACOBSON



Thomas S. Harman




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