NUVEEN TAX FREE UNIT TRUST SERIES 1001, 497J, 1998-05-22

NUVEEN TAX FREE UNIT TRUST SERIES 1001
497J, 1998-05-22

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                                                                    MAY 22, 1998
    
 
SECURITIES AND EXCHANGE COMMISSION
450 FIFTH STREET, N.W.
WASHINGTON, D.C. 20549
 
   
RE:  Nuveen Tax-Free Unit Trust, Series 1001
    
 
     File No. 333-52999
 
     Dear Sir or Madam:
 
     In accordance with the provisions of Rule 497(j) of Regulation C under the
     Securities Act of 1933 (the "Securities Act"), this letter serves to
     certify that the most recent amendment to the Registration Statement on
     Form S-6 (the "Registration Statement") of the above-referenced Series does
     not differ from that which would have been filed pursuant to Rule 487(b) of
     the Securities Act. Amendment No. 1, which was the most recent amendment to
     the Registration Statement, was filed electronically with the Commission on
     May 21, 1998.
 
     Very truly yours,
 
     JOHN NUVEEN & CO., INCORPORATED
 
     Gifford R. Zimmerman
    Vice President