NUVEEN TAX FREE UNIT TRUST SERIES 968, 497J, 1997-10-27

NUVEEN TAX FREE UNIT TRUST SERIES 968
497J, 1997-10-27

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                                                                OCTOBER 27, 1997
 
SECURITIES AND EXCHANGE COMMISSION
450 FIFTH STREET, N.W.
WASHINGTON, D.C. 20549
 
RE:  Nuveen Tax-Free Unit Trust, Series 968
 
     File No. 333-35957
 
     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
     October 27, 1997.
 
     Very truly yours,
 
     JOHN NUVEEN & CO., INCORPORATED
 
     Gifford R. Zimmerman
    Vice President