AMERICAN CENTURY TARGET MATURITIES TRUST
497J, 1999-02-05
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                          American Century Investments
                                4500 Main Street
                             Kansas City, MO 64111

February 5, 1999

Securities and Exchange Commission 
450 Fifth Street, N.W. 
Washington, DC 20549 

RE:  American Century Target Maturities Trust
       1933 Act File No. 2-94608
       1940 Act File No. 811-4165

Ladies and Gentlemen: 

     Pursuant to Rule 497(j) under the Securities  Act of 1933, as amended,  the
undersigned  hereby  certifies  that the form of  prospectus  and  statement  of
additional  information that would have been filed under paragraph (b) or (c) of
Rule 497 with respect to the  above-referenced  issuer  would not have  differed
from that  contained in  Post-Effective  Amendment  No. 31, filed on January 29,
1999 to the issuer's Registration Statement on Form N-1A.

     If there are any  questions  or  comments  regarding  this  filing,  please
contact the undersigned at (650)967-9683.


Sincerely,

/s/Charles C.S. Park
Charles C.S. Park
Assistant Secretary and
Assistant General Counsel


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