Rule 497(j)
                                             Reg. No. 33-21632


Pursuant to Rule 497 (j) promulgated under the Securities Act of
1933, the Registrant, Dean Witter Select Municipal Trust, Long Term
Portfolio Series 113, hereby certifies as follows:

1)   the form of prospectus that would have been filed under
     paragraph (b) of Rule 497 does not differ from that
     contained in the most recent amendment to the registration
     statement, and

2)   the text of the said amendment to the registration statement
     has been filed electronically.


                         DEAN WITTER SELECT MUNICIPAL TRUST,
                         LONG TERM PORTFOLIO SERIES 113

                         By:  Dean Witter Reynolds Inc.
                              (Depositor)


                              Thomas Hines
                              Thomas Hines
                              Authorized Signatory



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