Rule 497(j)
                                             Reg. No. 33-24778

Pursuant to Rule 497 (j) promulgated under the Securities Act of 1933, the
Registrant, Dean Witter Select Municipal Trust, Long Term Portfolio Series 124,
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 124

                         By:  Dean Witter Reynolds Inc.
                              (Depositor)


                                                       
                              Thomas Hines                  
                              Authorized Signatory



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