CERTIFICATION PURSUANT TO RULE 30A-2(B) UNDER THE 1940 ACT AND SECTION 906
                           OF THE SARBANES-OXLEY ACT

I, Bruce N. Alpert, Principal Executive Officer and Principal Financial Officer
of The Gabelli  Convertible and Income Securities Fund Inc. (the "Registrant"),
certify that:

     1.   The Form N-CSR of the Registrant  (the  "Report")  fully complies with
          the requirements of Section 13(a) or 15(d) of the Securities  Exchange
          Act of 1934, as amended; and

     2.   The  information  contained  in the  Report  fairly  presents,  in all
          material respects,  the financial  condition and results of operations
          of the Registrant.


Date:    September 7, 2005        /s/ Bruce N. Alpert
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                                  Bruce N. Alpert, Principal Executive Officer &
                                  Principal Financial Officer