EXHIBIT (b)

                          Rule 30a-2(b) CERTIFICATIONS

     Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (subsections (a)
and (b) of section 1350, chapter 63 of title 18, United States Code), each of
the undersigned officers of The Zweig Fund, Inc. (the Registrant), do hereby
certify, to such officer's knowledge, that:

     (1)  The Zweig Fund, Inc. on Form N-CSR of the Registrant for the period
          ended June 30, 2004 (the "Form N-CSR") fully complies with the
          requirements of Section 13(a) or 15(d) of the Securities Exchange Act
          of 1934;
          and

     (2)  the information contained in the Form N-CSR fairly presents, in all
          material respects, the financial condition and results of operations
          of the Registrant.

Dated:  September 3, 2004
       -----------------------------


/s/ Daniel T. Geraci
- -------------------------------------

Name: Daniel T. Geraci

Title: President

Dated:  September 3, 2004
        ----------------------------


/s/ Nancy Curtiss
- -------------------------------------

Name: Nancy Curtiss

Title: Treasurer

This certification is being furnished solely pursuant to 18 U.S.C. ss. 1350 and
is not being filed as part of the Report or as a separate disclosure document.