EXHIBIT 12(c)

CERTIFICATION PURSUANT TO SECTION 906 OF THE
SARBANES-OXLEY ACT

Pursuant to 18 U.S.C. 1350, each of the undersigned, being the Principal
Executive Officer and Principal Financial Officer of ACM Income Fund, Inc. (the
"Registrant"), hereby certifies that the Registrant's report on Form N-CSR for
the period ended June 30, 2006 (the "Report") fully complies with the
requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934
and that the information contained in the Report fairly presents, in all
material respects, the financial condition and results of operations of the
Registrant.

Date: August 28, 2006

                  By:    /s/ Marc O. Mayer
                         -------------------
                         Marc O. Mayer
                         President

                  By:    /s/ Joseph J. Mantineo
                         ------------------------
                         Joseph J. Mantineo
                         Treasurer and Chief Financial Officer

This certification is being furnished solely pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002 and is not being filed as part of the Report or as a
separate disclosure document.

A signed original of this written statement required by Section 906 has been
provided to the Registrant and will be retained by the Registrant and furnished
to the Securities and Exchange Commission or its staff upon request.