Exhibit 32(b)

CERTIFICATION PURSUANT TO

18 U.S.C. SECTION 1350,

AS ADOPTED PURSUANT TO

SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

In connection with the Quarterly Report of ABX Air, Inc. (the “Company”) on Form 10-Q for the period ending June 30, 2004 as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Quint O. Turner, Acting Chief Financial Officer and Vice President, Administration of the Company, certify, pursuant to 18 U.S.C. 1350, as enacted by § 906 of the Sarbanes-Oxley Act of 2002, that:

(1) The Report 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 Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

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

/s/ QUINT O. TURNER

Quint O. Turner

Vice President, Administration

Acting Chief Financial Officer

(Principal Financial and Accounting Officer)

Date: August 11, 2004