EXHIBIT 32.1

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 Alaska Air Group, Inc. (the
"Company") on Form 10-Q for the period ended June 30, 2004 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, William
S. Ayer, Chairman, President & Chief Executive Officer of the Company, certify,
pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 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, 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
Company.

By /s/ William S. Ayer
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William S. Ayer
Chairman, President & Chief Executive Officer
August 6, 2004