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 Annual Report of Alaska Air Group, Inc. (the
      "Company") on Form 10-K for the period ended December 31, 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
    -----------------------------------------
William S. Ayer
Chairman, President & Chief Executive Officer
February 22, 2005