EXHIBIT 31.1

                                 CERTIFICATIONS

      I, William S. Ayer, certify that:

      1.    I have reviewed this quarterly report on Form 10-Q of Alaska Air
            Group, Inc. for the period ended June 30, 2004;

      2.    Based on my knowledge, this quarterly report does not contain any
            untrue statement of a material fact or omit to state a material fact
            necessary to make the statements made, in light of the circumstances
            under which such statements were made, not misleading with respect
            to the period covered by this report;

      3.    Based on my knowledge, the financial statements, and other financial
            information included in this quarterly report, fairly present in all
            material respects the financial condition, results of operations and
            cash flows of the registrant as of, and for, the periods presented
            in this report;

      4.    The registrant's other certifying officer and I are responsible for
            establishing and maintaining disclosure controls and procedures (as
            defined in Exchange Act Rules 13a-15(e) and 15d-15(e)) for the
            registrant and we have:

            a) designed such disclosure controls and procedures, or caused such
            disclosure controls and procedures to be designed under our
            supervision, to ensure that material information relating to the
            registrant, including its consolidated subsidiaries, is made known
            to us by others within those entities, particularly during the
            period in which this report is being prepared;

            b) evaluated the effectiveness of the registrant's disclosure
            controls and procedures and presented in this report our conclusions
            about the effectiveness of the disclosure controls and procedures,
            as of June 30, 2004, based on such evaluation; and

            c) disclosed in this report any change in the registrant's internal
            control over financial reporting that occurred during the
            registrant's most recent fiscal quarter that has materially
            affected, or is reasonably likely to materially affect, the
            registrant's internal control over financial reporting; and

      5.    The registrant's other certifying officers and I have disclosed,
            based on our most recent evaluation of internal control over
            financial reporting, to the registrant's auditors and the audit
            committee of the registrant's board of directors (or persons
            performing the equivalent functions):

            a) all significant deficiencies and material weaknesses in the
            design or operation of internal control over financial reporting
            which are reasonably likely to adversely affect the registrant's
            ability to record, process, summarize and report financial
            information; and

            b) any fraud, whether or not material, that involves management or
            other employees who have a significant role in the registrant's
            internal control over financial reporting.

            August 6, 2004                       By   /s/ William S. Ayer
                                                    --------------------------
                                                    William S. Ayer
                                                    Chairman, President & CEO