<PAGE>   1
                                                                   Exhibit 10.37


                                SECOND AMENDMENT
                             TO EMPLOYMENT AGREEMENT

      This SECOND AMENDMENT TO EMPLOYMENT AGREEMENT (the "Second Amendment") is
entered into effective as of January 1, 2000, by and among AMERICA WEST HOLDINGS
CORPORATION, a Delaware corporation ("Holdings"), AMERICA WEST AIRLINES, INC., a
Delaware corporation and a wholly-owned subsidiary of Holdings ("AWA"), THE
LEISURE COMPANY, a Delaware corporation and a wholly-owned subsidiary of
Holdings ("Leisure," and, together with AWA and Holdings, "Employers" and
individually, an "Employer"), and WILLIAM A. FRANKE ("Franke").

                                    RECITALS

      A. The Employers and Franke have executed that certain Employment
Agreement dated as of February 17, 1998 (the "Original Agreement").

      B. The Employers and Franke have executed that certain Amendment to
Employment Agreement dated as of January 15, 1999 (the "First Amendment")
amending certain provisions of the Original Agreement (the Original Agreement,
as amended by the First Amendment, hereinafter referred to as the "Amended
Agreement").

      C. In consideration of the premises, and other good and valuable
consideration, the receipt of which is hereby acknowledged by the parties, the
Employers and Franke desire to further amend the Amended Agreement as specified
herein.

                                    AGREEMENT

      The Employers and Franke, intending to be legally bound, agree as follows:

1.    AMENDMENT.

      (a)   AMENDMENT OF SECTION 1.1.

            (i) Section 1.1 of the Amended Agreement is hereby amended to add a
definition of "Retirement," such definition to read in its entirety as follows:

            "'Retirement'" shall mean Franke's termination of employment on or
            after the Expiration Date, or such earlier date as may be approved
            by the Board, for any reason other than Misconduct."

            (ii) Section 1.1 of the Amended Agreement is hereby amended to
revise the definition of "Expiration Date" to read it its entirety as follows:

            "'Expiration Date'" shall mean December 31, 2002."


                                       1.
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      (b) AMENDMENT OF SECTION 3.1. Section 3.1 of the Amended Agreement is
hereby amended by replacing "$200,000" in paragraph (a) with "$600,000" and by
replacing paragraph (b) to read in its entirety as follows:

                  "(b) The Base Salary shall be reviewed at least annually by
            the Board at such time or times as the salaries of other senior
            executives of the Employers as a group are reviewed commencing in
            February 2001, and may be increased by the Board at any time or from
            time to time as the Board may deem appropriate."

      (c) AMENDMENT OF SECTION 3.2. Section 3.2 of the Amended Agreement is
hereby amended by adding a new Section 3.2(g) and redesignating existing Section
3.2(g) and the following sections accordingly, such new Section 3.2(g) to read
in its entirety as follows:

                  "(g) Notwithstanding the foregoing provisions of this Section
            3.2, in the event Franke's employment is terminated by reason of
            Retirement, the 1996 Stock Option may be exercised at any time
            within the 36-month period beginning on the date of such Retirement,
            but not thereafter (and in no event after October 28, 2006)."

      (d) AMENDMENT OF SECTION 3.3. Section 3.3 of the Amended Agreement is
hereby amended by adding a new Section 3.3(g) and redesignating existing Section
3.3(g) and the following sections accordingly, such new Section 3.3(g) to read
in its entirety as follows:

                  "(g) Notwithstanding the foregoing provisions of this Section
            3.3, in the event Franke's employment is terminated by reason of
            Retirement, the 1998 Stock Option may be exercised, to the extent
            then vested, at any time within the 36-month period beginning on the
            date of such Retirement, but not thereafter (and in no event after
            February 17, 2008). To the extent that the 1998 Stock Option is not
            vested on the date of such Retirement, the portion thereof that is
            not vested on the date of such Retirement shall automatically lapse
            and be cancelled unexercised as of such date."

      (e) AMENDMENT OF SECTION 3.4. Section 3.4 of the Amended Agreement is
hereby amended by adding a new Section 3.4(g) and redesignating existing Section
3.4(g) and the following sections accordingly, such new Section 3.4(g) to read
in its entirety as follows:

                  "(g) Notwithstanding the foregoing provisions of this Section
            3.4, in the event Franke's employment is terminated by reason of
            Retirement, the 1999 Stock Option may be exercised, to the extent
            then vested, at any time within the 36-month period beginning on the
            date of such Retirement, but not thereafter (and in no event after
            January 15, 2009). To the extent that the 1999 Stock Option is not
            vested on the date of such Retirement, the portion


                                       2.
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            thereof that is not vested on the date of such Retirement shall
            automatically lapse and be cancelled unexercised as of such date."

      (f) AMENDMENT OF SECTION 3.9. The final sentence of Section 3.9 of the
Amended Agreement is hereby deleted, and a new sentence is added at the end of
Section 3.9 to read in its entirety as follows:

                  "In addition, (x) Franke shall be considered for additional
            annual option grants under the Incentive Plan and other long-term
            incentive benefits at such time or times, commencing in December
            2000, as the senior executives of the Employers as a group are
            considered for such option grants and benefits, and (y) Franke shall
            be eligible to earn an annual bonus under the terms of any annual
            bonus program made available to other senior executives of the
            Employers, such bonus to be based on a target of not less than 60%
            of Base Salary and a maximum of not less than 120% of Base Salary,
            or such higher percentages as the Board may establish from time to
            time, and to be calculated using reasonable performance criteria
            established by the Board from time to time based 75% on the
            financial performance of Holdings and 25% on individual performance
            by Franke, or such other relative weighting as Franke and the Board
            may agree from time to time."

      (g) NEW SECTION 3.12. A new Section 3.12 is added to the Amended Agreement
to read in its entirety as follows:

                  "Effective as of January 5, 2000, Franke has been granted an
            option to purchase 110,000 Shares for $20.0625 per Share pursuant to
            the Incentive Plan (the "2000 Stock Option"). The following
            provisions of this Section 3.12 constitute the agreement required
            with respect to the 2000 Stock Option under Paragraph 4(i) of the
            Incentive Plan:

                  (a) The 2000 Stock Option shall be exercisable as to one-third
            of the Shares covered thereby on January 5, 2001, as to an
            additional one-third of the Shares covered thereby on January 5,
            2002 and as to the remaining one-third of the Shares covered thereby
            on December 31, 2002, so that the 2000 Stock Option will be
            exercisable in full on December 31, 2002.

                  (b) Upon the exercise of the 2000 Stock Option, the Person
            exercising the 2000 Stock Option shall pay to Holdings an amount
            equal to the exercise price, such amount to be paid (i) in cash,
            (ii) by delivering to Holdings issued and outstanding Shares which
            have an aggregate Market Value per Share at the date of exercise
            equal to the exercise price, (iii) by directing Holdings to sell a
            sufficient number of Shares to be acquired on exercise of the


                                       3.
<PAGE>   4
            2000 Stock Option through a broker approved by Holdings, in which
            event the proceeds of such sale shall be applied by Holdings to the
            payment of the exercise price and any applicable withholding taxes,
            with any surplus then remaining to be paid to the Person exercising
            the 2000 Stock Option or its designee or (iv) by any combination of
            the foregoing.

                  (c) Upon the occurrence of a Change in Control, or in the
            event Franke's employment is terminated by Franke pursuant to
            Section 4.1 for Good Reason or by Holdings pursuant to Section 4.2
            for a reason other than Misconduct or Disability, the 2000 Stock
            Option shall become automatically vested in full and may be
            exercised at any time thereafter; provided, however, in no event
            shall the 2000 Stock Option be exercisable after January 5, 2010.

                  (d) In the event Franke's employment is terminated by Franke
            pursuant to Section 4.1 other than for Good Reason or on account of
            Disability or by Holdings pursuant to Section 4.2 for Misconduct,
            the 2000 Stock Option, to the extent then vested, may be exercised
            at any time within six months following the Termination Date, but
            not thereafter (and in no event after January 5, 2010). To the
            extent the 2000 Stock Option is not vested on such Termination Date,
            the portion thereof that is not vested on such Termination Date
            shall automatically lapse and be canceled unexercised as of such
            Termination Date.

                  (e) The 2000 Stock Option shall become automatically vested in
            full on the date of Franke's death and may be exercised at any time
            within the one-year period beginning on the date of Franke's death,
            but not thereafter (and in no event after January 5, 2010).

                  (f) In the event Franke's employment is terminated by reason
            of Disability, the 2000 Stock Option shall become automatically
            vested in full on the date of such Disability and may be exercised
            at any time within the 36-month period beginning on the date of such
            Disability, but not thereafter (and in no event after January 5,
            2010).

                  (g) Notwithstanding the foregoing provisions of this Section
            3.12, in the event Franke's employment is terminated by reason of
            Retirement, the 2000 Stock Option may be exercised, to the extent
            then vested, at any time within the 36-month period beginning on the
            date of such Retirement, but not thereafter (and in no event after
            January 5, 2010). To the extent that the 2000 Stock Option is not
            vested on the date of such Retirement, the portion


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<PAGE>   5
            thereof that is not vested on the date of such Retirement shall
            automatically lapse and be cancelled unexercised as of such date.

                  (h) Except as otherwise provided herein, the 2000 Stock Option
            may be exercised in whole or in part or in two or more successive
            parts.

                  (i) The 2000 Stock Option shall not be transferable by Franke
            except for transfers permitted by the Incentive Plan and except for
            transfers by will or by laws of descent and distribution. During the
            lifetime of Franke, the 2000 Stock Option may not be exercised by
            anyone other than Franke or the Person to whom the 2000 Stock Option
            has been transferred in accordance with the Incentive Plan.

                  (j) The 2000 Stock Option may be exercised from time to time
            by a notice in writing which identifies the 2000 Stock Option and
            specifies the number of Shares in respect of which it is being
            exercised. Such notice shall be delivered to the Secretary of
            Holdings or addressed to the Secretary of Holdings at its principal
            corporate offices. The date of exercise of the 2000 Stock Option
            shall be the date the exercise notice is hand delivered or mailed to
            the Secretary of Holdings, whichever is applicable. An election to
            exercise the 2000 Stock Option shall be irrevocable.

                  (k) The 2000 Stock Option is not intended to qualify as an
            incentive stock option under Section 422 of the Code.

                  (l) The provisions of this Section 3.12 shall survive the
            termination of Franke's employment hereunder."

      (h) NEW SECTION 3.13. A new Section 3.13 is added to the Amended Agreement
to read in its entirety as follows:

                  "With respect to the outstanding options granted to Franke
            under the Incentive Plan prior to January 1, 1996 as listed in the
            following table (the "Pre-1996 Options"), notwithstanding any
            provisions to the contrary contained in the respective documents and
            agreements evidencing such Pre-1996 Options:

                  (a) in the event Franke's employment is terminated by reason
                  of Retirement or Disability, such Pre-1996 Options may be
                  exercised at any time within the 36-month period beginning on
                  the date of such Retirement or Disability, but not thereafter
                  (and in no event after the 10th anniversary of the grant date
                  (the "Expiry Date") of each such Pre-1996 Option,
                  respectively, as indicated in the following table);


                                       5.
<PAGE>   6
                  (b) upon the occurrence of a Change in Control, or in the
                  event Franke's employment is terminated by Franke pursuant to
                  Section 4.1 for Good Reason or by Holdings pursuant to Section
                  4.2 for a reason other than Misconduct or Disability, the
                  Pre-1996 Options may be exercised at any time thereafter, but
                  in no event after their respective Expiry Dates;

                  (c) in the event of Franke's death, the Pre-1996 Options may
                  be exercised at any time within the one-year period beginning
                  on the date of Franke's death, but in no event after their
                  respective Expiry Dates; and

                  (d) in the event Franke's employment is terminated by Franke
                  pursuant to Section 4.1 other than for Good Reason or on
                  account of Disability or by Holdings pursuant to Section 4.2
                  for Misconduct, the Pre-1996 Options may be exercised at any
                  time within six months following the Termination Date, but not
                  thereafter (and in no event after their respective Expiry
                  Dates).

<TABLE>
<CAPTION>
                      ------------------------------------
                      GRANT DATE   NUMBER    EXPIRY DATE
                      ------------------------------------
<S>                   <C>          <C>       <C>
                      12/1/94      255,000   12/1/04
                      ------------------------------------
                      12/1/94      100,000   12/1/04
                      ------------------------------------
                      8/30/95      50,000     8/30/05
                      ------------------------------------
                      8/30/95      100,000    8/30/95
                      ------------------------------------
                      11/9/95      150,000    11/9/05
                      ------------------------------------"
</TABLE>


      (i) NEW SECTION 3.14. A new Section 3.14 is added to the Amended Agreement
to read in its entirety as follows:

                  "The maturity dates of those certain promissory notes listed
            in the following table, which notes evidence loans made by Holdings
            to Franke to enable Franke to pay a portion of the taxes
            attributable to stock grants previously awarded to Franke, are
            extended to the dates indicated, and the interest rates on such
            notes are adjusted to the rates indicated, such maturity date
            extensions and interest rate adjustments to be further evidenced by
            such amendments, modifications or restatements of the notes and
            related agreements as may be reasonably acceptable in form and
            substance to Holdings and Franke:


                                       6.
<PAGE>   7
<TABLE>
<CAPTION>
--------------------------------------------------------------------------------------------------------------------
NOTE DATE       PRINCIPAL     CURRENT MATURITY DATES     NEW MATURITY DATES        CURRENT        NEW INTEREST
                AMOUNT                                                             INTEREST       RATE
                                                                                   RATE
--------------------------------------------------------------------------------------------------------------------
<S>             <C>           <C>                        <C>                       <C>            <C>
 9/20/94        $470,282      9/26/00 as to 50%          12/31/03                  8.00%          6.51%
                              9/26/01 as to 50%

--------------------------------------------------------------------------------------------------------------------
 11/15/95       $203,136      9/26/00 as to 50%          12/31/03                  6.02%          6.51%
                              9/26/01 as to 50%

--------------------------------------------------------------------------------------------------------------------
 1/16/96        $ 40,000      9/26/00 as to 50%          12/31/03                  6.02%          6.51%
                              9/26/01 as to 50%

--------------------------------------------------------------------------------------------------------------------
 1/31/96        $644,704      9/26/00 as to 50%          12/31/03                  5.65%          6.51%
                              9/26/01 as to 50%

--------------------------------------------------------------------------------------------------------------------
 4/9/97         $194,072      9/26/00 as to 50%          12/31/03                  6.35%          6.51%
                              9/26/01 as to 50%

--------------------------------------------------------------------------------------------------------------------
 10/15/98       $549,540      10/15/03 as to 50%         12/31/03 as to 50%        5.06%          5.06%
                              10/15/04 as to 50%         10/15/04 as to 50%                       (unchanged)

--------------------------------------------------------------------------------------------------------------------
</TABLE>


      (j) AMENDMENT OF SECTION 4.4(A). The phrase appearing in subclause (y) of
clause (ii) in the first sentence of Section 4.4(a) of the Amended Agreement
which currently reads "(y) 200% of the sum of Franke's Base Salary as in effect
on the date of termination plus a 50% target bonus" is hereby deleted and
replaced with a new phrase to read as follows:

            "(y) 200% of the sum of Franke's Base Salary as in effect on the
            date of termination plus a 60% target bonus or such higher target
            bonus percentage as the Board may have established under Section 3.9
            above"

      (k) NEW SECTION 6.5. A new Section 6.5 is added to the Amended Agreement
to read in its entirety as follows:

                  "In addition to the piggyback and demand registration rights
            provided by Sections 6.2 and 6.3 above, Holdings will use
            Commercially Reasonable Efforts to maintain the effectiveness for
            purposes of resale of Registrable Securities held by Franke of the
            following currently effective registration statements: Form S-3 no.
            333-02129 and Form S-8 no. 333-26935."


                                       7.
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2.  MISCELLANEOUS PROVISIONS.

      (a) ORIGINAL AGREEMENT. The Amended Agreement, as amended by this Second
Amendment, shall continue in full force and effect after the date hereof.

      (b) WHOLE AGREEMENT. No agreements, representations or understandings
(whether oral or written and whether express or implied) which are not expressly
set forth in the Amended Agreement, as amended by this Second Amendment, have
been made or entered into by either party with respect to the subject matter of
this Second Amendment.

      IN WITNESS WHEREOF, each of the parties has executed this Second
Amendment, in the case of the Employers by their duly authorized officers,
effective as of the day and year first above written.


                                    AMERICA WEST HOLDINGS CORPORATION



                                    By:   /s/ Richard C. Kraemer
                                        --------------------------------------
                                          Chairman of Compensation/Human
                                          Resources Committee

                                    AMERICA WEST AIRLINES, INC.


                                    By:   /s/ Richard C. Kraemer
                                        --------------------------------------
                                          Chairman of Compensation/Human
                                          Resources Committee


                                    THE LEISURE COMPANY


                                    By:   /s/ Richard C. Kraemer
                                        --------------------------------------
                                          Director




                                    /s/ William A. Franke
                                    ------------------------------------------
                                    WILLIAM A. FRANKE



                                       8.