<PAGE>   1


                                                                    EXHIBIT 10.4

                            AMENDMENT TO AVIALL, INC.
                            1998 STOCK INCENTIVE PLAN


         THIS AMENDMENT TO AVIALL, INC. 1998 STOCK INCENTIVE PLAN (this
"Amendment"), dated as of April 16, 1999 is made and entered into by Aviall,
Inc., a Delaware corporation (the "Company"). Terms used in this Amendment with
initial capital letters that are not otherwise defined herein shall have the
meanings ascribed to such terms in the Aviall, Inc.
1998 Stock Incentive Plan (the "Plan").

                                    RECITALS


         WHEREAS, Section 16 of the Plan provides that the Board of Directors of
the Company (the "Board") may at any time and from time to time amend the Plan
in whole or in part; and

         WHEREAS, the Board desires to amend the definition of Change in Control
set forth in Section 11 of the Plan;

         NOW, THEREFORE, in accordance with Section 16 of the Plan, the Company
hereby amends the Plan as follows:

                  1. Section 11 of the Plan is hereby amended and restated to
read in its entirety as follows:

                     "11. CHANGE IN CONTROL. For purposes of this Plan, except
                  as may be otherwise prescribed by the Board in an agreement
                  evidencing a grant or award made under the Plan, a "Change in
                  Control" shall mean if at any time any of the following events
                  shall have occurred:

                          (a) The Company is merged or consolidated or
                     reorganized into or with another corporation or other legal
                     person, and as a result of such merger, consolidation or
                     reorganization less than a majority of the combined voting
                     power of the then-outstanding securities of such
                     corporation or person immediately after such transaction
                     are held in the aggregate by the holders of securities
                     entitled to vote generally in the election of Directors
                     immediately prior to such transaction;

                          (b) The Company sells or otherwise transfers all or
                     substantially all of its assets to any other corporation or
                     other legal person, and less than a majority of the
                     combined voting power of the then-outstanding securities of
                     such corporation or person immediately after such sale or
                     transfer is held in the aggregate by the holders of Common
                     Shares immediately prior to such sale or transfer;



<PAGE>   2


                          (c) There is a report filed on Schedule 13D or
                     Schedule 14D-1 (or any successor schedule, form or report),
                     each as promulgated pursuant to the Exchange Act,
                     disclosing that any person (as the term "person" is used in
                     Section 13(d)(3) or Section 14(d)(2) of the Exchange Act)
                     has become the beneficial owner (as the term "beneficial
                     owner" is defined under Rule 13d-3 or any successor rule or
                     regulation promulgated under the Exchange Act) of
                     securities representing 20% or more of the Voting Power;

                          (d) If during any period of two consecutive years,
                     individuals who at the beginning of any such period
                     constitute the Directors cease for any reason to constitute
                     at least a majority thereof, unless the election, or the
                     nomination for election by the Company's stockholders, of
                     each Director first elected during such period was approved
                     by a vote of at least two-thirds of the Directors then
                     still in office who were Directors at the beginning of any
                     such period.

                     Notwithstanding the foregoing provisions of Section 11(b)
                  and (c) above, a "Change in Control" shall not be deemed to
                  have occurred for purposes of this Plan (i) solely because (A)
                  the Company; (B) a Subsidiary; or (C) any Company-sponsored
                  employee stock ownership plan or other employee benefit plan
                  of the Company either files or becomes obligated to file a
                  report under or in response to Schedule 13D, Schedule 14D-1 or
                  Form 8-K (or any successor schedule, form or report or item
                  therein) under the Exchange Act, disclosing beneficial
                  ownership by it of shares, whether in excess of 20% of the
                  Voting Power or otherwise, or because the Company reports that
                  a change of control of the Company has or may have occurred or
                  will or may occur in the future by reason of such beneficial
                  ownership or (ii) solely because of a change in control of any
                  Subsidiary."

                  2. This Amendment shall be effective immediately.

                  3. Except as expressly amended by this Amendment, the Plan
shall continue in full force and effect in accordance with the provisions
thereof.

         IN WITNESS WHEREOF, the Company has caused this Amendment to be duly
executed as of the date first above written.

                                       AVIALL, INC.



                                       By: /s/ Eric E. Anderson
                                           -------------------------------------
                                           Eric E. Anderson, President and
                                           Chief Executive Officer

                                       2