<PAGE>

EXHIBIT 10.72                                                    CONFORMED COPY
        -----                                                    --------------


                      ENGINE SECURITY AGREEMENT SUPPLEMENT
                      ------------------------------------

          This ENGINE SECURITY AGREEMENT SUPPLEMENT, dated as of January 25,
2000 (this "Security Agreement Supplement"), is between MIDWAY AIRLINES
CORPORATION, a Delaware corporation (herein, together with its successors and
permitted assigns, the "Borrower") and FLEET CAPITAL CORPORATION, a Rhode Island
corporation (together with its successors and permitted assigns, the "Lender").

          WHEREAS, the Borrower and the Lender have entered into the Engine
Security Agreement dated as of December 30, 1999 (the "Security Agreement"),
covering one (1) General Electric model CF34-3B1 aircraft engine, which is of
750 or more "rated take-off horsepower" or the equivalent of such horsepower
(the "Loan A Engine") (terms used in this Security Agreement Supplement having
the meanings assigned thereto in the Security Agreement).

          WHEREAS, the Security Agreement has been duly recorded with the FAA
on January 7, 2000, as Conveyance Number SS013550 pursuant to the Transportation
Code;

          WHEREAS, this Security Agreement Supplement relates to the Engine
described in Schedule I hereto (the "Loan B Engine"); and

          WHEREAS, the Security Agreement provides for the execution and
delivery of the Security Agreement Supplement for the purpose of subjecting the
Loan B Engine described in Schedule I hereto to the Lien of the Security
Agreement.

          NOW, THEREFORE, as security for the payment and performance of the
Obligations (whether as scheduled, upon acceleration or otherwise), including,
without limitation, all indebtedness, liabilities, fees, indemnities and
obligations of Borrower and any other Person to Lender arising under or relating
to the Operative Agreements, including, but not limited to, repayment of the
principal of the Loan and payment of interest thereon and of all costs of
collection and enforcement of the Obligations, the Borrower hereby mortgages,
pledges and assigns to the Lender, and hereby creates in and grants to the
Lender a continuing security interest in, but none of its obligations or
liabilities respecting, all of the Borrower's right, title and interest in and
to the property described in Schedule I to this Security Agreement Supplement.

          This Security Agreement Supplement shall be construed as supplemental
to the Security Agreement and shall form a part thereof; and the Security
Agreement is hereby incorporated by reference herein to the same extent as if
fully set forth herein and is hereby ratified, approved and confirmed in all
respects.
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          IN WITNESS WHEREOF, the Lender and the Borrower have each caused this
Security Agreement Supplement to be duly executed by their authorized officers
as of the day and year first above written.


                                         MIDWAY AIRLINE CORPORATION, as Borrower


                                         By:  /s/ Jonathan S. Waller
                                              -------------------------------
                                              Name: Jonathan S. Waller
                                              Title: Senior Vice President
                                                   General Counsel



                                         FLEET CAPITAL CORPORATION, as Lender


                                         By:  /s/ Edward W. O'Brien
                                              -------------------------------
                                              Name: Edward W. O'Brien
                                              Title: Vice President
<PAGE>

                                                                      Schedule I


         The aircraft engine listed below shall constitute an "Engine"
              as such term is defined in the Security Agreement:



<TABLE>
<CAPTION>
                                       ENGINE
                                       ------
      <S>                        <C>                      <C>
      Manufacturer               Manufacturer's Model     Manufacturer's Serial No.
      ------------               --------------------     -------------------------

General Electric Company                CF34-3B1                  GE-E-872555
</TABLE>

The Engine is of 750 or more "rated take-off horsepower" or the equivalent of
such horsepower.