<PAGE>

                                                                    EXHIBIT 10.1

                              DELTA AIR LINES, INC.

                                 FIRST AMENDMENT
                                       TO
                          DELTASHARE STOCK OPTION PLAN

      THIS FIRST AMENDMENT ("Amendment") to the Delta Air Lines, Inc. DeltaShare
Stock Option Plan (the "Plan") amends the Plan effective as of such time as this
Amendment is approved by the shareowners of the Company. Capitalized terms not
otherwise defined herein will have the meaning ascribed to such terms in the
Plan.

      1. Section 2.16 of the Plan is amended and restated to read in its
entirety as follows:

            "2.16 "Stock" means the Common Stock, $1.50 par value, of the
      Company."

      2. Section 4.1 of the Plan is amended and restated to read in its entirety
as follows:

            "4.1 Stock Reserved. The total number of shares of Stock reserved
      and available for distribution under the Plan shall be 29,400,000, which
      number reflects the two-for-one split of the Common Stock of the Company
      effective in 1998. Stock issued under the Plan may be either authorized
      and unissued shares or treasury shares. Notwithstanding the foregoing,
      such number of shares of Stock as are subject to Stock Options that are
      cancelled pursuant to the Stock Option Exchange Program (as defined in
      Article 12 hereof) and as are necessary to grant Replacement Options (as
      defined in Article 12 hereof) in exchange for such cancelled Stock Options
      will again be available for distribution pursuant to such Replacement
      Options and, otherwise, shares of Stock subject to such cancelled Stock
      Options will not be available for distribution under the Plan."

      3. The Plan is amended to add the following Article 12, which reads in its
entirety as follows:

                   "ARTICLE 12 - STOCK OPTION EXCHANGE PROGRAM

            12.1 In General. At such time as the Committee determines advisable,
      the Company will be permitted (but not required) to offer certain
      Participants, to be designated by the Committee in its sole discretion
      ("Eligible Participants"), who hold Eligible Options (as defined below), a
      one-time opportunity to elect to surrender such Eligible Participant's
      Eligible Options for cancellation ("Surrendered Options") in exchange for
      the grant of replacement options to purchase shares of Stock to be granted
      under the Plan ("Replacement Options") on a date to be determined by the
      Committee that is no less than six months and one day following the
      cancellation of such Surrendered Options (such exchange,
<PAGE>
      the "Stock Option Exchange Program"). The Stock Option Exchange Program
      and the Replacement Options shall have the terms and conditions set forth
      or provided for in this Article 12. Except to the extent otherwise
      determined by the Committee, the Stock Option Exchange Program will be
      structured so that the Company avoids incurring financial accounting
      charges as a result thereof.

            To participate in the Stock Option Exchange Program and receive any
      grant of Replacement Options, a Participant must be an Eligible
      Participant on each of the following dates: (i) the date the Stock Option
      Exchange Program commences, (ii) the date the period during which
      Surrendered Options may be surrendered for cancellation pursuant to the
      Stock Option Exchange Program expires and (iii) the date of grant of the
      Replacement Options.

            12.2 Eligible Options. For purposes of the Stock Option Exchange
      Program, the term "Eligible Option" shall mean an outstanding Stock Option
      granted under the Plan having an Option Price equal to or in excess of
      $25.00 per share.

            12.3 Exchange Ratio. In exchange for three shares of Stock subject
      to Surrendered Options, a Replacement Option to purchase one share of
      Stock will be granted, subject to any adjustments for transactions or
      events specified in Section 4.2 of the Plan. Notwithstanding the
      foregoing, if the number of shares subject to a Replacement Option
      determined by application of the foregoing exchange ratio is a fractional
      number, such fractional number will be rounded up to the nearest whole
      number for the purposes of determining the number of such shares. In
      determining the number of Replacement Options to be granted in exchange
      for Surrendered Options, the foregoing exchange ratio shall be applied
      separately to Surrendered Options having the same Grant Date and the
      resulting number of Replacement Options shall then be rounded in
      accordance with the foregoing.

            12.4 Terms of Replacement Options. Notwithstanding any other
      provision of the Plan, Replacement Options shall have the terms set forth
      in this Section 12.4 and such other terms and conditions as may be
      determined by the Committee in accordance with the provisions hereof.

                  12.4.1. Exercise Price. The price at which a share of Stock
      covered by a Replacement Option may be purchased shall be the closing
      price of the Stock on the New York Stock Exchange on the date of grant, if
      the date is a trading day, and, if not, on the previous trading day.

                  12.4.2. Option Exercise Period and Term. Each Replacement
      Option will become exercisable on the first anniversary of its date of
      grant and immediately exercisable, vested and nonforfeitable upon a change
      in control of the Company. For the purpose of the foregoing, a "change in
      control of the Company" shall have such meaning as may be determined by
      the Committee in

                                       2
<PAGE>
      accordance with the provisions hereof. Subject to Article 7 of the Plan,
      each Replacement Option, once exercisable, will be exercisable for the
      remaining term of the Surrendered Options in exchange for which it is
      granted and for an additional period of time beyond such remaining term
      equal to the period of time from the date of cancellation of such
      Surrendered Options through and including the date of grant of such
      Replacement Option. Following such period for which a Replacement Option
      is exercisable, such Replacement Option shall expire and no shares of
      Stock may be purchased thereunder.

                  12.4.3. Non-Qualified Options. All Replacement Options shall
      be deemed "non-qualified" for purposes of the Internal Revenue Code of
      1986, as amended from time to time, and any successor thereto.

            12.5 Administration. In addition to the authority of the Committee
      set forth in Section 3.2 of the Plan, which authority the Committee shall
      have with respect to the Stock Option Exchange Program and the Replacement
      Options, the Committee shall have full discretionary authority to
      establish rules, terms and conditions for the commencement, continuation
      and/or consummation of the Stock Option Exchange Program, to establish the
      forms of award agreements for Replacement Options, to determine the extent
      to which the Stock Option Exchange Program will result in the Company
      incurring financial accounting charges and to adopt such further rules,
      terms and conditions relating to the Stock Option Exchange Program and the
      Replacement Options that are consistent with the provisions set forth in
      this Article 12, including, without limitation, provisions specifying
      and/or limiting the Eligible Participants. The Committee will have total
      and exclusive responsibility to control, operate, manage and administer
      the Stock Option Exchange Program in accordance with its terms and
      conditions and all the authority that may be necessary or helpful to
      enable it to discharge its responsibilities with respect to the Stock
      Option Exchange Program. Without limiting the generality of the preceding
      sentences, the Committee will have the exclusive right to interpret the
      Stock Option Exchange Program, decide all questions concerning eligibility
      for and the terms of the exchange pursuant to the Stock Option Exchange
      Program, construe any ambiguous provision of the Stock Option Exchange
      Program, correct any default, supply any omission, reconcile any
      inconsistency, and decide all questions arising in the administration,
      interpretation and application of the Stock Option Exchange Program. The
      Committee will have full discretionary authority in all matters related to
      the discharge of its responsibilities and the exercise of its authority
      under the Program, including, without limitation, its construction of the
      terms of the Stock Option Exchange Program. It is the intent of the Stock
      Option Exchange Program that the decisions of the Committee and its
      actions with respect to the Stock Option Exchange Program will be final
      and binding upon all persons having or claiming to have any right or
      interest in or under the Stock Option Exchange Program.

                                       3
<PAGE>
            Without limiting the generality of the foregoing, the Committee
      shall have the right in its sole discretion to provide for such
      modifications and additional terms and conditions ("special terms") to the
      Stock Option Exchange Program as the Committee may consider necessary or
      appropriate to accommodate differences in local law, policy or custom, or
      to facilitate administration of the Stock Option Exchange Program. The
      Committee may adopt or approve sub-plans, appendices or supplements to, or
      amendments, restatements, or alternative versions of, the Stock Option
      Exchange Program as it may consider necessary or appropriate for purposes
      of implementing any special terms, without thereby affecting the terms of
      the Stock Option Exchange Program."

      4. All references in the Plan and this Amendment to the "Plan" shall be
deemed to be references to the Plan as amended hereby. Unless the context
requires otherwise, references in Sections 3.2, 4.2, 6.2, 6.5, 6.6, 6.7, 7.2,
7.3, 9.4, 9.6 and the first sentence of Section 7.1 of the Plan to "Stock
Options," "Participants" and "Option Price" shall, in addition, be deemed to be
references to "Replacement Options," "Eligible Participants" and "the price at
which a share of Stock covered by a Replacement Option may be purchased" (as
described in Section 12.4.1), respectively.

      5. This Amendment does not supersede the terms and conditions of the Plan,
except to the extent expressly described herein, and the Plan, as amended
hereby, shall remain in full force and effect as so amended.

                                       4