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                                                           EXHIBIT (10)(b)(xiii)

                     AMERICAN SCIENCE AND ENGINEERING, INC.
        
                      1998 NON-QUALIFIED STOCK OPTION PLAN

    SECTION I. PURPOSE OF THE PLAN.

         The purposes of this American Science and Engineering, Inc. 1998
    Non-Qualified Stock Option Plan (the "1998 Plan") are (i) to provide
    long-term incentives and rewards to those key employees (the "Employee
    Participants") of American Science and Engineering, Inc. (the "Corporation")
    and its subsidiaries (if any), and any other persons (the "Non-employee
    Participants") who are in a position to contribute to the long-term success
    and growth of the Corporation and its subsidiaries, (ii) to assist the
    Corporation in retaining and attracting executives and key employees with
    requisite experience and ability, and (iii) to associate more closely the
    interests of such executives and key employees with those of the
    Corporation's stockholders.

    SECTION II. DEFINITIONS.

         "Common Stock" is the $.66 2/3 par value common stock of the
         Corporation.

         "Committee" is defined in Section III, paragraph (a).

         "Corporation" is defined in Section I.

         "Employee Participants" is defined in Section I.

         "Fair Market Value" of any property is the value of the property as
         reasonably determined by the Committee.

         "1998 Plan" is defined in Section I.

         "Non-employee Participants" is defined in Section I.

         "Non-qualified Option" is a Stock Option which does not qualify as an
         Incentive Stock Option or for which the Committee provides, in the
         terms of such option and at the time such option is granted, that the
         option shall not be treated as an Incentive Stock Option.

         "Parent Corporation" has the meaning provided in Section 424(e) of the
         Code.


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         "Participants" are all persons who are either Employee Participants or
         Non-employee Participants.

         "Permanent and Total Disability" has the meaning provided in Section
         22(e)(3) of the Code. 

         "Rule 16b-3" means Securities and Exchange Commission Rule 16b-3.

         "Section 16" means Section 16 of the Securities Exchange Act of 1934,
         as amended, or any similar or successor statute, and any rules,
         regulations, or policies adopted or applied thereunder.

         "Stock Options" are rights granted pursuant to this 1998 Plan to
         purchase shares of Common Stock at a fixed price.

         "Subsidiary Corporation" has the meaning provided in Section 424(f) of
         the Code.

     SECTION III. ADMINISTRATION.

     (a) The Committee. This 1998 Plan shall be administered by the Board of
Directors or by a compensation committee consisting solely of two or more
"non-employee directors", as defined in Rule 16b-3, who shall be designated by
the Board of Directors of the Corporation (the administering body is hereafter
referred to as the "Committee"). The Committee shall serve at the pleasure of
the Board of Directors, which may from time to time, and in its sole discretion,
discharge any member, appoint additional new members in substitution for those
previously appointed and/or fill vacancies however caused. A majority of the
Committee shall constitute a quorum and the acts of a majority of the members
present at any meeting at which a quorum is present shall be deemed the action
of the Committee. No person shall be eligible to be a member of the Committee if
that person's membership would prevent the plan from complying with Section 16,
if applicable to the Corporation.

     (b) Authority and Discretion of the Committee. Subject to the express
provisions of this 1998 Plan and provided that all actions taken shall be
consistent with the purposes of this 1998 Plan, and subject to ratification by
the Board of Directors only if required by applicable law, the Committee shall
have full and complete authority and the sole discretion to: (i) determine those
persons who shall constitute key employees eligible to be Employee Participants;
(ii) select the Participants to whom Stock Options shall be granted under this
1998 Plan; (iii) determine the size and the form of the Stock Options, if any,
to be granted to any Participant; (iv) determine the time or times such Stock
Options shall be granted including the grant of Stock Options in connection with
other awards made, or compensation paid, to the Participant; (v) estab-


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lish the terms and conditions upon which such Stock Options may be exercised
and/or transferred, including the exercise of Stock Options in connection with
other awards made, or compensation paid, to the Participant; (vi) make or alter
any restrictions and conditions upon such Stock Options and the Stock received
on exercise thereof, including, but not limited to, providing for limitations on
the Participant's right to keep any Stock received on termination of
employment; (vii) determine whether the Participant or the Corporation has
achieved any goals or otherwise satisfied any conditions or requirements that
may be imposed on or related to the exercise of Stock Options; and (viii) adopt
such rules and regulations, establish, define and/or interpret these and any
other terms and conditions, and make all determinations (which may be on a
case-by-case basis) deemed necessary or desirable for the administration of this
1998 Plan.

     (c) Applicable Law. This 1998 Plan and all Stock Options shall be governed
by the law of the state in which the Corporation is incorporated.

    SECTION IV. TERMS OF STOCK OPTIONS.

     (a) Agreements. Stock Options shall be evidenced by a written agreement
between the Corporation and the Participant awarded the Stock Option. This
agreement shall be in such form, and contain such terms and conditions (not
inconsistent with this 1998 Plan) as the Committee may determine. The agreement
shall include the following or a similar statement: "This stock option is not
intended to be an Incentive Stock Option, as that term is described in Section
422 of the Internal Revenue Code of 1986, as amended."

     (b) Term. Stock Options shall be for such periods as may be determined by
the Committee.

     (c) Purchase Price. The purchase price of shares purchased pursuant to any
Stock Option shall be determined by the Committee, and shall be paid by the
Participant or other person permitted to exercise the Stock Option in full upon
exercise, (i) in cash, (ii) by delivery of shares of Common Stock (valued at
their Fair Market Value on the date of such exercise), (iii) any other property
(valued at its Fair Market Value on the date of such exercise), or (iv) any
combination of cash, stock and other property, with any payment made pursuant to
subparagraphs (ii), (iii) or (iv) only as permitted by the Committee, in its
sole discretion. In no event will the purchase price of Common Stock be less
than the par value of the Common Stock.

     (d) Restrictions. At the discretion of the Committee, the Common Stock
issued pursuant to the Stock Options granted hereunder may be subject to
restrictions on vesting or transferability. For the purposes of this limitation,
options shall be taken into account in the order granted.

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     (e) Withholding of Taxes. Pursuant to applicable federal, state, local or
foreign laws, the Corporation may be required to collect income or other taxes
upon the grant of a Stock Option to, or exercise of a Stock Option by, a holder.
The Corporation may require, as a condition to the exercise of a Stock Option,
or demand, at such other time as it may consider appropriate, that the
Participant pay the Corporation the amount of any taxes which the Corporation
may determine is required to be withheld or collected, and the Participant shall
comply with the requirement or demand of the Corporation. In its discretion, the
Corporation may withhold shares to be received upon exercise of a Stock Option
if it deems this an appropriate method for withholding or collecting taxes.

     (f) Securities Law Compliance. Upon exercise (or partial exercise) of a
Stock Option, the Participant or other holder of the Stock Option shall make
such representations and furnish such information as may, in the opinion of
counsel for the Corporation, be appropriate to permit the Corporation to issue
or transfer Stock in compliance with the provisions of applicable federal or
state securities laws. The Corporation, in its discretion, may postpone the
issuance and delivery of Stock upon any exercise of this Option until completion
of such registration or other qualification of such shares under any federal or
state laws, or stock exchange listing, as the Corporation may consider
appropriate. Furthermore, the Corporation is not obligated to register or
qualify the shares of Common Stock to be issued upon exercise of a Stock Option
under federal or state securities laws (or to register or qualify them at any
time thereafter), and it may refuse to issue such shares if, in its sole
discretion, registration or exemption from registration is not practical or
available. The Corporation may require that prior to the issuance or transfer of
Stock upon exercise of a Stock Option, the Participant enter into a written
agreement to comply with any restrictions on subsequent disposition that the
Corporation deems necessary or advisable under any applicable federal and state
securities laws. Certificates of Stock issued hereunder shall bear a legend
reflecting such restrictions.

     (g) Right to Stock Option. No employee of the Corporation or any other
person shall have any claim or right to be a participant in this 1998 Plan or to
be granted a Stock Option hereunder. Neither this 1998 Plan nor any action taken
hereunder shall be construed as giving any person any right to be retained in
the employ of the Corporation. Nothing contained hereunder shall be construed
as giving any person any equity or interest of any kind in any assets of the
Corporation or creating a trust of any kind or a fiduciary relationship of any
kind between the Corporation and any such person. As to any claim for any unpaid
amounts under this 1998 Plan, any person having a claim for payments shall be an
unsecured creditor.

     (h) Indemnity. Neither the Board of Directors nor the Committee, nor any
members of either, nor any employees of the Corporation or any parent,
subsidiary, or other affiliate, shall be liable for any act, omission,
interpretation, construction or determination made in good faith in connection
with their responsibilities with respect to this 1998 Plan, and the Corporation
hereby



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agrees to indemnify the members of the Board of Directors, the members of
the Committee, and the employees of the Corporation and its parent or
subsidiaries in respect of any claim, loss, damage, or expense (including
reasonable counsel fees) arising from any such act, omission, interpretation,
construction or determination to the full extent permitted by law.

     (i) Participation by Foreigners. Without amending this 1998 Plan, the
Committee may modify grants made to participants who are foreign nationals or
employed outside the United States so as to recognize differences in local law,
tax policy, or custom.

     SECTION V. AMENDMENT AND TERMINATION: ADJUSTMENTS UPON CHANGES IN STOCK.

     The Board of Directors of the Corporation may at any time, and from time to
time, amend, suspend or terminate this 1998 Plan or any portion thereof,
provided that no amendment shall be made without approval of the Corporation's
stockholders if such approval is necessary to comply with any applicable rules
or regulations of the Securities and Exchange Commission, including Rule 16b-3
(or any successor rule thereunder), or the rules and regulations of any exchange
or stock market on which the Corporation's securities are listed or quoted.
Except as provided herein, no amendment, suspension or termination of this 1998
Plan may affect the rights of a Participant to whom a Stock Option has been
granted without such Participant's consent. If there shall be any change in the
Common Stock or to any Stock Option granted under this 1998 Plan through merger,
consolidation, reorganization, recapitalization, stock dividend, stock split or
other change in the corporate structure of the Corporation, appropriate
adjustments may be made by the Committee (or if the Corporation is not the
surviving corporation in any such transaction, the Board of Directors of the
surviving corporation, or its designee) in the aggregate number and kind of
shares subject to this 1998 Plan, and the number and kind of shares and the
price per share subject to outstanding options. In connection with the
foregoing, the Committee may issue new Stock Options in exchange for outstanding
Stock Options.

     SECTION VI. SHARES OF STOCK SUBJECT TO THE PLAN.

     The number of shares of Common Stock that may be the subject of awards
under this 1998 Plan shall not exceed an aggregate of 300,000 shares. Shares to
be delivered under this 1998 Plan may be either authorized but unissued shares
of Common Stock or treasury shares. Any shares subject to an option hereunder
which for any reason terminates, is cancelled or otherwise expires unexercised,
and any shares reacquired by the Corporation due to restrictions imposed on the
shares, shares returned because payment is made hereunder in stock of equivalent
value rather than in cash, and/or shares reacquired from a recipient for any
other reason shall, at such time, no longer count towards the aggregate number
of shares which have been the subject of Stock Options issued hereunder, and
such number of shares shall be subject to further awards under this 1998 Plan,
provided, first, that the total number of shares then eligible for award under

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this 1998 Plan may not exceed the total specified in the first sentence of this
Section VI, and second, that the number of shares subject to further awards
shall not be increased in any way that would cause this 1998 Plan or any Stock
Option to not comply with Section 16, if applicable to the Corporation.

    SECTION VII. EFFECTIVE DATE AND TERM OF THIS PLAN.

    The effective date of this 1998 Plan is            1998 (the "Effective
Date") and awards under this 1998 Plan may be made for a period of ten years
commencing on the Effective Date. The period during which a Stock Option may be
exercised may extend beyond that time as provided herein.

DATE OF APPROVAL BY STOCKHOLDERS: N/A

DATE OF APPROVAL BY BOARD OF DIRECTORS:           , 1998

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