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                                                                    EXHIBIT 10.2

                ZIX CORPORATION 2004 DIRECTORS' STOCK OPTION PLAN

   SECTION 1.  Purpose

   The purpose of the Zix Corporation 2004 Directors' Stock Option Plan
(hereinafter called the "Plan") is to advance the interests of Zix Corporation,
a Texas corporation (hereinafter called the "Company"), by strengthening the
ability of the Company to attract, on its behalf, and retain Non-Employee
Directors (as defined below) of high caliber through encouraging a sense of
proprietorship by means of stock ownership.

   SECTION 2.  Definitions

   "Board" shall mean the Board of Directors of the Company.

   "Code" shall mean the Internal Revenue Code of 1986, as amended from
time-to-time.

   "Committee" shall mean the entire Board of Directors, or if the
administration of the Plan has been delegated to a committee of the Board, a
committee selected by the Board and comprised of at least two directors. To the
extent necessary to comply with applicable rules and regulations, the Committee
shall consist of two or more independent directors.

   "Common Stock" shall mean the Common Stock of the Company, par value $.01 per
share.

   "Date of Grant" shall mean the date on which an Option is granted under the
Plan.

   "Designated Beneficiary" shall mean the beneficiary designated by the
Optionee, in a manner determined by the Committee, to receive amounts due the
Optionee in the event of the Optionee's death. In the absence of an effective
designation by the Optionee, Designated Beneficiary shall mean the Optionee's
estate.

   "Fair Market Value" shall mean the closing sales price (or average of the
quoted closing bid and asked prices if there is no closing sales price reported)
of the Common Stock on the date specified as reported by the Nasdaq Stock
Market, or by the principal national stock exchange on which the Common Stock is
then listed. If there is no reported price information for such date, the Fair
Market Value will be determined by the reported price information for Common
Stock on the day nearest preceding such date.

   "Non-Employee Director" shall mean a member of the Board who is not an
employee of the Company or a subsidiary.

   "Option" shall mean a nonqualified option to purchase shares of the Company's
Common Stock.

   "Optionee" shall mean the person to whom an Option is granted under the Plan
or who has obtained the right to exercise an Option in accordance with the
provisions of the Plan.

   SECTION 3.  Administration

   The Plan shall be administered by the Committee. The Committee shall have
sole and complete authority to adopt, alter and repeal such administrative
rules, guidelines and practices governing the operation of the Plan as it shall
from time-to-time deem advisable, and to construe, interpret and administer the
terms and provisions of the Plan and the agreements thereunder. The
determinations and interpretations made by the Committee are final and
conclusive and binding on all persons.

   SECTION 4.  Eligibility

   All Non-Employee Directors shall be eligible to receive awards of Options
under the Plan.

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   SECTION 5.  Maximum Amount Available for Awards

   Subject to the provisions of Section 9, the maximum number of shares of
Common Stock in respect of which Options may be granted under the Plan shall be
300,000 shares of Common Stock. Shares of Common Stock may be made available
from authorized but unissued shares of the Company or from shares reacquired by
the Company, including shares purchased in the open market. In the event that an
Option is terminated unexercised as to any shares of Common Stock covered
thereby, such shares shall thereafter be again available for award pursuant to
the Plan.

   SECTION 6.  Stock Options

   (a) During the term of the Plan, on the day that an Non-Employee Director is
first appointed or elected to the Board, such director shall be granted
nonqualified Options to purchase 25,000 shares of the Company's Common Stock.
The Options shall vest quarterly and pro-rata over one year. Also, on the first
business day in January of each year during the term of the Plan, each
Non-Employee Director that has served on our Board for at least six months as of
the grant date shall be granted nonqualified Options to purchase a number of
shares of our common stock equal to the greater of (i) one-half of one percent
of the number of our outstanding shares (measured as of the immediately
preceding December 31) or (ii) 200,000 shares, divided by the greater of (i)
five or (ii) the number of Non-Employee directors that have served on the Board
for at least six months as of the grant date. The options shall vest quarterly
and pro-rata over three years from the grant date.

   Also, any Non-Employee director that had served on the Board for at least six
months (but not 12 months) as of January 1, 2004, shall be entitled to receive
an option grant covering 50,000 shares. The effective date of the grant shall be
the date of the Company's 2004 annual meeting of stockholders. The exercise
price of these options shall be 100% of the Fair Market Value of the Common
Stock on the Date of Grant. The options shall vest quarterly and pro-rata over
three years from the grant date.

   (b) The exercise price of the 25,000 share option grants and of the January
share option grants shall be 100% of the Fair Market Value of the Common Stock
on the Date of Grant. The Options may not be exercised after the tenth
anniversary of the Date of Grant.

   (c) Each Option hereunder shall be evidenced in writing, delivered to the
Optionee, and shall be exercisable at such times and subject to such terms and
conditions as specified in the applicable grant and agreement.

   The Committee may impose such conditions with respect to the exercise of
Options (that are consistent with the foregoing principles), including without
limitation, any relating to the application of federal or state securities laws,
as it may deem necessary or advisable.

   (d) No shares shall be delivered pursuant to any exercise of an Option until
cash payment in full of the option price therefor is received by the Company. If
the shares to be purchased are covered by an effective registration statement
under the Securities Act of 1933, any Option may be exercised by a broker-dealer
acting on behalf of an Optionee if (a) the broker-dealer has received from the
Optionee instructions signed by the Optionee requesting the Company to deliver
the shares of Common Stock subject to such Option to the broker-dealer on behalf
of the Optionee and specifying the account into which such shares should be
deposited, (b) adequate provision has been made with respect to the payment of
any withholding taxes due upon such exercise, and (c) the broker-dealer and the
Optionee have otherwise complied with Section 220.3(e)(4) of Regulation T, 12
CFR Part 220, or any successor provision. The Company shall have the right to
deduct from all amounts paid to an Optionee in cash (whether under the Plan or
otherwise) any taxes the Company withholds in respect of Options under the Plan.

   (e) The Company shall not be required to issue any fractional shares upon the
exercise of any Options granted under the Plan. No Optionee or such Optionee's
legal representatives, legatees or distributees, as the case may be, will be, or
will be deemed to be, a holder of any shares subject to an Option unless and
until said Option has been exercised and the purchase price of the shares in
respect of which the Option has been exercised has been paid. Unless otherwise
provided in the agreement applicable thereto, an Option shall not be exercisable
except by the Optionee or by a person who has obtained the Optionee's rights
under the Option by will or under the laws of descent and distribution or
pursuant to a "qualified domestic relations order" as defined in the Code, and
no right or interest of any Optionee shall be subject to any lien, obligation or
liability of the Optionee.

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   SECTION 7.  Plan Amendments

   The Board may amend, abandon, suspend or terminate the Plan or any portion
thereof at any time in such respects as it may deem advisable in its sole
discretion, provided that no amendment shall be made without stockholder
approval if such amendment is material or if stockholder approval is necessary
to comply with any tax or regulatory requirement.

   SECTION 8.  Restrictions on Issuance of Options and Option Shares

   The Company shall not be obligated to issue any shares upon the exercise of
any Option granted under the Plan unless: (1) the shares pertaining to such
Option have been registered under applicable securities laws or are exempt from
such registration; (2) if required, the prior approval of such sale or issuance
has been obtained from any state regulatory body having jurisdiction; and (3) in
the event the Common Stock has been listed on any exchange, the shares
pertaining to such Option have been duly listed on such exchange in accordance
with the procedure specified therefor. The Company shall be under no obligation
to effect or obtain any listing, registration, qualification, consent or
approval with respect to shares pertaining to any Option granted under the Plan.
If the shares to be issued upon the exercise of any Option granted under the
Plan are intended to be issued by the Company in reliance upon the exemptions
from the registration requirements of applicable federal and state securities
laws, the recipient of the Option, if so requested by the Company, shall furnish
to the Company such evidence and representations, including an opinion of
counsel satisfactory to it as the Company may reasonably request.

   The Company shall not be liable for damages due to a delay in the delivery or
issuance of any stock certificates for any reason whatsoever, including, but not
limited to, a delay caused by listing, registration or qualification of the
shares of Common Stock pertaining to any Option granted under the Plan upon any
securities exchange or under any federal or state law or the effecting or
obtaining of any consent or approval of any governmental body.

   The Committee may impose such other restrictions on the ownership and
transfer of shares issued pursuant to the Plan as it deems desirable; any such
restrictions shall be set forth in the agreement applicable thereto.

   SECTION 9.  Adjustment to Shares

   In the event that the Committee shall determine that any stock dividend,
recapitalization, reorganization, merger, consolidation, split-up, spin-off,
combination, exchange of shares, warrants or rights offering to purchase Common
Stock at a price substantially below Fair Market Value or other similar
corporate event affects the Common Stock such that an adjustment is required in
order to preserve the benefits or potential benefits intended to be made
available under the Plan, then the Committee shall adjust appropriately any or
all of (a) the number and kind of shares that thereafter may be optioned under
the Plan, (b) the number and kind of shares subject of Options and (c) the
exercise price with respect to any of the foregoing and/or, if deemed
appropriate, make provision for cash payment to an Optionee or a person who has
an outstanding Option; provided, however, that the number of shares subject to
any Option shall always be a whole number.

   SECTION 10.  Effective Date; Term

   The Plan shall be effective as of May 6, 2004. No Options may be granted
under the Plan after May 6, 2014.

   SECTION 11.  General Provisions

   (a) Neither the Plan nor any Option granted hereunder is intended to confer
upon any Optionee any rights with respect to continuance of the utilization of
his or her services by the Company, nor to interfere in any way with his or her
right or that of the Company to terminate his or her services at any time
(subject to the terms of any applicable contract, law, regulation, and the
articles and bylaws of the Company).

   (b) No Optionee or Designated Beneficiary shall have any rights as a
stockholder with respect to any shares of Common Stock to be distributed under
the Plan until he or she has become the holder thereof.

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   (c) The validity, construction, interpretation, administration and effect of
the Plan and of its rules and regulations, and rights relating to the Plan,
shall be determined solely in accordance with the laws of the State of Texas
(without giving effect to its conflicts of laws rules) and, to the extent
applicable, federal law.

   IN WITNESS WHEREOF, the Company has caused this Plan to be executed on its
behalf as of the 6th day of May 2004.


                                          ZIX CORPORATION


                                          By:      /s/ Ronald A. Woessner
                                              ----------------------------------

                                          Title:   SVP
                                                 -------------------------------

                                          Date:    5/6/04
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