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                                                                    Exhibit 10.1
                                                               Execution Version

                THIS AGREEMENT CONTAINS AN ARBITRATION PROVISION

                    AMENDED AND RESTATED EMPLOYMENT AGREEMENT

      THIS AMENDED AND RESTATED EMPLOYMENT AGREEMENT (this "Agreement") is made
and entered into effective as of June 1, 2004, by and between Zix Corporation, a
Texas corporation (the "Company"), and Daniel S. Nutkis ("Employee"), and amends
and restates that certain Employment Agreement, dated December 1, 2003.

                                    RECITALS

      A.    The Company desires to provide for the continuing employment by
            Employee with the Company.

      B.    Employee is willing to continue to serve the Company on the terms
            and conditions provided in this Agreement.

      C.    The Company and the Employee are parties to that certain Severance
            Agreement, dated as of July 1, 2003, between the Company and the
            Employee (the "Severance Agreement"), which is intended to be
            cancelled following the execution of this Agreement.

      THEREFORE, in consideration of the covenants and agreements contained in
this Agreement and other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the parties to this Agreement
agree as follows:

      1.    Employment. The Company shall employ Employee, and Employee accepts
such employment, on the terms and conditions set forth in this Agreement.

      2.    Term. Subject to Section 8 and the other terms and conditions in
this Agreement, the employment of Employee by the Company as provided in Section
1 will be as follows: Employee's employment with the Company shall be on a "full
time" basis for the period beginning June 1, 2004, and ending the later of (i)
November 30, 2004, or (ii) such later date as the parties may mutually agree.
This period of employment is referred to as the period of "full time"
employment. Following this period of full time employment, Employee shall be a
part time employee of the Company for a period of an additional six months. This
period of employment is referred to as the period of "retainer employment."
Following the period of retainer employment, the Employee shall be a consultant
to the Company for an additional two months. This period is referred to as the
"consulting period." Following the execution of this Agreement, Company shall no
longer consider Employee to be a "16-b" officer of the Company, although the
Employee is to be mindful of the continued applicability of certain provisions
of Section 16(b) of the Securities Exchange Act of 1934 and applicable
securities laws relating to insider trading.

AMENDED AND RESTATED
EMPLOYMENT AGREEMENT - Page 1

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      3.    Position and Duties. During the "full time" employment period of
this Agreement, Employee shall serve as Executive Vice President Strategy of the
Company and shall report to the Company's Chief Executive Officer. The duties of
the Employee during the full time employment period shall be to (i) evaluate the
overall marketplace and advise the Company's Chief Executive Officer on
appropriate strategic direction for the Company; (ii) evaluate the Company's key
strategic relationships and advise as to recommended courses of action with
respect to these relationships; (iii) advise as to recommended courses of action
with respect to potential acquisition or business combination candidates; (iv)
provide leadership in the area of regulation and standards; (v) assist the
Company's Chief Medical Officer in establishing the Company's Medical Advisory
Board; and (vi) perform such other tasks as may be reasonably assigned by the
Company's Chief Executive Officer. During the retainer employment period,
Employee shall perform such tasks as may be reasonably assigned by the Company's
Chief Executive Officer for up to 4 days per calendar month and additional work
as mutually agreed. During the "full time" and "retainer employment" periods,
Employee shall not be assigned any duties that will necessitate a change in the
location of his home (presently in the Dallas, Texas area). Employee shall
devote substantially all his working time and efforts to the business and
affairs of the Company during the full time period of this Agreement;
thereafter, Employee shall devote an amount of working time and efforts as is
commensurate with the duties being undertaken by Employee. Notwithstanding the
foregoing, the Company acknowledges that Employee may provide consulting
services to other persons and entities during the term of this Agreement
provided that such consulting services (1) do not interfere with Employee's
duties to the Company pursuant to this Section 3, and (ii) do not violate the
provisions of Section 10 hereof. During the consulting period, Employee shall be
available for telephone consultation and discrete projects as mutually agreed by
the parties. Employee shall be deemed to be an employee until the expiration of
the consulting period for purposes of the Employee's existing stock option
agreements; for purposes of Section 10, Employee shall be deemed to be an
employee through the duration of the full time period and the retainer period.

      4.    Compensation.

      Full-Time Period. During the full time period of employment, Company shall
pay Employee a monthly salary of $27,083, payable semi-monthly.

      Retainer Period. During the retainer period of employment, the Company
shall pay Employee a monthly payment equal to the sum of (i) $18,750 per month
plus (ii) $2,500 per day of services rendered during the month to Company (with
the understanding that each of the Company and Employee commits to a minimum of
four days of service per month during the retainer period of employment
resulting in a minimum retainer fee of $10,000 per month). The amounts payable
to Employee during the retainer period of employment are payable in cash or the
Company's common stock, in the Company's discretion. If paid in stock, in
accordance with current Company policy, Employee shall have one (1) business day
(or other mutually agreed period) after receipt of such stock to liquidate all
or any portion of such stock as Employee

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determines in his sole discretion and if, at the time of the final retainer
period payment to Employee, the cumulative sale prices realized by Employee are
less than the price used to value the stock paid to Employee, then the Company
shall pay Employee such difference in cash or the Company's common stock, in the
Company's discretion. To the extent Employee chooses not to sell the stock
during the one (1) business day (or other mutually agreed period), then Employee
shall not be entitled to any "make whole" payment, even if Employee subsequently
sells the stock at a price(s) that is lower than the price used to value the
stock.

      Consulting Period. During the consulting period, the Company shall pay
Employee at the rate of $2,500 per day of service (pro-rated as appropriate to
account for partial days of service).

      Stock Options. As additional compensation, the Company shall grant to
Employee an option to purchase 164,000 shares of the common stock of the
Company, at an exercise price of $8.50 per share, with vesting to occur pro-rata
and monthly over a twelve month period commencing June 15, 2004, and on the 15th
day of each month thereafter.

      Nashville Home Loss Allowance Reimbursement. Company has paid to Employee
a home loss reimbursement allowance as set forth in the Company's employment
offer letter dated June 19, 2003. Employee shall be entitled to retain this
allowance except that if (a) Employee resigns employment from the Company for
any reason other than the Company does not pay the amounts it is required to pay
to Employee hereunder or (b) the Company terminates Employee's employment for
"Cause" (as defined under the Severance Agreement), then Employee shall within
20 days of the effective date of the employment termination pay to the Company
in cash $25,000 of the home loss reimbursement allowance if the effective date
of the employment separation is before July 31, 2004.

      5.    Expenses and Services. During the term of Employee's employment
under this Agreement, Employee shall be entitled to receive prompt reimbursement
for all reasonable expenses incurred by Employee by reason of his employment,
provided that such expenses are incurred and accounted for in accordance with
reasonable policies and procedures established by the Company and in effect when
the expenses are incurred. The Company shall furnish Employee with office space,
secretarial assistance, office supplies, office equipment, and such other
facilities and services as are suitable to Employee's position and adequate for
the performance of his duties.

      6.    Confidential Information. Employee recognizes and acknowledges that
Employee will have continue to have access to confidential information of the
Company and its affiliated companies, including, without limitation, customer
information, lists of suppliers and costs, information concerning the business
and operations of the Company and its affiliated companies, and proprietary
data, information, concepts and ideas (whether or not patentable or
copyrightable) relating to the business of the Company and its affiliated
companies, as applicable. Employee agrees not to disclose such confidential
information, except as may be necessary in the performance of Employee's duties
hereunder, to any person, nor use such confidential information in any way,
unless Employee has received the written consent of the Company or unless such
confidential information becomes public knowledge through no

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wrongful act of Employee. Upon expiration of the consulting period (or earlier
if requested by Company), Employee shall promptly deliver to the Company all
drawings, manuals, letters, notebooks, customer lists, documents, records,
equipment, files, computer disks or tapes, reports or any other materials
relating to the business of the Company and its affiliated companies, and all
copies, that are in Employee's possession or under Employee's control.
"Confidential information" shall not include information that constitutes
general skills, knowledge, and experience acquired by Employee before and/or
during his employment with the Company. All intellectual property that is
created, conceived, developed, and the like by Employee during the term of the
full time employment period, retainer employment period, and consulting period
in connection with services rendered to the Company by Employee shall be owned
by the Company. Employee will render to the Company such assistance as may be
reasonably necessary to evidence and protect the ownership of its intellectual
property. If such assistance is required after Employee's separation from
employment with the Company, reasonable compensation will be paid to Employee
for such assistance.

      7.    Rights under Certain Plans. During the full time employment period,
Employee will be entitled to participate in the insurance and employee benefit
plans and programs maintained by the Company and its affiliated companies
applicable to similarly situated employees on the same basis as such other
employees of the Company or its affiliated companies, as applicable, subject
only to the possible substitution by or on behalf of the Company or its
affiliated companies of other plans or programs providing substantially similar
or increased benefits for Employee. Employee will also be entitled to reasonable
vacation time, with no reduction in compensation, in keeping with Employee's
duties and responsibilities to the Company. Following the expiration or
termination of the full time employment period, Employee shall be eligible to
elect COBRA continuation benefits under the applicable benefit plans. Company
shall pay Employee's COBRA premiums during the retainer period to the extent
Employee elects to exercise his COBRA rights during such period. If required by
applicable law, Company shall include the amount of the premiums paid on behalf
of Employee in Employee's W-2 or 1099, as applicable.

      8.    Early Termination. Employee may terminate Employee's employment
under this Agreement only if the Company does not pay the amounts it is required
to pay to Employee hereunder or issue the stock required hereunder or under any
of the applicable stock option agreements, provided that Employee's termination
shall not release the Company from its obligations to pay all such amounts and
issue such stock. Company may terminate Employee's employment under this
Agreement only with Cause, as defined in the Severance Agreement.

      9.    Effects of Termination. If the Company terminates Employee's
employment for any reason other than as permitted in Section 8 or if Employee
terminates his employment because the Company does not pay the amounts it is
required to pay to Employee hereunder, then Employee shall be entitled to
receive the amounts and vesting rights that he would have been entitled to
receive through the duration of the full time employment and retainer and
consulting periods.

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      10.   Non-competition. Employee agrees and covenants that Employee will
not, during the term of his employment under this Agreement and the 12 month
period following the time Employee is no longer an employee for purposes of this
Agreement (as previously stated in the last sentence of Section 3):

            (A)   compete, directly or indirectly, with the Company's secure
      messaging business or care delivery services business (including the
      Company's e-prescription business) as they exist at the end of retainer
      employment period. The Company shall inform Employee in writing of changes
      in Company's business during the full time and retainer employment periods
      so that Employee may comply with this Section 10. If Employee has
      theretofore been conducting activities that were not in violation of this
      non-competition provision but became a violation of this non-competition
      provision because of changes in the Company's business, then Employee
      shall have thirty (30) days after receipt of such notice to terminate any
      activities that would be violation of this Section 10. For purposes of
      this Agreement, "Competition" shall include, without limitation, engaging
      in any business, whether as proprietor, partner, joint venture, employee,
      agent, officer, or holder of more than five percent (5%) of any class of
      equity ownership of a business enterprise, that is competitive with the
      Company's secure messaging business or care delivery services business
      (including the Company's e-prescription business).

            (B)   solicit to do, or do, competing business with any then-current
      customer of the Company's secure messaging business or care delivery
      services business (including the Company's e-prescription business) or any
      person that has been a customer within the six months preceding the date
      of Employee's separation from employment with the Company.

            (C)   solicit to hire, or hire, any then-current employee of the
      Company (including its affiliated companies), except by way of general
      advertising.

      Although the Company and Employee have, in good faith, used their best
efforts to make the non-competition covenants reasonable in all pertinent
respects, and it is not anticipated, nor is it intended, by either party to this
Agreement that any arbitrator or court will find it necessary to reform any
non-competition covenant to make it reasonable in all pertinent respects, the
Company and Employee understand and agree that if an arbitrator or court
determines it necessary to reform any non-competition covenant in order to make
it reasonable in all pertinent respects, damages, if any, for a breach of the
non-competition covenant, as so reformed, will be deemed to accrue to the
Company as and from the date of such a breach only and so far as the damages for
such breach related to an action which accrued within the scope of the
non-competition covenant as so reformed.

      The provisions of this Section 10 shall be the only non-competition
covenants applicable to Employee and all other such covenants, including,
without limitation, any non-competition covenants of any stock option agreements
between the Company and Employee, are no longer applicable.

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      11.   Waiver. No waiver of any provision of this Agreement shall be
deemed, or shall constitute, a waiver of any other provision, whether or not
similar, nor shall any waiver constitute a waiver of any continuing or
succeeding breach of such provision, a waiver of the provision itself, or a
waiver of any right under this Agreement. No waiver shall be binding unless
executed in writing by the party making the waiver.

      12.   Limitation of Rights. Nothing in this Agreement, except as
specifically stated in this Agreement, is intended to confer any rights or
remedies under or by reason of this Agreement on any persons other than the
parties to it and their respective permitted successors and assigns and other
legal representatives.

      13.   Remedies. Employee hereby agrees that a violation of the provisions
of Section 6 or 10 hereof would cause irreparable injury to the Company for
which it would have no adequate remedy at law. Accordingly, in the event of any
such violation, the Company shall be entitled to preliminary and other
injunctive relief. Any such injunctive relief shall be in addition to any other
remedies to which the Company may be entitled at law or in equity, or otherwise.

      14.   Notice. Any consent, notice, demand, or other communication
regarding any payment required or permitted hereby must be in writing to be
effective and shall be deemed to have been received on the date delivered, if
personally delivered, or the date received, if delivered otherwise, addressed to
the applicable party at the address for such party set forth below or at such
other address as such party may designate by like notice:

                             The Company:

                             Zix Corporation
                             2711 North Haskell Avenue
                             Suite 2850, LB 36
                             Dallas, Texas 75204-2911, Attn: General Counsel

                             Employee:

                             Daniel S. Nutkis
                             5252 Longvue Drive
                             Frisco, Texas 75034

      15.   Entirety and Amendments. This Agreement embodies the entire
agreement between the parties with respect to the subject matter hereof and
supersedes all prior agreements and understandings relating to the subject
matter hereof. The $18,750 per month payments payable during the retainer
employment period are in lieu of payments payable under the Severance Agreement.
Accordingly, the Severance Agreement is hereby terminated. Employee acknowledges
that other than the Company's obligation to make the payments as provided for
herein, he shall not be entitled to any other compensation payments, or
severance payments, or payments in lieu of notice in connection with his
employment with, or separation from employment with, the Company.

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      16.   Successors and Assigns. This Agreement will be binding upon and
inure to the benefit of the parties to this Agreement and any successors in
interest to the Company, but otherwise, neither this Agreement nor any rights or
obligations under this Agreement may be assigned by Employee.

      17.   Governing Law. This Agreement shall be governed by and construed and
enforced in accordance with the laws of the State of Texas (excluding its
conflict of laws rules) and applicable federal law.

      18.   Cumulative Remedies. No remedy in this Agreement conferred upon any
party is intended to be exclusive of any other benefit or remedy, and each and
every such remedy shall be cumulative and shall be in addition to every other
benefit or remedy given under this Agreement or now or hereafter existing at law
or in equity or by statute or otherwise. No single or partial exercise by any
party of any right, power, or remedy under this Agreement shall preclude any
other or further exercise thereof.

      19.   Multiple Counterparts. This Agreement may be executed in a number of
identical counterparts, each of which constitute collectively, one agreement;
but in making proof of this Agreement, it shall not be necessary to produce or
account for more than one counterpart.

      20.   Descriptive Headings. The headings, captions, and arrangements used
in this Agreement are for convenience only and shall not be deemed to limit,
amplify, or modify the terms of this Agreement, nor affect the meaning hereof.

      21.   Arbitration. The Company and the Employee agree to the resolution by
binding arbitration of all claims, demands, causes of action, disputes,
controversies, or other matters in question ("Claims") arising out of this
Agreement or the Employee's employment (or its termination), whether sounding in
contract, tort, or otherwise and whether provided by statute or common law, that
the Company or its affiliated companies may have against the Employee or that
the Employee may have against the Company or any and its affiliated companies,
or any benefit plans of the Company or any of its affiliated companies, or any
fiduciaries, administrators, and affiliates of any of such benefit plans, or
their respective officers, directors, employees, or agents in their capacity as
such. This agreement to arbitrate shall not limit the Company's or the
Employee's right to seek equitable relief, including, but not limited to,
injunctive relief and specific performance in a court of competent jurisdiction.
Claims covered by this agreement to arbitrate include, but are not limited to,
claims by the Employee for breach of this Agreement, wrongful termination,
discrimination (based on age, race, sex, disability, national origin, or other
factor), and retaliation. The only Claims otherwise within the definition of
Claims that are not covered by this Section 21 are: (1) any administrative
actions that the Employee is permitted to pursue under applicable law that are
not precluded by virtue of the Employee having entered into this Section 21; (2)
any Claim by the Employee for workers' compensation benefits or unemployment
compensation benefits; or (3) any Claim by the Employee for benefits under a
Company or affiliated company pension or benefit plan that provides its own
non-judicial dispute resolution procedure.

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      Claims shall be submitted to arbitration and finally settled under the
Employment Dispute Resolution Rules of the American Arbitration Association
("AAA") in effect at the time the written notice of the Claim is received. An
arbitrator shall be selected in the manner provided for in the Employment
Dispute Resolution Rules of the AAA, except that the parties agree that the
arbitrator shall be an attorney licensed in the state where the arbitration is
being conducted. If any party refuses to honor its obligations under this
agreement to arbitrate, the other party may compel arbitration in either federal
or state court. The arbitrator will have exclusive authority to resolve any
dispute relating to the interpretation, applicability, enforceability, or
formation of this agreement to arbitrate, including, but not limited to, any
claim that all or part of this Agreement is void or voidable and any claim that
an issue is not subject to arbitration. The arbitration will be held in Dallas
County, Texas. The arbitrator shall issue a written decision that identifies the
factual findings and principles of law upon which any award is based. The award
and findings of such arbitrator shall be conclusive and binding upon the
parties. Any and all of the arbitrator's orders, decisions, and awards may be
enforceable in, and judgment upon any award rendered by the arbitrator may be
confirmed and entered by, any federal or state court having jurisdiction. The
Company shall pay all costs and expenses of its advisors and expert witnesses,
and Employee shall pay all costs and expenses of his advisors and expert
witnesses. The costs and expenses of the arbitration proceedings will be paid by
the non-prevailing party or as the arbitrator otherwise determines. Discovery
will be permitted to the extent directed by the arbitrator. EMPLOYEE UNDERSTANDS
THAT BY AGREEING TO SUBMIT CLAIMS TO ARBITRATION, HE GIVES UP THE RIGHT TO SEEK
A TRIAL BY COURT OR JURY AND THE RIGHT TO APPEAL A COURT OR JURY DECISION AND
FORGOES ANY AND ALL RELATED RIGHTS HE MAY OTHERWISE HAVE UNDER FEDERAL AND STATE
LAWS.

      22.   Authority. The Company represents and warrants to Employee that the
execution, delivery and performance by the Company of this Agreement has been
duly authorized by the Company and constitutes the legal, valid and binding
obligation of the Company, enforceable against the Company in accordance with
its terms.

                                   Signatures

      To evidence the binding effect of the covenants and agreements described
above, the parties to this Agreement have executed this Agreement on the dates
set forth below, to be effective as of the date first above written.

                                   THE COMPANY:

                                   ZIX CORPORATION

                                   /s/ John A. Ryan
                                   ---------------------------------
                                   John A. Ryan
                                   President and Chief Executive Officer

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                                   Date: 6-24-04

                                   EMPLOYEE:

                                   /s/ Daniel S. Nutkis
                                   ---------------------------------
                                   Daniel S. Nutkis

                                   Date: 6/14/04

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