<PAGE>
 
                                                                   EXHIBIT 10.34

                        EXECUTIVE CONTINUITY AGREEMENT


     THIS EXECUTIVE CONTINUITY AGREEMENT ("Agreement") made and entered into as
of the 31st day of August, 1998 by and between Maxxim Medical, Inc., a Texas
corporation (the "Company") and Joseph D. Dailey, an individual (the
"Executive").

                                   RECITALS:

     A.   The Executive is a principal officer of the Company and an integral
          part of its management.

     B.   The Company wishes to assure both itself and the Executive of
          continuity of management in the event of any actual or threatened
          change in control of the Company.

     C.   This Agreement is not intended to alter materially the compensation
          and benefits that the Executive could reasonably expect in the absence
          of a change in control of the Company and, accordingly, this
          Agreement, though taking effect upon the parties' execution hereof,
          will be operative only upon a change of control of the Company, as
          that term is defined herein.

                                   AGREEMENT

     NOW, THEREFORE, in consideration of the foregoing recitals and the
agreements of the parties contained herein, the parties do hereby agree as
follows:

1.   Operation of Agreement.
     ---------------------- 

     This Agreement shall be effective immediately upon its execution by the
parties hereto as of the date first above written.  Anything in this Agreement
to the contrary notwithstanding, neither this Agreement nor any provision
thereof shall be operative unless and until there has been a "Change in Control"
of the Company as defined in Section 5 below.  Upon such a Change in Control of
the Company, this Agreement and all provisions hereof shall become operative
immediately.

2.   Purpose and Intent.
     ------------------ 

     The Board of Directors of the Company (the "Board") recognizes that the
possibility of a Change in Control of the Company exists and that such
possibility, and the uncertainty and questions which it necessarily raises among
management, may 

                                     67 -
<PAGE>
 
result in the departure or distraction of key management personnel to the
detriment of the Company and its shareholders in this period when their
undivided attention and commitment to the best interests of the Company and its
shareholders are particularly important. Accordingly, the Board has determined
that appropriate steps should be taken to reinforce and encourage the continued
attention and dedication of members of the Company's management, including the
Executive, to their assigned duties without distraction in the face of
potentially disturbing circumstances arising from the possibility of a Change in
the Control of the Company.

3.   Term of Agreement.
     ----------------- 

     This Agreement shall be effective upon the execution thereof by the
parties, and shall remain in effect until December 31, 2004, at which time it
shall terminate; provided, however, that the term of this Agreement shall be
extended by one day for each day after December 31, 2002 that notice of
termination by either party has not been given to the other, so that at all
times after December 31, 2004, if neither party has given notice of termination
then this Agreement shall have a two (2) year remaining term.  Either party may
give notice of termination of this Agreement at any time, with or without cause.
If any notice of termination is given on or before December 31, 2002, then this
Agreement shall terminate December 31, 2004.  If any notice of termination is
given after December 31, 2002, then this Agreement shall terminate on that date
two years after such notice is given.

4.   Termination Following Change in Control.
     --------------------------------------- 

     For purposes hereof only, a termination of the Executive's employment
following a Change in Control ("Termination Following Change in Control") shall
be deemed to occur if at any time during the two-year period immediately
following a Change in Control:

     (a)  there has been an actual termination by the Company of the Executive's
          employment, other than "for cause" as defined herein;

     (b)  the Company reduces the Executive's base salary, bonus computation or
          changes his title without his prior express approval;

     (c)  the Company substantially reduces the Executive's responsibilities as
          in effect immediately prior to the Change in Control or as the same
          may be increased from time to time, or there is a change in employment
          conditions deemed by the Executive to be materially adverse as
          compared to those in effect immediately prior to the Change in
          Control, any of which is not remedied within 30 days after receipt by
          the Company of notice by the Executive, of such reduction in
          responsibilities or change in employment conditions;

                                     68 -
<PAGE>
 
     (d)  without the Executive's express written consent, the Company requires
          the Executive to be based anywhere other than Pinellas County,
          Florida, except for required travel on the Company's business to an
          extent substantially consistent with that prior to the Change in
          Control;

     (e)  the Company fails to obtain the assumption of the performance of this
          Agreement by any successor of the Company; or

     (f)  the Company takes any action which would deprive the Executive of any
          material fringe benefit enjoyed by the Executive at the time of the
          Change in Control, or the Company fails to provide the Executive with
          the number of paid vacation days to which the Executive is entitled in
          accordance with the Company's normal vacation policy in effect on the
          date of the Change in Control.

     The voluntary termination by the Executive of his employment by the Company
     shall in no event constitute a "Termination Following Change in Control."

5.   Definition of Change in Control.
     ------------------------------- 

     A Change in Control will be deemed to have occurred if:

     (a)  any "person" as such term is used in Sections 13(d) and 14(d)(2) of
          the Securities Exchange Act of 1934 (the "Exchange Act"), is or
          becomes a beneficial owner, directly or indirectly, of securities of
          the Company representing 25% or more of the combined voting power of
          the Company's then outstanding equity securities ("Equity
          Securities");

     (b)  individuals are elected to the Board causing a majority of the Board
          to consist of persons other than (i) persons who were members of the
          Board as of the date of the adoption of this Agreement by the Board
          and (ii) persons who were nominated for election as members of the
          Board at a time when the majority of the Board consisted of persons
          who were members of the Board as of the date of the adoption of this
          Agreement by the Board; provided, that any person nominated for
          election by the Board composed entirely of persons described in (i) or
          (ii) , or of persons who were themselves nominated by such Board,
          shall for this purpose be deemed to have been nominated by a Board
          composed of persons described in (i);

     (c)  an event occurs which constitutes a change in control of a nature that
          would be required to be reported in response to Item 6(e) of Schedule
          14A of Regulation 14A promulgated under the Exchange Act, whether or
          not the Company is then subject to such reporting requirements;

                                     69 -
<PAGE>
 
     (d)  there is a merger or consolidation of the Company in which the Company
          does not survive as an independent public company other than a merger
          of the Company in which the holders of Equity Securities immediately
          prior to the merger have the same proportionate ownership of Equity
          Securities of the surviving company immediately after the merger; or

     (e)  the business or businesses of the Company for which the Executive's
          services are principally performed are disposed of by the Company
          pursuant to a partial or complete liquidation of the Company, a sale
          of assets (including stock of a subsidiary) of the Company, or
          otherwise.

6.   Compensation Following Termination.
     ---------------------------------- 

     (a)  Subject to the terms and conditions of this Agreement, upon a
          Termination Following Change in Control, as defined in Section 4,
          which occurs during the term of this Agreement, the Executive shall be
          entitled to (i) a lump sum payment, within fifteen (15) days following
          the date of such termination, in an amount equal to the highest annual
          level of total taxable compensation paid to the Executive by the
          Company (including any and all bonus amounts, transfers of stock and
          other property or other items recognized as "annualized includable
          compensation" under Code Section 280G(d)(1) and reported on Form W-2)
          during the three calendar years ended immediately prior to such
          termination, (ii) the immediate vesting of and an extended period of
          at least 180 days following the date of such termination in which to
          exercise all previously granted but unvested and/or unexercised
          options to acquire securities from the Company which were outstanding
          on the date of the termination (any of the Company's Stock Option
          Agreements with the Executive shall hereby be deemed to be amended to
          modify any provisions inconsistent with the vesting and extended
          exercise period terms herein stated), and (iii) continuing health
          coverage for the Executive and his family for a period of twelve (12)
          months following the date of such termination, at the level, benefits
          and cost commensurate with that which the Executive enjoyed with the
          Company immediately prior to such Change in Control. This continuing
          health coverage shall apply to the Company's obligation to provide the
          Executive with COBRA continuation coverage through 608 Section 601 et.
          seq. of the Employee Retirement Income Security Act of 1974, as
          amended.

     (b)  The executive shall not be required to mitigate the amount of any
          payment provided for in this Section 6 by seeking other employment or
          otherwise, nor shall the amount of any payment or benefit provided for
          in this Section 6 be reduced by any amounts to which the Executive
          shall be entitled by law (nor shall payment hereunder be deemed in
          lieu of such amounts), by any compensation earned by the Executive as
          a result of employment by

                                     70 -
<PAGE>
 
          another employer or by retirement benefits after the date of
          termination or voluntary termination, or otherwise.

     (c)  Anything to the contrary notwithstanding, all payments required to be
          made by the Company hereunder to the Executive or his estate or
          beneficiaries shall be subject to the withholding of such amounts, if
          any, relating to tax and other payroll deductions as the Company may
          reasonably determine it should withhold pursuant to any applicable law
          or registration. In lieu of withholding such amounts, the Company may
          accept other provisions to the end that it has sufficient funds to pay
          all taxes required by law to be withheld in respect of any or all of
          such payments.

7.   Definition of "For Cause".
     ------------------------- 

     The termination of the Executive's employment by the Company shall be
deemed "For Cause" if it results from:

     (a)  the willful and continued failure by the Executive substantially to
          perform his employment duties or regular failure to follow the
          specific directives of the Executive's supervisor, after written
          demand for substantial performance that specifically identifies the
          manner in which the Company believes the Executive has not
          substantially performed his duties is delivered by the Company to the
          Executive;

     (b)  the willful engaging by the Executive in misconduct which is
          materially injurious to the Company, monetarily or otherwise;

     (c)  the Executive's death; or

     (d)  an accident or illness which renders the Executive unable, for a
          period of two (2) consecutive months or an aggregate of sixty-one (61)
          days in any calendar year, to perform the essential functions of his
          job notwithstanding the provision of reasonable accommodation by
          Employer.

     For purposes of this section, no act, or failure to act, on the Executive's
part shall be considered "willful" unless done, or omitted to be done, by him
not in good faith and without reasonable belief that his action or omission was
in the best interest of the Company.  Notwithstanding the foregoing, the
Executive shall not be deemed to have been terminated For Cause under subsection
(a) or (b) without (i) reasonable advance written notice to the Executive
setting forth the reasons for the Company's intention to terminate For Cause,
and (ii) delivery to the Executive of written notice of termination from the
Company finding that the Executive was guilty of conduct set forth above in
clause (a) or (b) and specifying the particulars thereof in detail.

                                     71 -
<PAGE>
 
8.   Tax Treatment.
     ------------- 

     It is the intention of the parties that no portion of the payment made
under Section 6 hereof (the "Termination Payment") or any other payment under
this Agreement, or payments to or for the Executive's benefit under any other
agreement or plan, be deemed to be an excess parachute payment as defined in
Section 280G of the Internal Revenue Code of 1986, as amended (the "Code"), or
its successors.  It is agreed that the present value of the Termination Payment
and any other payment to or for the Executive's benefit in the nature of
compensation, receipt of which is contingent on the Change in Control of the
Company, and to which Section 280G of the Code or any successor provision
thereto applies (in the aggregate "Total Payments") shall not exceed an amount
equal to one dollar less than the maximum amount which the Executive may receive
without becoming subject to the tax imposed by Section 4999 of the Code or any
successor provisions or which the Company may pay without loss of deduction
under Section 280G of the Code or any successor provision.  Present value for
purposes of this Agreement shall be calculated in accordance with Section
1274(b)(2) of the Code or any successor provision.

     Within six (6) days following delivery of written notice by the Company to
the Executive of the Company's belief that there is a payment or benefit due
which will result in an excess parachute payment as defined in Section 280G of
the Code or any successor provision, the Company and the Executive, at the
Company's expense, shall obtain the opinion of legal counsel and certified
public accountants, as the Company and Executive may mutually agree upon, which
opinions need not be unqualified, which sets forth (i) the amount of the
Executive's Base Period Income, as defined in Section 280G of the Code, (ii) the
present value of Total Payments, and (iii) the amount and present value of any
excess parachute payments.

     In the event such opinions determine that there would be an excess
parachute payment, the Termination Payment hereunder, or any other payment
determined by such counsel to be includable in Total Payments, shall be reduced
or eliminated in the following order: (i) by the amount of any options to
purchase securities of the Company which have had their vesting rights
accelerated hereunder, and (ii) by the amount of any cash received hereunder, so
that under the bases of calculation set forth in such opinions there will be no
excess parachute payment.  The provisions of this Section, including the
calculations, notices and opinions provided herein, shall be based upon the
conclusive presumption that (i) the compensation and benefits provided herein
and (ii) any other compensation, including but not limited to any accrued
benefits, earned by the Executive prior to the Change in Control of the Company
pursuant to the Company's compensation programs, would have been reasonable if
made in the future in any event, even though the timing of such payment is
triggered by the Change in Control of the Company.  In the event such legal
counsel so requests, in connection with the Section 280G opinion required by
this Section, the Company and Executive shall obtain, at the Company's expense,
the advice of a firm of recognized executive compensation consultants concerning
the reasonableness of any item of compensation 

                                     72 -
<PAGE>
 
to be received by the Executive, on which advise legal counsel may rely in
providing their opinion. In the event that the provisions of Sections 280G and
4999 of the Code or any successor provision are repealed without succession,
this Section shall be of no further force or effect.

9.   Miscellaneous.
     ------------- 

     (a)  Intent.  This Agreement is made by the Company in order to induce the
          ------                                                               
          Executive to remain in the Company's employ, with the Company's
          acknowledgment and intent that it will be relied upon by the
          Executive, and in consideration of the services to be performed by the
          Executive from time to time hereafter. However, this Agreement is not
          an agreement to employ the Executive for any period of time or at all,
          and the terms and conditions of the Executive's employment, other than
          those expressly addressed herein, shall be subject to and governed by
          a separate agreement of employment between the Company and the
          Executive, if any. This Agreement is intended only as an agreement to
          provide the Executive with specified compensation and benefits if he
          or she is terminated following a Change in Control.

     (b)  Attorney's Fees. If any action at law or in equity is commenced to
          ---------------   
          enforce any of the provisions or rights under this Agreement, the
          unsuccessful party to such litigation, as determined by the court in a
          final judgment or decree, shall pay the successful party all costs,
          expenses and reasonable attorneys' fees incurred by the successful
          party or parties (including, without limitation, costs, expenses and
          fees on any appeals), and if the successful party recovers judgment in
          any such action or proceeding, such costs, expenses and attorneys'
          fees shall be included as part of the judgment.

     (c)  Governing Law.  This Agreement shall be governed by and construed and
          -------------                                                        
          interpreted in accordance with the laws of the State of Florida.

     (d)  Successors and Assigns.
          ---------------------- 

          (i)  The Company will require any successor (whether direct or
     indirect, by purchase, merger, consolidation or otherwise) to all or
     substantially all of the business and/or assets of the Company to assume
     expressly and agree in writing to perform this Agreement.  Failure of the
     Company to obtain such assumption and agreement prior to the  effectiveness
     of any such succession shall be a breach of this Agreement and shall
     require the Company to pay to the Executive compensation from the Company
     in the same amount and on the same terms as the Executive would be entitled
     hereunder in the event of a 

                                     73 -
<PAGE>
 
     Termination Following Change in Control of the Company, except that for
     purposes of implementing the foregoing, the date on which any such
     succession becomes effective shall be deemed to be the date on which the
     Executive shall receive such compensation from the Company. As used in this
     Agreement, "Company" shall mean the Company as herein above defined and any
     successor to its business and/or assets as aforesaid which assumes and
     agrees to perform this Agreement by operation of law or otherwise.

     (ii) This Agreement shall inure to the benefit of, and be enforceable by,
          the Executive's personal or legal representatives, executors,
          administrators, successors, heirs, distributees, devisees and
          legatees. If the Executive should die while any amount would still be
          payable to the Executive hereunder if the Executive had continued to
          live, all such amounts, unless otherwise provided herein, shall be
          paid in accordance with the terms of this Agreement to the Executive's
          devisee, legatee or other designee or, if there is no such designee,
          to Executive's estate.

     e.   Notices. Except as otherwise expressly provided herein, any notice,
          -------   
          demand or payment required or permitted to be given or paid shall be
          deemed duly given or paid only if personally delivered or sent by
          United States mail and shall be deemed to have been given when
          personally delivered or three (3) days after having been deposited in
          the United States mail, certified mail, return receipt requested,
          properly addressed with postage prepaid. All notices or demands shall
          be effective only if given in writing. For the purpose hereof, the
          addresses of the parties hereto (until notice of a change thereof is
          given as provided in this Section 9(e)), shall be as follows:

          The Company:        Maxxim Medical, Inc.
                              10300 49/th/ Street
                              Clearwater, Florida  33762
                              Attention:  Compensation Committee

          Executive:          Joseph D. Dailey
                              6875 San Jose Loop
                              New Port Richey, Florida  34655

     f.   Severability.  In the event any provision in this Agreement shall be
          ------------                                                        
          invalid, illegal or unenforceable, such provision shall be severed
          from the rest of this Agreement and the validity, legality and
          enforceability of the remaining provisions shall not in any way be
          affected or impaired thereby.

     g.   Setoff.  The Company shall have no right of setoff or counterclaim, in
          -------                                                               
          respect of any claim, debt or obligation to it, against any payments
          to the 

                                     74 -
<PAGE>
 
          Executive, his dependents, beneficiaries or estate provided for in
          this Agreement.

     h.   Entirety. This Agreement constitutes the entire agreement of the
          --------   
          parties with respect to the subject matter hereof and supersedes any
          prior or contemporaneous agreement or understandings relating to the
          subject matter hereof.

     i.   Amendment.  This Agreement may be amended only by a written instrument
          ---------                                                             
          signed by the parties hereto, which makes specific reference to this
          Agreement.


     IN WITNESS WHEREOF, the undersigned have executed this Agreement as of the
date first set forth above.


"COMPANY"                                      "EXECUTIVE"
 
MAXXIM MEDICAL, INC.
 
By:  /s/ Donald R. DePriest                    /s/ Joseph D. Dailey
     ----------------------------------        -------------------------------
     Donald R. DePriest                        Joseph D. Dailey
     Member of Maxxim Medical
     Board of Directors -
     Compensation Committee

                                     75 -