<PAGE>
                                                                    EXHIBIT 10.6

                  ADVISORY AGREEMENT WITH CHAIRMAN OF THE BOARD

      This Agreement is entered into between HORNBECK-LEEVAC Marine Operators,
Inc., (the "Company"), a wholly owned subsidiary of HORNBECK-LEEVAC Marine
Services, Inc., which is also included in the definition of Company, as used
herein, and Bernie W. Stewart (the "Advisor") upon the following terms and
conditions:

      Preamble: The parties acknowledge and agree that in no way does this
agreement negate, supercede, detract from, reduce or limit the inherent
responsibilities, obligations, or fiduciary duties associated with the role
Bernie W. Stewart is also performing as a member of the Board of Directors of
Company or as Chairman of the Board.

      1. Services. Advisor is also serving, at the direction of the Board of
Directors and consistent with Company's bylaw provisions governing such
position, as the Chairman of the Board of Directors, subject to reelection
annually at the meeting of the Board of Directors held in conjunction with the
annual meeting of shareholders of Company. In addition to such service as
Chairman of the Board of Directors, Advisor agrees to provide management
consulting services to Company, including the following:

            (a) Advisor will advise Company's executive officers and other
      existing management regarding the operation of Company's business, make
      recommendations relating to Company's operations, administrative
      functions, systems and procedures and otherwise foster and promote the
      positive attributes of the existing company in all respects;

            (b) Advisor will advise Company's Chief Executive Officer, and such
      other members of management as the Chief Executive Officer may direct,
      regarding Company's finances, strategic planning, new-vessel building
      program, mergers and acquisitions, public disclosures, financial community
      relations, public and private equity and debt transactions or similar
      matters; and

            (c) Advisor will provide such other advisory and/or management
      services as the Board of Directors or Chief Executive Officer may request
      from time to time.

      2. Term. The term of this Agreement shall have two phases totalling 12
months (subject to extension):

            (a) Full time. Advisor's services hereunder shall be for an initial
      three month term beginning February 27, 2002, and ending May 31, 2002 (the
      "Full Time Term"). During the Full Time Term, Advisor shall devote his
      full time employment efforts to the advisory duties hereunder; provided,
      however, that Company acknowledges that Advisor has other investment
      interests for which he does not have any management or employment role
      that require a portion of his business time and effort; and provided
      further that Advisor shall accept no other employment during the Full Time
      Term.
<PAGE>
            (b) Part time. At the end of the Full Time Term, Advisor shall
      continue as a part-time Advisor for nine months (the "Initial Part Time
      Term," and together with the Full Time Term, the "Initial Term") devoting
      such time and effort to the business of Company as is reasonably required
      to perform his duties hereunder, and/or may be reasonably requested by
      Company. At the end of the Initial Term, this Agreement may be extended by
      agreement of the parties. During the part-time phase, whether the Initial
      Part Time Term or any extension thereof, Advisor may accept other than
      full time employment with another business or company; provided that,
      during the Initial Term of this Agreement and any extension thereof,
      Advisor shall not perform, consult with or be employed by a company that
      competes with Company or its subsidiaries in any line of business in which
      Company or any such subsidiary is engaged during the term of this
      Agreement without the prior written approval of Company.

            (c) Meaning. For purposes of determining "full time employment
      efforts," that phrase shall mean at least 40 hours per week, exclusive of
      travel time and time expended in his capacity as a director or carrying
      out his duties as Chairman, and in the Full Time Term shall mean such
      additional hours as may be required to effectively carry out Advisor's
      responsibilities under this Agreement. For purposes of determining any
      percentage of "business time" under Section 3(b) below, the percentage
      shall be calculated by dividing the number of hours of business effort in
      the applicable calendar quarter on behalf of Company, exclusive of travel
      time and time expended as a director or Chairman, by the product obtained
      by multiplying the number of calendar weeks in such calendar quarter by
      40. The partial calendar quarter from the end of the Full Time Term until
      June 30, 2002 shall be added to the calendar quarter ended September 30,
      2002 for purposes of evaluating the first such evaluative period.

      3. Compensation and Benefits.

            (a) During the Full Time Term, Company shall pay Advisor a fee in
      the gross amount of $20,000, per month payable in arrears on the last
      calendar day of each month of the Full Time Term; provided that the first
      such month shall run from the effective date of this Agreement through
      March 31, 2002.

            (b) After the Full Time Term, Company shall pay Advisor a monthly
      fee equal to 1/12 of $100,000 (rounded to $8,335 per month), payable in
      arrears on the last calendar day of each month during the part-time phase
      of this Agreement; provided that should the demands on Advisor's time
      significantly exceed 25% of his business time, when considered on a
      quarterly basis, Company and Advisor will in good faith discuss any
      equitable adjustment to Advisor's cash compensation for such month or
      longer period as applicable.

            (c) Company shall reimburse Advisor for all reasonable and necessary
      expenses incurred by him in the performance of his duties hereunder, upon
      presentation of reasonable written evidence of the incurring or paying of
      such expenses. Such reimbursement shall be made in accordance with the
      Company's usual policy regarding reimbursement of business expenses by its
      employees.


                                       2
<PAGE>
            (d) During the Initial Term of this Agreement, Advisor shall be
      entitled in his capacity as Advisor, in addition to any option grants he
      receives as a member of the Board of Directors, to be granted at the same
      time as and in an amount equal to the amount of options to purchase common
      stock of Company that then constitute the standard grant to the outside
      directors of the Company under the HORNBECK-LEEVAC Marine Services, Inc.
      Incentive Compensation Plan (the "Plan"), subject to the other terms and
      conditions of the Plan.

            (e) Recognising Advisor's previously expressed intent to purchase
      additional shares of Company's common stock since joining the Board in
      November 2001, in addition to the options described above, Advisor, for
      his personal account and without a view to distribution, shall have the
      option for 30 days from the effective date hereof to purchase that number
      of shares of common stock of Company set forth next to his signature on
      the signature page of this Agreement at a price of $2.65 per share. Such
      purchase shall be subject to execution and delivery by Advisor of
      Company's standard form Subscription Agreement and Investor Suitability
      Questionaire. This option must be exercised during the initial 30 days of
      the term of this Agreement, by written notice to the Company of its
      exercise and by tender of the purchase price for the shares to be
      purchased. For each share which Advisor purchases under this provision,
      the Company will provide additional matching options in accordance with
      the following conditions:

                  (i) The option price for each share of stock shall be $2.65
            per share;

                  (ii) These options shall be exercised in accordance with, and
            subject to the other terms and conditions of the Plan; and

                  (iii) The maximum number of shares of common stock of Company
            to be issued pursuant to the exercise of these matching options
            shall be determined by dividing the purchase price of the shares
            purchased pursuant to the first sentence of this Section 3(e) by
            $2.65 and rounding up any fractional share; provided that the
            numerator in such calculation may not in any event exceed $100,000
            (the maximum number of shares that could be covered by such options
            being 37,736).

      4. Communications. Advisor shall, in such capacity, coordinate with the
Chief Executive Officer and, from time to time, report directly to the Board of
Directors.

      5. Termination.

            (a) Company shall have the right to terminate this Agreement at any
      time for any reason by providing notice thereof to Advisor. If this
      Agreement is terminated because Advisor (1) breaches the terms of this
      Agreement; (2) fails to provide the services required hereunder in a
      reasonable and workmanlike manner; (3) is convicted of a felony or other
      crime involving moral turpitude; (4) dies; (5) commits any act of fraud or
      bad faith; and/or (6) becomes totally disabled and unable to provide the
      services described hereunder as certified by a qualified physician
      (acceptable to Advisor and Company), Advisor shall be entitled to be paid
      the fees described herein, through the date


                                       3
<PAGE>
      of termination, and neither Company nor Advisor shall have any further
      obligation thereafter. If during the Initial Term, Company shall terminate
      this Agreement for any other reason, Advisor shall, upon such termination,
      be entitled to be paid the balance of the fees described herein in a lump
      sum.

            (b) Advisor shall have the right to terminate this Agreement if (1)
      Company breaches the terms of this Agreement; (2) Company fails to pay the
      compensation and/or reimbursement of expenses described herein; (3)
      Company is declared bankrupt, or initiates bankruptcy or insolvency
      proceedings. If Advisor terminates this Agreement for any of the reasons
      described above during the Initial Term hereof, Advisor shall be entitled
      to be paid the full consulting fee for the balance of the Initial Term. If
      Advisor terminates this Agreement for any reason set forth above
      thereafter, Advisor shall be entitled to his consulting fee for the month
      in which such termination occurs, and neither Advisor nor Company shall
      have any further right nor obligation thereafter. If Advisor terminates
      for any other reason than the reasons set forth above, he shall give
      Company 30 days advance written notice thereof and shall only be entitled
      to his consulting fee through the last date of service provided under this
      Agreement, and neither Advisor nor Company shall have any further right
      nor obligation under this Agreement thereafter.

      6. Confidential Information.

            (a) Confidential Information shall mean and include any and all
      information or material proprietary to the Company, or designated as
      confidential by it, and not generally known by persons who are not
      employees of Company, which Advisor develops or of which Advisor obtains
      knowledge or access through, or as a result of, Advisor's engagement
      hereunder (including information and materials conceived, originating,
      discovered, or developed, in whole or in part, by Advisor at the request
      or for the benefit of Company, pursuant to this Agreement). "Confidential
      Information" includes, but is not limited to, the following types of
      information, whether written, verbal or recorded by electronic, magnetic
      or other methods and whether or not expressly identified as confidential
      by Company (1) financial information about the Company, its revenues,
      expenses, profits and prospects; (2) specific information about the
      Company's customers, including prices, terms and conditions of specific
      orders or contracts; (3) information about the Company's personnel,
      including background, expertise and experience, compensation, and
      abilities; (4) confidential or proprietary information about the Company's
      products, services, equipment and operations; (5) information concerning
      the strategic plans, new vessel building programs and acquisition plans of
      the Company; (6) other material non-public information.

            (b) Company agrees to provide Advisor with access to, and use of,
      Confidential Information during the term of this Agreement for the purpose
      of allowing Advisor to perform its services hereunder. Advisor
      acknowledges that it would not be able to perform its duties under this
      Agreement effectively without access to and use of such Confidential
      Information.

            (c) Advisor acknowledges that the Confidential Information, and any
      document, file, or record, including electronic or magnetic records, which
      contain or


                                       4
<PAGE>
      constitute Confidential Information belonging to Company. Advisor shall
      properly deliver such materials and all copies thereof to Company on the
      date this Agreement terminates or at any other time upon request of
      Company, other than any copies to which he has been entitled as a member
      of the Board of Directors.

Without modifying in any way his duties and obligations as a member and Chairman
of the Board of Directors, during and after the term of this Agreement, Advisor
will not disclose or use, directly or indirectly, for his own benefit or for the
benefit of any person or entity, except Company, any Confidential Information.
Advisor acknowledges that, because the Company reports under the Securities
Exchange Act of 1934, disclosure of material non-public information could result
in liability under applicable securities laws.

      7. Non-Competition; Non-Solicitation. Because of the sensitive nature of
Advisor's position, and his access to the Company's Confidential Information,
including the Company's marketing, budget and sales forecasts, and business
plan, Advisor agrees that he shall not be employed by, nor consult with, nor
enter into any other contractual arrangement which requires him to perform
personal services of any kind, either directly or indirectly (including, without
limitation, through the ownership of more than a 5% in any entity), in any
corporation or other business entity or activity that competes with the Company
or any of its subsidiaries in any line of business in which the Company or its
subsidiaries is engaged during the term of this Agreement. During the term of
this Agreement and for a period of two years thereafter, Advisor shall not:

            (a) directly or indirectly recruit, solicit, induce or influence any
      then current employee (or person who was an employee of Company or any of
      its subsidiaries at any time within ninety (90) days prior to the date of
      such potentially interfering activity), customer, supplier or sales agent
      of Company or any of its subsidiaries to discontinue or reduce the extent
      of such employment, supplier, customer or agency relationship with Company
      or any of its subisdiaries; or

            (b) directly or indirectly employ, seek to employ, or cause any
      competitor of Company or any of its subsidiaries to employ or seek to
      employ, as a sales representative, contractor, Advisor or employee, any
      person who is, or at any time within ninety (90) days prior to the date of
      such potentially interfering activity was, an employee, sales
      representative, contractor, Advisor or agent of Company or any of its
      subsidiaries.

      8. Authority. Advisor understands and agrees that Advisor has no power to
bind the Company or any of its subsidiaries, except to the extent, if any, such
authority is hereafter granted to Advisor by the Board in writing. Advisor shall
not bind, or attempt to bind, or contract for, or on behalf of, the Company or
any of its subsidiaries, except to the extent that Advisor is specifically
authorized to do so by vote, resolution or consent of the Board of Directors of
the Company.

      9. Independent Parties. This Agreement does not create, nor shall it be
construed to create any joint venture or partnership between the parties.
Advisor is and shall remain an independent contractor and not an employee of the
Company. Advisor further acknowledges and agrees that (i) he will not be
eligible for or entitled to participate in any employee benefit plans,


                                       5
<PAGE>
arrangements, distributions, insurance or other similar benefits that may be
provided by the Company to its employees; (ii) he will not be treated as an
employee for purposes of any federal or state law regarding any income tax
withholding or for purposes of contributions required by any unemployment,
insurance or compensatory program; and (iii) he will be solely responsible for,
and will indemnify the Company from any liability for, payment of any taxes or
assessments imposed on him on account of the payment of compensation to, or the
performance of consulting services by him pursuant to this Agreement.

      10. Miscellaneous. The headings in this Agreement are for convenience
only, they form no part of this Agreement and shall not affect its
interpretation. The express terms hereof control and supersede any course of
performance and/or usage of the trade inconsistent with any of the terms hereof.

      11. Notices. Any notice given hereunder by any party to the other shall be
deemed to have been given upon (i) delivery, if hand delivered, (ii) three days
after the mailing, if mailed by registered or certified mail, return receipt
requested, postage prepaid, or (iii) on the next business day after facsimile
transmission, addressed to such address as any party hereunder may designate for
notice purposes. Notices shall be sent to:

             For Advisor:    Bernie W. Stewart
                             2607 Countryside Circle
                             Spicewood, Texas 78669
                             Facsimile: 830/693-6540

             For Company:    HORNBECK-LEEVAC Marine Operators, Inc.
                             414 North Causeway Boulevard
                             Mandeville, Louisiana 70448
                             Facsimile : 985/727-2006

                             Attention: President and Chief Executive Officer

            For the Company: R. Clyde Parker, Jr.
                             Winstead Sechrest & Minick P.C.
                             600 Town Center One
                             1450 Lake Robbins Drive
                             The Woodlands, Texas  77380
                             Facsimile: 281/681-5901

      12. Severability. In case any term, phrase, clause, paragraph, section,
covenant or agreement contained in this Agreement shall be held to be invalid or
unenforceable, the same shall be deemed and it is hereby agreed that same is
meant to be severable, and such invalidity or unenforceability shall not defeat
or impair the remaining provisions hereof.

      13. Entire Agreement, Amendments and Waivers. This Agreement constitutes
the entire agreement of the parties with respect to the Services to be rendered
by Advisor to the Company. It expressly supersedes all prior and contemporaneous
understandings and commitments, whether written or oral, between Advisor and the
Company. No variations, modifications, change or extensions of this Agreement or
any of the terms hereof shall be


                                       6
<PAGE>
binding upon any party hereto unless set forth in a document duly executed by
such party or an authorized officer or other duly authorized agent of such
party. This Agreement shall be construed in accordance with and governed by the
laws of the State of Louisiana; provided that should the Company relocate its
headquarters to the state of Texas, from and after the date of such relocation
this Agreement shall be governed by the laws of Texas. The failure of either
party to insist in any one or more instances upon the performance of any of the
terms or conditions of this Agreement shall not be construed as a waiver or
relinquishment of any right granted hereunder or of the future performance of
such term, covenant, or condition and the obligations of either party with
respect thereto shall continue in full force and effect.

      14. Binding Effect and Assignability. The provisions of this Agreement
shall be binding upon and inure to the benefit of the parties hereto and their
respective successors and permitted assigns. The rights and interests of the
Company hereunder shall be freely assignable by them. This Agreement is for
Advisor's personal services and may not be assigned by him.

      15. Third Party Beneficiaries. Any Agreement to pay any amount and any
assumption of any liability herein contained, express or implied, shall only be
for the benefit of the undersigned parties and their successors and permitted
assigns, it being the intention of the undersigned that no one (other than the
Company) shall be deemed to be a third party beneficiary of this Agreement.

      16. Effective Date. This Agreement shall become effective the 27th day of
February, 2002.

                     HORNBECK-LEEVAC MARINE OPERATORS, INC.


                     By: /s/ TODD M. HORNBECK
                        ------------------------------------------------------
                              Todd M. Hornbeck
                              President and Chief Executive Officer

                        /s/ BERNIE W. STEWART
                        ------------------------------------------------------
                        Bernie W. Stewart, Advisor

Number of Shares of Common Stock
of Company to be Purchased

      37,736
-----------------


                                       7