<PAGE>   1

                                  EXHIBIT 10.6


                         EXECUTIVE EMPLOYMENT AGREEMENT

         THIS EMPLOYMENT AGREEMENT (this "Agreement") dated effective as of May
1, 1999, (the "Start Date") is between Petsec Energy Inc., a corporation formed
under the laws of Nevada (the "Company"), and James E. Slatten III, an
individual resident of the State of Louisiana (the "Executive").

                              W I T N E S S E T H:

         WHEREAS, Company and Executive desire to enter into a written agreement
providing for the continued employment of Executive by Company upon the terms
and subject to the conditions set forth herein;

         WHEREAS, Executive will report to the Chief Executive Officer (the
"CEO") of the Company or his designee, and he shall have the right, under the
terms and conditions specified in this Agreement, to recommend to Company's
Board of Directors (the "Company Board") any determination made under the
Agreement;

         NOW, THEREFORE, in consideration of the premises, the mutual covenants
and agreements herein contained, and other good and valuable consideration, the
receipt, adequacy and sufficiency of which hereby are acknowledged, the parties
agree as follows:

         1.       EMPLOYMENT. Subject to the provisions of this Agreement,
                  Company hereby agrees to employ Executive and Executive hereby
                  agrees to accept such employment with, and to provide to
                  Company the services described in Section 3 below.

         2.       TERM. Executive shall be employed by Company for a period
                  commencing on the Start Date and, except as otherwise provided
                  herein, ending on the third anniversary of the Start Date. The
                  term of this Agreement shall be extended annually without the
                  necessity of any affirmative action by any party for an
                  additional one year term (to make an aggregate three year
                  commitment on the part of Company and Executive) on May 1 of
                  each year that Executive is employed by Company, unless prior
                  to May 1 of each such year Company terminates this Agreement
                  by sending written notice to Executive (in which case, the
                  provisions of Section 8.1 shall apply). The period during
                  which Company employs Executive shall hereinafter be referred
                  to as the "Term of Employment."

         3.       NATURE OF SERVICE. During the Term of Employment, Executive
                  agrees to perform such services as are consistent with his
                  position as Vice-President--Land and Legal, Secretary and
                  Director or as from time to time shall be assigned to him by
                  the CEO


                                       -1-
<PAGE>   2

                  or his designee. Executive shall devote so much of his time,
                  attention and skills to the business of Company as is
                  necessary to properly perform his duties and responsibilities.
                  Executive shall not, during the Term of Employment, be engaged
                  in, or represent any party other than Company in connection
                  with the provision of any services whatsoever without the
                  prior written consent of the CEO or his designee. Executive
                  shall perform his duties under this Agreement diligently with
                  fidelity and loyalty and in a competent manner consistent with
                  the level of his responsibilities.

         4.       COMPENSATION.

                  4.1.     BASE SALARY. During the Term of Employment, Company
                           shall pay to Executive a base salary payable in equal
                           periodic installments in accordance with the
                           established payroll practices of Company. Initially,
                           the Executive's base salary shall be $157,600 per
                           year. Executive's base salary shall be reviewed
                           annually on or before July 1 by the Remuneration
                           Committee (the "Committee") of the Petsec Energy
                           Ltd's (the "Parent") Board of Directors (the " Parent
                           Board"). (If the Parent no longer has beneficial
                           ownership of at least a majority of the outstanding
                           voting stock of the Company, then the
                           responsibilities of the Committee shall be performed
                           by the Company Board.) The Committee may recommend
                           increases to the Executive's base salary, which if
                           accepted by the Company Board, shall become effective
                           in the manner determined by the Company Board. ("Base
                           Salary," as used hereinafter, shall mean at any
                           particular time the periodic payment last paid to
                           Executive pursuant to this Section 4.1, multiplied by
                           the appropriate factor to arrive at an annualized
                           number.)

                  4.2.     CASH INCENTIVE COMPENSATION. On or before April 1 of
                           each year, the Committee shall recommend to the
                           Company Board the amount, if any, that shall be
                           awarded to all senior executives (including
                           Executive) of the Company who are eligible to
                           participate in the cash incentive compensation
                           program. The Committee shall recommend to the Company
                           Board the cash award, if any, to be paid to Executive
                           up to a maximum of 100% of Executive's Base Salary.
                           The amounts available for distribution under the
                           Company's cash incentive compensation program shall
                           take into account Company financial and operating
                           results. The incentive compensation amount awarded to
                           Executive shall be weighted evenly between Company
                           performance and individual performance to reward both
                           cooperative management efforts to attain Company
                           objectives and individual achievement. Fifty percent
                           of the cash incentive compensation available to
                           Executive shall be based on Company performance and
                           50% shall be based on the individual performance of
                           Executive. Company performance shall be measured
                           subjectively by the Committee with input from the
                           CEO. The Committee shall evaluate individual
                           performance of the Executive with input


                                      -2-
<PAGE>   3


                           from the CEO. The cash incentive compensation, if
                           paid, will be paid to Executive in a lump sum in
                           April of each year.

                  4.3.     TAXES. All taxes and governmentally required
                           withholdings shall be deducted in conformity with
                           applicable laws.

         5.       STOCK OPTIONS.

                  5.1.     GRANT OF OPTION. As additional compensation to
                           Executive, Parent has issued to Executive as of the
                           Start Date options to purchase 300,000 ordinary
                           shares of Parent, and from time to time the Parent
                           may issue additional options (collectively, the
                           "Options"). The Options are governed by the Petsec
                           Energy Ltd Employee Option Plan, as may be amended
                           from time to time and one or more times (the "Option
                           Plan"). Executive agrees that the issue and exercise
                           of the Options are governed by the rules of the Plan,
                           and by the additional terms and conditions set by the
                           Committee and described in the Option Certificates
                           delivered to Executive with respect to the Options.
                           Copies of the Option Certificates are attached hereto
                           as Exhibit A. Award of additional Options to
                           Executive shall be considered annually on or before
                           May 1 of each year by the Committee, and a
                           recommendation with respect thereto made to the
                           Parent Board.

                  5.2.     TAX CONSEQUENCES. Executive shall be responsible for
                           the payment of all income taxes, alternative minimum
                           taxes or other taxes or governmental charges that may
                           accrue on account of the issuance or exercise of the
                           Options or the acquisition or sale by Executive of
                           Parent stock acquired with respect to the Options.
                           Executive should consult his own tax advisor
                           regarding the specific tax consequences of
                           participation in the Plan, including the application
                           of any federal, state and local tax laws and the
                           effect of other state and local laws, including
                           community property laws. Executive agrees to defend
                           and indemnify Company and Parent for any claims made
                           against Company, Parent or Executive by any taxing
                           authority for income or alternative minimum taxes
                           that may be owed by Executive on account of the
                           issuance, exercise or sale of the options or the
                           acquisition or sale by Executive of any Parent stock
                           acquired with respect to any Options.

         6.       BENEFITS. Executive shall receive the employee benefits as may
                  be provided by Company from time to time to employees of
                  Company holding executive offices and positions, all as
                  approved by the Company Board. These benefits shall include:

                  6.1.     VACATION TIME. Executive will be eligible for twenty
                           working days of vacation time per year together with
                           all public holidays recognized by Company. The use
                           and accrual of such vacation time shall be governed
                           by the


                                      -3-
<PAGE>   4

                           Company's vacation policy, as the same may be amended
                           from time to time and one or more times.

                  6.2.     DEATH BENEFIT. The Company shall maintain life
                           insurance for the benefit of the beneficiary(ies) of
                           Executive that shall pay to Executive's
                           beneficiary(ies) a death benefit in an amount equal
                           to at least three times the lowest Base Salary in
                           effect during the twelve months preceding Executive's
                           death.

                  6.3.     DISABILITY BENEFIT. The Company shall maintain
                           disability insurance for the benefit of Executive
                           that is commensurate with the disability policy in
                           place as of the Start Date.

                  6.4.     SEVERANCE BENEFIT. Executive shall receive the
                           severance benefit provided for in Section 8.4.2.

         7.       REIMBURSEMENT OF BUSINESS EXPENSES. Company shall reimburse
                  Executive for all reasonable and proper travel and
                  out-of-pocket expenses (including but not limited to industry
                  association fees and industry entertainment expenses) incurred
                  by him for the purpose of and in connection with the
                  performance of his duties pursuant to this Agreement during
                  the Term of Employment, all in accordance with the policies
                  relating to the allowable amount of such expenses and the
                  provision of itemized reports and receipts with respect
                  thereto that may from time to time be adopted by Company.

         8.       TERMINATION.

                  8.1.     TERMINATION BY COMPANY.

                           8.1.1.   FOR CAUSE. Executive's employment under this
                                    Agreement may be terminated for cause at any
                                    time, effective immediately, after formal
                                    action by the CEO acting at the direction of
                                    the Company Board following a meeting of the
                                    Company Board, duly called for the purpose
                                    of considering the termination of Executive
                                    for "cause," as defined herein. As used in
                                    this Section 8.1.1, "cause" shall mean that
                                    the Company Board in good faith either
                                    determines or has reasonable suspicions that
                                    one or more of the following has occurred:
                                    (1) Executive has engaged in gross
                                    negligence or willful misconduct in the
                                    performance of his duties; (2) Executive has
                                    willfully refused without proper legal
                                    reason to perform his duties and
                                    responsibilities; (3) Executive has
                                    materially breached any material provision
                                    of any agreement between Executive and
                                    Company; (4) Executive has materially
                                    breached any material corporate policy of
                                    the Company; or (5) Executive has engaged in
                                    illegal conduct, or has violated any


                                      -4-
<PAGE>   5

                                    statute, rule or regulation under federal
                                    securities laws, or has engaged in any act
                                    of serious dishonesty which adversely
                                    affects, or reasonably could in the future
                                    adversely affect, Executive's value,
                                    reliability or performance in a material
                                    manner or the business reputation of the
                                    Company. In the event that Company acts to
                                    terminate Executive for cause in accordance
                                    with this Section 8.1.1, Executive shall be
                                    entitled to receive only the compensation
                                    provided for in Section 8.4.1 and any rights
                                    provided under the Option Plan with respect
                                    to the Options.

                           8.1.2.   WITHOUT CAUSE. Company may terminate
                                    Executive's employment under this Agreement
                                    at any time, in which case Executive will be
                                    entitled to receive only the compensation
                                    provided for in Section 8.4.1, the severance
                                    benefit provided for in Section 8.4.2 and
                                    any rights provided under the Option Plan
                                    with respect to the Options.

                  8.2.     TERMINATION BY EXECUTIVE.

                           8.2.1.   FOR CAUSE. Executive may terminate his
                                    employment under this Agreement if Company
                                    does any one or more of the following: (1)
                                    Company makes a material reduction in
                                    Executive's job duties, authority or
                                    responsibilities with the Company from that
                                    exercised by him immediately prior to such
                                    change (however, a reduction in the size of
                                    Company and/or in the number of employees
                                    working under the supervision of Executive,
                                    shall not constitute a material reduction
                                    hereunder); (2) a reduction of more than 10%
                                    in any twelve month period from the Base
                                    Salary paid by the Company to Executive
                                    during the twelve months immediately
                                    preceding such Base Salary reduction; (3) a
                                    change in location of Executive's primary
                                    place of employment by the Company by more
                                    than 30 miles from the location where he was
                                    primarily employed prior to such change; (4)
                                    a material reduction in the value of or
                                    change in the scope or terms of the benefits
                                    to which the Executive, taken as a whole,
                                    was entitled prior to such reduction or
                                    change; or (5) Company otherwise fails to
                                    comply with any material provision of this
                                    Agreement. Before terminating his employment
                                    for cause under this Section 8.2.1,
                                    Executive shall first provide the Company
                                    with written notice specifying in detail the
                                    reasons why Executive believes he has the
                                    right to terminate his employment for cause
                                    and allowing Company ten (10) days to cure
                                    any such default. If Executive provides such
                                    a notice to Company and then fails to
                                    terminate his employment for cause within
                                    five days after the expiration of the (10)
                                    day cure period (because Company has cured
                                    such default, because Executive decides


                                      -5-
<PAGE>   6

                                    he no longer wants to terminate this
                                    Agreement or for any other reason),
                                    Executive shall be deemed to have waived his
                                    right to terminate this Agreement for the
                                    reasons specified in the notice. If
                                    Executive does terminate his employment for
                                    cause under this Section 8.2.1, Executive
                                    will be entitled to receive only the
                                    compensation provided for in Section 8.4.1,
                                    the severance benefit provided for in
                                    Section 8.4.2 and any rights provided under
                                    the Option Plan with respect to the Options.

                           8.2.2.   WITHOUT CAUSE. Executive may terminate his
                                    employment under this Agreement without
                                    cause by giving Company at least sixty (60)
                                    days' prior written notice of the effective
                                    date of his termination of employment. In
                                    the event that Executive terminates his
                                    employment under this Section 8.2.2,
                                    Executive shall be entitled to receive only
                                    the compensation provided for in Section
                                    8.4.1 and any rights provided under the
                                    Option Plan with respect to the Options.
                                    Provided that Executive complies with this
                                    Section, Executive shall not be liable for
                                    any damages to Company on account of such
                                    termination.

                  8.3.     TERMINATION UPON DEATH OR DISABILITY.

                           8.3.1.   If Executive becomes permanently disabled so
                                    as to become eligible for permanent
                                    disability insurance benefits under a long
                                    term disability policy maintained by the
                                    Company for the benefit of Executive, at
                                    such time as Executive is determined to be
                                    permanently disabled, Executive's employment
                                    shall be deemed terminated. In the event
                                    that Executive's employment is terminated
                                    under this Section 8.3.1, Executive shall be
                                    entitled to receive only the compensation
                                    provided for in Section 8.4.1, the benefit
                                    provided under Section 6.3, and any rights
                                    provided under the Option Plan with respect
                                    to the Options.

                           8.3.2.   If Executive dies, his employment shall be
                                    deemed to be terminated as of the date of
                                    his death. In such a case, Executive's heirs
                                    or successors shall be entitled to receive
                                    only the benefit provided for in Section
                                    6.2, the compensation provided for in
                                    Section 8.4.1 and any rights provided under
                                    the Option Plan with respect to the Options.

                  8.4.     DAMAGES TO EXECUTIVE IN THE EVENT OF TERMINATION.

                           8.4.1.   COMPENSATION IN THE EVENT OF TERMINATION.
                                    Upon the termination of Executive's
                                    employment with Company, Company shall pay
                                    to Executive (or Executive's heirs or
                                    successors) all unpaid Base Salary


                                      -6-
<PAGE>   7

                                    for the period through the date of
                                    termination and reimbursement for allowable
                                    expenses incurred by Executive through such
                                    date. Company shall not be obligated to pay
                                    Executive any Base Salary for periods beyond
                                    the date of termination.

                           8.4.2.   SEVERANCE BENEFIT. Upon the termination of
                                    Executive's employment with Company under
                                    circumstances set forth in Sections 8.1.2 or
                                    8.2.1, Company shall pay to Executive in a
                                    lump sum an amount equal to the product of
                                    (a) the number of months (prorated for a
                                    partial month) remaining on the term of this
                                    Agreement (which number shall be greater
                                    than or equal to 24 and less than or equal
                                    to 36) times (b) the quotient of the Base
                                    Salary divided by 12. This lump sum payment
                                    shall be made within five days of the
                                    termination of Executive's employment. The
                                    severance benefit provided for under this
                                    Section 8.4.2 shall be reduced dollar for
                                    dollar by any amount to which Executive is
                                    or may become entitled pursuant to the
                                    Petsec Energy Inc. Change in Control Bonus
                                    and Severance Plan or any similar plan.

                           8.4.3.   OPTIONS. Upon Executive's termination of
                                    employment for any reason, Executive's
                                    rights and Company's obligations with
                                    respect to the Options shall be governed by
                                    the Employee Option Plan.

         9.       CERTAIN COVENANTS OF EXECUTIVE.

                  9.1.     Executive agrees that during the Term of Employment,
                           he will not (a) directly or indirectly engage or
                           invest in any business other than Company's business
                           without the prior approval of the CEO or his designee
                           or (b) otherwise act as a director, officer,
                           employee, agent, owner, partner or consultant to any
                           such business. It is understood and agreed that
                           Executive shall not be deemed to be in default with
                           respect to this Section 9.1 as a result of any
                           investment he may make in not more than five percent
                           of the outstanding shares or other units of any
                           security registered pursuant to Section 12 of the
                           Securities Exchange Act of 1934, as amended (the
                           "1934 Act") or in not more than fifty percent of the
                           outstanding shares or other units of any security not
                           registered pursuant to Section 12 of the 1934 Act.

                  9.2.     Executive will not during his employment or
                           thereafter (except in the course of his duties as
                           authorized by Company or as required by law) use or
                           disclose to any person any confidential information
                           or trade secrets belonging or relating to Company or
                           any person or entity with whom Executive have come
                           into contact as a result of his employment. Upon
                           termination of this Agreement, Executive promptly
                           shall return all originals and copies of such


                                      -7-
<PAGE>   8

                           papers, lists, documents and records that are in his
                           possession, custody or control.

                  9.3.     If the provisions contained in this Section 9 are
                           more restrictive than permitted by applicable law,
                           the parties agree that the covenants contained in
                           this Section 9 shall be enforceable and in force to
                           the extent permitted by law.

         10.      AMENDMENT. This Agreement may not be modified or amended
                  except by a written instrument executed by or on behalf of
                  both Company and Executive.

         11.      WAIVERS. The observance of any term of this Agreement may be
                  waived (either generally or in a particular instance and
                  either retroactively or prospectively) by the party entitled
                  to enforce such term, but except as otherwise expressly
                  provided herein, such waiver shall be effective only if in a
                  writing signed by the party or parties against which such
                  waiver is to be asserted. Except as otherwise expressly
                  provided herein, no delay or omission on the part of any party
                  in exercising any right, power or privilege hereunder shall
                  operate as a waiver thereof, nor shall any waiver on the part
                  of any party of any right, power or privilege hereunder
                  operate as a waiver of any other right, power or privilege
                  hereunder, nor shall any single or partial exercise of any
                  right, power or privilege hereunder preclude any other or
                  further exercise thereof or the exercise of any other right,
                  power or privilege hereunder. All remedies, either under this
                  Agreement or by law or otherwise afforded to any party, shall
                  be cumulative and not alternative.

         12.      ENTIRE AGREEMENT. This Agreement and the documents expressly
                  referred to herein constitute the entire agreement between the
                  parties with respect to the matters covered hereby, and any
                  other prior or contemporaneous oral or written understandings
                  or agreements with respect to the matters covered hereby are
                  expressly superseded by this Agreement. There are no unwritten
                  or oral agreements between the parties.

         13.      SEVERABILITY. If any provision of this Agreement, or the
                  application of such provision to any person or circumstance,
                  shall be declared judicially to be invalid, unenforceable or
                  void, such decision will not have the effect of invalidating
                  or voiding the remainder of this Agreement or affect the
                  application of such provision to other persons or
                  circumstances, and the parties agree that the part or parts of
                  this Agreement so held to be invalid, unenforceable or void
                  will be deemed to have been stricken here from and the
                  remainder of this Agreement will have the same force and
                  effect as if such part or parts had never been included
                  herein. Any such finding of invalidity or unenforceability
                  shall not prevent the enforcement of such provision in any
                  other jurisdiction to the maximum extent permitted by
                  applicable law.


                                      -8-
<PAGE>   9
         14.      NOTICES. Unless otherwise expressly provided herein, all
                  notices, requests, demands, consents, waivers, instructions,
                  approvals and other communications hereunder shall be in
                  writing and shall be deemed to have been duly given if
                  personally delivered to or mailed, certified mail, return
                  receipt requested, first-class postage paid, or delivered by
                  messenger service with receipt acknowledged, addressed as
                  follows:


                                            If to Company:

                                            Level 13, 1 Alfred Street
                                            Sydney, NSW 1225, Australia
                                            Attn: Terrence N. Fern

                                            If to Executive:

                                            James E. Slatten III
                                            10 Courtyard Circle
                                            Lafayette, LA  70508

                  or to such other address or to such other individuals as any
                  party shall have last designated by notice to the other party.
                  All notices and other communications given to any party in
                  accordance with the provisions of this Agreement shall be
                  deemed to have been given when delivered to the intended
                  recipient thereof in accordance with the provisions of this
                  Section 14.

         15.      GOVERNING LAW; FORUM; CONSENT TO JURISDICTION. This Agreement
                  shall be construed in accordance with, and the rights of the
                  parties governed by, the laws of the State of Louisiana
                  without regard to the principles of conflict of laws. The
                  parties agree that all disputes in any way relating to,
                  arising under, connected with, or incident to this Agreement,
                  and over which the federal courts have subject matter
                  jurisdiction, shall be litigated exclusively in the United
                  States District Court for the Western District of Louisiana,
                  Lafayette Division, and, if necessary, the corresponding
                  appellate courts. The parties further agree that all disputes
                  in any way relating to, arising under, connected with, or
                  incident to this Agreement, and over which the federal courts
                  do not have subject matter jurisdiction, shall be litigated,
                  if at all, exclusively in the Courts of the State of
                  Louisiana, in Lafayette Parish, and, if necessary, the
                  corresponding appellate courts. The parties expressly submit
                  themselves to the personal jurisdiction of the State of
                  Louisiana.

         16.      SUCCESSORS AND ASSIGNS. Except as otherwise expressly provided
                  herein, Executive agrees on behalf of himself and his
                  executors and administrators, heirs, legatees, distributees
                  and any other person or persons claiming any benefits under
                  him by virtue of this Agreement, that this Agreement and the
                  rights, interests and benefits



                                      -9-
<PAGE>   10

                  hereunder shall not be assigned, transferred, pledged or
                  hypothecated in any way by Executive or any executor,
                  administrator, heir, legatee, distributee or person claiming
                  under Executive by virtue of this Agreement and shall not be
                  subject to execution, attachment or similar process. Except as
                  otherwise expressly provided herein, Company agrees that this
                  Agreement shall not be assigned or transferred to any other
                  party; provided, however, a merger or consolidation of Company
                  into a successor entity other than Company shall not be
                  considered a transfer or assignment. Any attempt at
                  assignment, transfer, pledge or hypothecation or other
                  disposition of this Agreement or of such rights, interest and
                  benefits contrary to the foregoing provisions, or the levy of
                  any attachment or similar process thereupon, shall be null and
                  void and without effect.

         17.      THIRD PARTY BENEFICIARIES. This Agreement does not create, and
                  shall not be construed as creating, any rights enforceable by
                  any person or entity not a party to this Agreement (except as
                  otherwise provided in Section 8.3.2 or in Section 16).

         18.      HEADINGS. The section headings in this Agreement are for
                  convenience of reference only and shall not be deemed to alter
                  or affect the meaning or interpretation of any provisions
                  hereof.

         19.      ARBITRATION. Any controversy or claim arising out of or
                  relating to this contract, or the breach thereof, shall be
                  settled by arbitration in Lafayette, Louisiana, in accordance
                  with the applicable Rules of the American Arbitration
                  Association using three (3) impartial arbitrators and judgment
                  upon the award rendered by the arbitrators may be entered in
                  any court having jurisdiction thereof. Each party shall select
                  one arbitrator and the selected arbitrator shall designate a
                  third arbitrator. If unable to agree to a third arbitrator,
                  the presiding judge in the United States District Court for
                  the Western District of Louisiana shall designate the third
                  arbitrator. This Section 19 shall take precedence over the
                  provisions of Section 15.

         20.      COUNTERPARTS. This Agreement may be executed in two or more
                  counterparts, each of which shall be deemed to be an original
                  and all of which together shall be deemed to be one and the
                  same instrument.

         21.      CURRENCY REFERENCES. All references to "$" are to United
                  States currency unless otherwise specifically stated in the
                  Agreement.



                                      -10-
<PAGE>   11

         IN WITNESS WHEREOF, this Agreement has been duly executed and delivered
to be effective as of the date first above written.

WITNESSES:                                   COMPANY:

                                             PETSEC ENERGY INC.
Printed Name:
             ------------------------


Printed Name:                                By: /s/ Terrence N. Fern
             ------------------------           -------------------------------
                                                  Terrence N. Fern
                                                  Chief Executive Officer



                                             EXECUTIVE:
Printed Name:
             ------------------------

                                             /s/ James E. Slatten III
                                             ----------------------------------
Printed Name:                                James E. Slatten III
             ------------------------



                                      -11-