<PAGE>   1

                                    AGREEMENT

       Agreement, dated as of July 20, 1998 (this "Agreement"), by and between
RMS Titanic, Inc. (The "Customer"), a corporation organized under the laws of
the State of Florida corporation with offices located at 17 Battery Place, Suite
203, New York, New York 10004, and Oceaneering International, Inc.
("Oceaneering"), a corporation organized under the laws of the State of
Delaware, USA, with offices located at 501 Prince George's Boulevard, Upper
Marlboro, Maryland 20774.

                                    RECITALS

       WHEREAS, the RMS Titanic sank in approximately 12,000 feet of water at a
place located approximately 400 miles south of Newfoundland ("Project Site"),
and Customer has an interest in proceeding to the Titanic Project Site for the
purpose of obtaining video documentation of the wreck, supporting completion of
a television series, including a live video feed to national television
audiences, and of performing scientific tasks; and

       WHEREAS, Oceaneering is experienced in underwater Remotely Operated
Vehicle ("ROV") operations; and

       WHEREAS, Customer wishes to engage Oceaneering to exercise Oceaneering's
best efforts to proceed to the location designated by Customer and operate
Oceaneering's Magellan 725 ROV System (the "Magellan") to obtain broadcast
quality video of the Titanic, to provide umbilical and mother ROV pass through
support to Customer Supplied Equipment as defined in Exhibit B (hereinafter
referred to as "Customer Supplied Equipment"), and to place and retrieve
non-hazardous microbiological test apparatus, and to recover objects at the
Project Site consistent with the Magellan's lifting capabilities (such as coal
or other small objects); and

       WHEREAS, the broadcast quality video cameras will be provided by others,
along with interfacing assistance; and the Customer Supplied Equipment will be
provided by others, along with interfacing assistance; and

       WHEREAS, Oceaneering has agreed to provide such services upon the terms
set forth herein.

       NOW, THEREFORE, in consideration of the foregoing, and for other good and
valuable consideration, the receipt and adequacy of which is hereby
acknowledged, the parties hereto hereby agree as follows:

1. Services. During the time period set forth on Exhibit A hereto, Oceaneering
shall provide the Magellan and appropriate crew therefor and use its best
efforts operate the Magellan, in accordance with the terms set forth herein, to
obtain broadcast quality video of the Titanic, to
<PAGE>   2

provide umbilical and mother ROV pass through support to, Customer's Supplied
Equipment, and to place and retrieve non-hazardous microbiological test
apparatus, as more specifically set forth below.

2. The Vessel

       The Customer shall provide the M/V OCEAN VOYAGER (Vessel) to support the
Customer Supplied Equipment and the operations described herein. If necessary
and with Customer's approval, Oceaneering shall make a representative available
under this Agreement to inspect the Vessel with the understanding that the
Oceaneering representative, in his reasonable opinion, can request Vessel
modifications essential to interfacing the Magellan to the Vessel. The
involvement of Oceaneering in requesting or approval of modifications to the
Vessel does not in any way lessen the Customer's complete and total
responsibility for all aspects of the Vessel. The Customer shall be responsible
for all direct and indirect costs associated with provision and operation of the
Vessel, including but without limitation to: vessel hire, fuel lube oil,
victualing, port/dock fees, garbage removal, security guards, pilotage,
anchorage, agent's fees, surveys, gas-freeing, communications, etc.

       Oceaneering acknowledges that it has received and review the "Safety
Requirements" set forth in Section 20.5 of the Agreement between Customer and
French Institute for the Research and Exploration of the Seas ("IFREMER"),
relating to the vessel "The Nadir", which shall also be at the site during the
expedition to the Titanic. Oceaneering accepts and agrees to comply with such
"Safety Requirements".

3. Pre-mobilization, Mobilization and Demobilization

       3.1 Oceaneering shall participate with others, including Nauticos LLC and
Woods Hole Oceanographic Institution, to interface the Customer Supplied
Equipment and the broadcast video equipment, respectively, to the Magellan
system. In all cases Oceaneering shall have approval authority regarding such
interfaces and the potential impact on the safe and effective operation of the
total interfaced system. Oceaneering will not be responsible for the Customer
Supplied Equipment nor warranty the working of the said equipment.

       3.2 Oceaneering shall mobilize the Magellan system and eight (8)
operating Personnel at the Port of Boston. Oceaneering shall transport Personnel
to Boston, and in general, will equip the Customer supplied Vessel with the
Magellan system, making her ready for the activities required under this
Agreement. The Customer's representative on board the vessel shall direct the
Vessel to the location of the Titanic. At the end of the operational activities
and upon return of the Vessel to Boston, Oceaneering shall offload and
demobilize the Magellan system. Oceaneering shall instruct the Crew to use best
efforts to carry out the services set forth herein promptly and within the
Magellan system's capabilities by day and by night in accordance with
<PAGE>   3

this Agreement and at such time and on schedules as the Customer may reasonably
require without any obligations of the Customer to pay to Oceaneering or its
crew any excess or overtime payments. If the Customer has reason to be
dissatisfied with the conduct of any member of the Crew, Oceaneering on
receiving particulars of the complaint shall promptly investigate the matter
and, if, in their opinion, it is necessary and practicable, make a change in the
appointment.

       3.3 Oceaneering shall advise the Customer of the expected date of arrival
of the Magellan system at Boston. The Customer will ensure the Vessel is in
Boston and available for onload of the Magellan system during the period 24 July
1998 to 29 July 1998 and shall use commercially reasonable effort to make the
Vessel available and ready for the onload of the Customer Supplied Equipment as
soon as reasonably possible. There shall be no additional charge for the
Customer Supplied Equipment for any delays following its arrival at Boston,
while standing by for on-load availability. The operation will terminate on or
about 01 September and the vessel will return to Boston and be immediately
offloaded. Should Customer extend the Magellan beyond 01 September 1998,
Customer agrees to pay a day rate in the amount of U.S. Fifteen Thousand Dollars
($15,000) per day until such time as the Magellan has departed the RMS Titanic
to return to Boston.

4. Costs. The cost for the Equipment, Consumables (estimated) and all Personnel
for the operation, to be paid by Customer to Oceaneering, is as set forth in
Exhibit C (Oceaneering's Proposal dated 05/14/98). If during the period of hire,
the Magellan is unable to dive due to a technical failure, i.e. technical
breakdown, crew illness or any other reason under the control of Oceaneering
during a total period(s) exceeding an aggregate of 48 hours, the amount paid by
Customer to Oceaneering shall be lowered, for each period totaling 24 hours
without dive for technical failure arising after the said period(s) aggregating
48 hours by $4,500. If the Magellan System does not make any dive due to
technical failure of the Magellan System, then Oceaneering shall refund to
Customers all sums paid hereunder, and shall release Customers from any further
obligations under this Agreement excluding mobilization costs.

5. Payment Terms. Customer shall remit to Oceaneering the amount of US $600,000
via wire transfer, to the account set forth on Exhibit A, pursuant to the
payment terms set forth on such Exhibit A. In addition, Customer has agreed to
an additional payment amount of $45,000, for modifications to the Magellan.
Oceaneering hereby confirms that such $45,000 has been paid on behalf of
Customer prior to execution this Agreement. Oceaneering further confirms that
there has been made on behalf of Customer the first payment due in accordance
with such Exhibit A (i.e. $120,000) prior to execution of this Agreement. Upon
completion of each milestone listed on Exhibit A, Oceaneering will submit an
invoice to Customer via facsimile (addressed to the attention of Eloise
Patterson, facsimile number 301-986-4828). Customer agrees to remit payment to
Oceaneering via wire transfer within two business days of receipt of each such
faxed invoice.
<PAGE>   4

       Oceaneering has no obligation to remain at the Project Site and may
demobilize at any time the daily rate and charges incurred or to be incurred for
requested services that have not been paid by Customer when due. Customer agrees
to return back to Boston of off-load the Magellan.

       Time is of the essence with respect to all payments to be made by
Customer. Failure of Customer to timely make any payment when due is cause for
suspension of performance by Oceaneering and/or termination of the Agreement by
Oceaneering without prejudice to any sums that may be due Oceaneering under the
Agreement.

6. Best Efforts. The undertaking of Oceaneering under this Agreement is to put
forth its best efforts to photo/video document the Wreckage, and to recover
objects at the Project Site consistent with the Magellan's lifting capabilities
(such as coal and other small objects) utilizing the Magellan System, as
interfaced with the Customer Supplied Equipment and cameras, and Personnel
herein specified and relying upon the information provided by the Customer.
Because of inherent and unforeseeable risks in seabed operations, the Customer
assumes the risk of location of the Wreckage and the success of obtaining, and
the usefulness of the photo/video documentation as information, and if the
Customer objectives are not achieved, unless as a result of the gross negligence
or willful misconduct of Oceaneering or its Crew, and except as a result of the
technical failure of the Magellan System as set forth above, Oceaneering shall
nevertheless be entitled to full mobilization and demobilization fees, the
applicable day rates for Magellan System and Crew, and all other fees and
charges due Oceaneering under this Agreement. With respect to the Customer
Supplied Equipment, Customer acknowledges that Oceaneering does not warrant nor
assume any liability for the operational performance or interfacing of the
Customer Supplied Equipment with the Magellan.

7. Liability and Insurance For purposes of this Clause 7, the term "Oceaneering,
ET AL" is used as a reference individually and collectively for Oceaneering and
its parent, subsidiary and affiliated companies, Oceaneering's subcontractors
and all other parties with whom Oceaneering has a contractual relationship
(excluding Customer) and its and all of their officers, directors, employees,
agents, assigns, representatives, contractors, and subcontractors, and the
subrogees of said parties. Similarly, the term "Customer, ET AL" is used as a
reference individually and collectively for Customer and its parent, subsidiary
and affiliated companies and its and their officers, directors, employees,
agents, assigns representatives, contractors, and subcontractors, and the
subrogees of said parties.

A. Customer's Liability and Indemnity. Other than as a result of the gross
negligence or willful misconduct of Oceaneering, Customer shall be solely
responsible for and shall protect, defend, indemnify and hold harmless
Oceaneering, et al and any vessel owned, operated or controlled by Oceaneering,
et al from and against any and all claims, demands, judgments, awards, debts,
damages, losses, causes of action, suits, expenses and costs arising out of or
in connection with illness, injury to or death of employees of Customer, et al
or damage to or loss
<PAGE>   5

of any property or equipment owned, operated or controlled by Customer, et al
and in any way sustained or alleged to have been sustained in connection with or
by reason of Oceaneering, et al's performance of the work.

B. Oceaneering's Liability and Indemnity. Other than as a result of the gross
negligence or willful misconduct of Customer, Oceaneering shall be solely
responsible for and shall protect, defend, indemnify and hold harmless Customer,
et al and any vessel owned, operated or controlled by Customer, et al from and
against any and all claims, demands, judgments awards, debts, damages, losses,
causes of action, suits, expenses and costs arising out of or in connection with
illness, injury to or death of employees of Oceaneering, et al or damage to or
loss of any property or equipment owned, operated or controlled by Oceaneering,
et al and in any way sustained or alleged to have been sustained in connection
with or by reason of Customer, et al's performance of the work.

C. Other than as a result of the gross negligence or willful misconduct of
Customer, Oceaneering shall be responsible for and defend, indemnify and hold
harmless Customer, et al and any vessel owned, operated or controlled by
Customer, et al for any loss or damage arising from pollution emanating from the
equipment or vessels owned, operated or controlled by Oceaneering, et al and
irrespective of the negligence or other fault of Customer et al. Other than as a
result of the gross negligence or willful misconduct of Oceaneering, Customer
shall be responsible for and defend, indemnify and hold harmless Oceaneering, et
al and any vessel owned, operated or controlled by Oceaneering, et al for any
loss or damage from pollution emanating from equipment or vessels owned,
operated or controlled by Customer, et al or from pollution, contamination or
seepage which may result from fire, pipeline, well or reservoir damage or any
other manner as a result of the performance of the work by Oceaneering.

D. Insurance. Irrespective of the negligence (sole, concurrent, or gross) or
other fault of an indemnified party, the parties shall cause to be carried
insurance sufficient to cover their respective indemnification obligation under
this Agreement.

E. Loss or Damage occasioned during operations authorize by Customer which are
extra hazardous or otherwise out of the normal course of operation will be for
the account of the Customer, whose responsibility shall be to reimburse for
actual cost of items lost or damages. Customer's authorization to conduct
Hazardous Operations will be obtained prior to commencement of operations and
approval will be evidenced by signature on the daily log by the Customer's
representative designated in writing by the Customer pursuant to Exhibit A.

F. In the event of a claim that the salvage of items or artifacts form the
Project Site is in violation of applicable law or rights claimed by others,
Customer agrees to defend, indemnify and hold harmless Oceaneering, its
subsidiaries, and their officers, directors, employees, agents and
representatives and the Vessel harmless from and against all losses, damages or
judgments incurred by the indemnified parties, including the costs and expenses
of defending any claim,
<PAGE>   6

including reasonable attorney's fees. Customer at its option shall have the
right at its sole expense to defend any such claim, provided it furnishes
Oceaneering with security deemed adequate for any possible judgment.

8. Hazardous Operations. For the purposes of this clause, Hazardous Operations
shall mean operating the Customer Supplied Equipment from the Magellan. In the
event the Magellan is lost or damaged due to the operation from the Magellan of
the Customer Supplied Equipment, Customer shall be solely responsible for the
repair and/or replacement of the Magellan and defend, indemnify and hold
harmless Oceaneering for any claims arising out the loss or damage to Customer
Supplied Equipment. Customer's insurance coverage shall be primary with respect
to a loss as a result of Hazardous Operations.

9. Limitation of Liability. In no event shall a party be liable to the other
party hereto for any consequential or indirect loss or damage whether arising
under contract, admiralty, tort or otherwise by operation of law and whether or
not foreseeable at the date hereof howsoever caused.

10. The ROV Operations

       10.1 The Customer's representatives on board the Vessel shall supervise
the voyage from the Port of Boston to the Titanic site (the Operation Area).

       10.2 Oceaneering shall prepare the equipment for the operation, shall
work with the other equipment providers to complete interfacing the Customer
Supplied Equipment and cameras, and shall operate the Magellan system in the
Operation Area. Continuously during periods where the weather and sea states
permit, and during periods where the necessary emissions from the global
positioning satellite are received, Oceaneering shall conduct operations in
accordance with an agreed Titanic detailed operations plan, set forth in Annex
A, as nearly as navigational equipment, ship handling, weather, and sea states
permit. Annex A will be prepared and coordinated prior to commencement of ROV
operations. Oceaneering, within the applicable operational constraints, will use
its best endeavors to maximize ROV operations and effectiveness.

       10.3 In case of break-down affecting durably technical or operational
capabilities of the Magellan System before or after the delivery to Customer,
Oceaneering shall use best efforts to restore the same as quickly as possible.

11. Government Approvals. Customer shall bear the responsibility for obtaining
any necessary government approvals including without limitation permission of
the government having jurisdiction under international law over the Operations
Site.
<PAGE>   7

12. Force Majeure. Neither party shall be liable for failure to perform or delay
in performance when such failure or delay shall be occasioned by external causes
beyond the control of the parties, including among such causes (but without in
any way limiting the generality of the foregoing), acts of God, weather and sea
conditions; insurrection, riot, fire, terrorism, piracy, strikes or other labor
difficulty, embargoes, and war and other armed conflict. Nothing herein shall
excuse Customer from making payments that are due Oceaneering under this
Agreement.

13. Governing Law. The validity, construction and performance of this Agreement
and the rights and obligations of the parties arising in connection with this
Agreement, shall in all respects be governed by the laws of Texas, excluding the
conflicts of law rules, and by the applicable maritime law of the United States
of America.

14. Jurisdiction. The Parties agree to the exclusive jurisdiction of courts of
competent jurisdiction situated in Harris County, Texas for the resolution of
any controversy or claim arising out of or in relation to this Agreement or
breach thereof.

15. Entire Agreement. The terms and conditions of this Agreement, read with
Exhibit A, B and C constitute the entire agreement between the parties and any
amendment thereof shall have no force or effect unless recorded in writing and
signed by or on behalf of both parties. This Agreement may be signed in separate
counterparts, each of which shall be deemed an original.

       In Witness Whereof, the parties hereto have executed this Agreement as of
the date first written above.

RMS TITANIC, INC.


/s/ George Tullech by AHC
--------------------------------------------
By:  George Tullech by Allan H. Carlin, its counsel
Its: President

OCEANEERING INTERNATIONAL, INC.

/s/ Donald R. Dean
--------------------------------------------
By:  Donald R. Dean
Its: Vice President, Cable Operations
<PAGE>   8

                            EXHIBIT A - PAYMENT TERMS

The following are the Payment Terms as referred to in Article 5.

1.    20%   Due upon contract signing. Also at contract signing, the costs for
            any agreed modifications to the MAGELLAN 725 for the Titanic
            Expedition. (Both amounts previously paid; Oceaneering acknowledges
            receipt thereof.)

2.    20%   Upon completion of system mobilization onto Customer-supplied vessel
            (Assumed that payment will be due on July 29, 1998).

3.    20%   Two (2) weeks after departure from mobilization port (Assumed
            payment will be due on August 13, 1998).

4.    20%   Upon departure from site (Assumed payment will be due on September
            2, 1998.)

5.    20%   Upon completion of demobilization from the vessel at the
            demobilization port (Assumed payment will be due on September 8,
            1998.)
<PAGE>   9

                                    EXHIBIT B

                                Additional Terms

A.     All items supplied to Customer and authorized in advance in writing. e.g.
       video tapes, film, etc., will be charged at cost plus fifteen percent
       (15%) (authorizations to be on a daily basis.)

B.     If the Operations extend beyond forty five (45) days, the operations crew
       will be rotated approximately every 45 days. The cost of the rotation and
       transportation of personnel will be to Customer's account.

C.     Except for initial mobilization and demobilization, all customs, entrance
       fees, duty, carnet, dockage, etc., incurred during the period of the
       charter will be charged to the Customer's account at cost plus fifteen
       percent (15%).

D.     Extra services, materials, fabricating ship modifications, additional
       equipment installation, crew and equipment ordered and approved in
       writing by Customer and Oceaneering will be charged to the Customer at
       cost plus fifteen percent (15%).

E.     Customer shall appoint its own customs broker/shipping agent for any
       equipment, parts or artifacts owned by Customer.

F.     Customer's designated representative: Allan H. Carlin

G.     Customer Supplied Equipment

o      T-Rex MiniROV. This is a miniROV being built specifically for this
       project to allow penetration into the TITANIC hull to obtain video of
       areas which cannot be reached by the Magellan, or which would be deemed
       unsafe for Magellan. The vehicle has been designed to work with Magellan
       as a "mother" or support platform and T-Rex is considered sacrificial to
       protect and insure recovery of Magellan. Customer representatives and
       Oceaneering personnel have had ongoing discussions of interface
       requirements, weights, and deployment options. Final evaluations of
       integration and operation issues will be made jointly during the
       mobilization period. The vehicle specifications and requirements are as
       follows:

       Vehicle in-air weight  300 lbs.
       Vehicle in-water weight  Neutral
       Vehicle Dimensions       32" x 26" x 19"
       Tether in-air weight   100 lbs. 
       Tether in-water weight  30 lbs.
<PAGE>   10

       Tether length           300 feet.

       Power and Signal
       120 VAC@ approx 20 amps (single phase)
       one bidirectional RS-422 channel@ up to 38.4 Kbaud one coax for 
       connection to one of the Magellan video uplink channels

o      Remora MiniROV. This is a MiniROV which has been built for other similar
       applications, and which is being upgraded with a Woods Hole supplied
       camera system to serve as a backup for either the T-Rex system or for use
       on one of the other support platforms being utilized for this project in
       a similar manner. This assures a backup vehicle capability through the
       live broadcast period. In regards to its use with Magellan support, a
       joint evaluation will be made and emergency backup plans generated during
       the mobilization period.
<PAGE>   11

                                    EXHIBIT C

                            [OCEANEERING LETTERHEAD]

TELEFAX

                                             Number of Pages: (Includes cover) 3
REF:      DRD-099/514
DATE:     14 May 1998

TO:       TITANIC
ATTN:     George Tulloch
FAX NO:   212-482-1912

FROM:     Donald R. Dean
SUBJECT:  MAGELLAN 725 System

As per our conversations over this week, OCEANEERING thanks you for the
opportunity to provide a quotation for our MAGELLAN 725 system to support the
TITANIC operation which will take place in July/August 1998. Our proposal
consists of the following:

o      Mobilizing the MAGELLAN 725 and crew to Boston
o      Loading and unloading the MAGELLAN 725 onto customer supplied vessel.
o      The MAGELLAN 725 and crew for 45 days total.
o      Demobilization of the MAGELLAN 725 and crew

TOTAL PROJECT COST                                                  $600,000 USD

The total project cost is based on the MAGELLAN 725 system as is without any
changes to the basic system and personnel necessary to operate the system for 24
hours a day throughout the complete project. Any changes required to the system
to meet customer requirements will be performed at cost plus.

Mobilization / Demobilization

MAGELLAN 725 System

The cost provided will include the following items:

o      System preparation for the operation including a complete operational
       check-out.
o      System packing for shipment
o      Round trip shipping to Boston.
o      Round trip personnel transportation to Boston.
<PAGE>   12

OPERATIONS

The cost is based on the following schedule:

o      Mobilization on board the vessel July 22 through 27
o      Transit to site
o      Operations on site through September 1
o      Return transit to Boston
o      System offload

The MAGELLAN system is presently available. The cost of ship modifications,
welding, cranage etc required to install and remove the Magellan 725 from
customer supplied vessel will be provided by the customer at no cost to
OCEANEERING. If additional time is required or the schedule extends beyond
the stated times, then the extra days will be charged out at the following
Day Rates:

<TABLE>
<CAPTION>
<S>                                <C>        
Operations:                        $15,000 USD
Standby:                           $12,500 USD
</TABLE>

TERMS AND CONDITIONS

1.     This offer is made subject to the availability of equipment and personnel
       at time of award, and to a mutually acceptable Form of Contract.

2.     Rates quoted are exclusive of video tapes, photographic material and any
       yet to be identified "job-specific" consumable which will be re-charged
       at documented cost plus 10%.

3.     Rates quoted are exclusive of all foreign income taxes (Corporate and
       Personal), value added taxes (VAT), visa costs, Customs, import and agent
       fees, local licenses/fees, and all other "special" charges of a similar
       nature. All such costs incurred by Oceaneering will be invoiced to
       Customer at our cost plus fifteen percent (15%). This invoice is payable
       in full to Oceaneering in United States Dollars and is to be deposited
       directly into our designated bank in the United States.

4.     Client/Company shall provide the following services at no cost to
       Oceaneering: quayside, offshore cranage and transportation,
       sea-fastening, welding, testing and subsequent removal of the ROV system
       onboard Company Vessel, suitable stable electrical power for proposed ROV
       system and associated equipment, accommodation, victualing and reasonable
       business communications for Oceaneering' s personnel.

5.     Client will provide for all work permits and visas, and will pay for all
       taxes and duties according to the law, rules, and regulations of the
       authorities concerned.

6.     Oceaneering would reserve the right at any time to assign our
       sub-contract, if we are the successful bidder, to any other Company
       within the Oceaneering group of companies.
<PAGE>   13

7.     Oceaneering would reserve the right to be reimbursed at documented cost
       plus 15% for the provision of any reporting that may ultimately be
       required.

8.     This offer is valid for thirty (30) days from the date of submission and
       subject to revalidation thereafter.

We look forward to working with you on the TITANIC Project.

Sincerely,


/s/Donald R Dean

Donald R. Dean
Vice President, Cable Operations