<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-Q

(Mark One)

[ X ]       Quarterly report pursuant to Section 13 or 15(d) of the
            Securities Exchange Act of 1934

            For the quarterly period ended May 31, 1998

[   ]       Transition report pursuant to Section 13 or 15(d) of the
            Securities Exchange Act of 1934

            For the transition period from            to

Commission file number:  000-24452

                                RMS TITANIC, INC.

             (Exact name of registrant as specified in its charter)


           Florida                            59-2753162
(State or other jurisdiction of               (IRS Employer Identification No.)
incorporation or organization)

17 Battery Place, Suite 203, New York, NY     10004
(Address of principal executive offices)      (Zip Code)

Registrant's telephone number, including area code: (212) 558-6300


      Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes     No  X
                                              ---    ---

      The number of shares outstanding of the registrant's common stock on July
17, 1998 was 16,187,119.
<PAGE>   2
                                                                          PAGE
                                                                          NUMBER
                                                                          ------
                                     PART I

                              FINANCIAL INFORMATION

Item 1.     Financial Statements                                          3

Item 2.     Management's Discussion and Analysis of
            Financial Condition and Results of Operations                 8

                                     PART II

                                OTHER INFORMATION

Item 1.     Legal Proceedings                                             14

Item 2.     Changes in Securities                                         15

Item 3.     Defaults Upon Senior Securities                               15

Item 4.     Submission of Matters to a Vote of Security Holders           15

Item 5.     Other Information                                             15
                                                                           
Item 6.     Exhibits and Reports on Form 8-K                              15

Signatures                                                                16


                                       2
<PAGE>   3
                                     PART I

                              FINANCIAL INFORMATION

ITEM 1.     FINANCIAL STATEMENTS.

      The financial statements of RMS Titanic, Inc. (the "Company"), included
herein were prepared, without audit, pursuant to rules and regulations of the
Securities and Exchange Commission. Because certain information and notes
normally included in financial statements prepared in accordance with generally
accepted accounting principles were condensed or omitted pursuant to such rules
and regulations, these financial statements should be read in conjunction with
the financial statements and notes thereto included in the audited financial
statements of the Company for the year ended February 28, 1998 as included in
the Company's Form 8-K dated June 15, 1998.


                                       3
<PAGE>   4
                                                               RMS TITANIC, INC.

                                                                   BALANCE SHEET
================================================================================

<TABLE>
<CAPTION>
                                                                         MAY 31,     FEBRUARY 28,
                                                                            1998             1998
                                                                    ------------     ------------
                                                                     (UNAUDITED)
<S>                                                                 <C>              <C>         
ASSETS

Current Assets:
  Cash and cash equivalents                                         $  1,643,861     $  1,000,269
  Accounts receivable                                                  1,515,591          640,760
  Refundable withholding tax                                             176,418           45,848
                                                                    ------------     ------------
    TOTAL CURRENT ASSETS                                               3,335,870        1,686,877

Artifacts Recovered, at cost                                           7,697,710        7,700,340

Deferred Income Tax Asset, net of valuation allowance of
 $486,000 and $503,000, respectively                                          --               --

Property and Equipment, net of accumulated depreciation
 of $103,432 and $73,207, respectively                                   764,944          652,599

Other Assets                                                              91,510           38,880
                                                                    ------------     ------------
    TOTAL ASSETS                                                    $ 11,890,034     $ 10,078,696
                                                                    ============     ============

LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
  Accounts payable and accrued liabilities                          $  2,285,852     $  2,483,200
  Income taxes payable                                                   826,344          143,960
  Deferred revenue                                                            --           14,943
                                                                    ------------     ------------
    TOTAL CURRENT LIABILITIES                                          3,112,196        2,642,103
                                                                    ------------     ------------

Stockholders' Equity:
  Common stock - $.0001 par value; authorized 30,000,000 shares,
   issued and outstanding 16,187,128 shares                                1,619            1,619
  Additional paid-in capital                                          13,915,748       13,915,748
  Accumulated deficit                                                 (5,139,529)      (6,480,774)
                                                                    ------------     ------------
    STOCKHOLDERS' EQUITY                                               8,777,838        7,436,593
                                                                    ------------     ------------
    TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                      $ 11,890,034     $ 10,078,696
                                                                    ============     ============
</TABLE>

                                               See Notes to Financial Statements


                                       4
<PAGE>   5
                                                               RMS TITANIC, INC.

                                                         STATEMENT OF OPERATIONS
                                                                     (UNAUDITED)
================================================================================


<TABLE>
<CAPTION>
THREE-MONTH PERIOD ENDED MAY 31,                               1998            1997
                                                        -----------     -----------
<S>                                                     <C>             <C>       
Revenue:
  Exhibitions and related merchandise sales             $ 2,097,019     $   377,320
  Licensing fees                                            115,941              --
  Merchandise, books and other                              272,020          28,354
  Sale of coal                                               77,339              --
                                                        -----------     -----------
Total revenue                                             2,562,319         405,674
                                                        -----------     -----------
Expenses:                                               
  Cost of coal sold                                           2,630              --
  General and administrative                                387,395         345,916
  Depreciation and amortization                              30,225           2,192
                                                        -----------     -----------
Total expenses                                              420,250         348,108
                                                        -----------     -----------
                                                        
Income from operations                                    2,142,069          57,566
                                                        
Interest income                                              10,440              --
                                                        -----------     -----------
Income before provision for income taxes                  2,152,509          57,566
                                                        
Provision for income taxes                                  811,264              --
                                                        -----------     -----------
Net income                                              $ 1,341,245     $    57,566
                                                        ===========     ===========
Basic income per common share                           $       .08     $       .00
                                                        ===========     ===========
Weighted-average number of common shares outstanding     16,187,128      16,177,128
                                                        ===========     ===========
</TABLE>

                                               See Notes to Financial Statements


                                       5
<PAGE>   6
                                                               RMS TITANIC, INC.

                                                         STATEMENT OF CASH FLOWS
                                                                     (UNAUDITED)
================================================================================

<TABLE>
<CAPTION>
THREE-MONTH PERIOD ENDED MAY 31,                                                   1998            1997
                                                                            -----------     -----------
<S>                                                                         <C>             <C>        
Cash flows from operating activities:
  Net income                                                                $ 1,341,245     $    57,566
                                                                            -----------     -----------
  Adjustments to reconcile net income to net cash provided by
   operating activities:
    Depreciation and amortization                                                30,225           2,192
    Noncash financing costs                                                          --              --
    Other                                                                       (76,500)             --
    Reduction in artifacts recovered                                              2,630              --
    Changes in operating assets and liabilities, net of
     effect from acquisition:
      Increase in accounts receivable                                          (874,831)       (236,723)
      (Increase) decrease in refundable withholding tax                        (130,570)         87,500
      Increase in other assets                                                  (52,630)             --
      Decrease in notes payable, accounts payable
       and accrued liabilities                                                 (197,348)       (172,560)
      Increase in income taxes payable                                          682,384              --
      Decrease (increase) in deferred revenue                                   (14,943)        288,333
                                                                            -----------     -----------
      TOTAL ADJUSTMENTS                                                        (631,583)        (31,258)
                                                                            -----------     -----------
      NET CASH PROVIDED BY OPERATING ACTIVITIES                                 709,662          26,308

Cash flows from investing activity - purchases of property and equipment        (66,070)             --

Cash flows from financing activity - repayment of notes payable                      --         (25,772)
                                                                            -----------     -----------
Net increase in cash                                                            643,592             536

Cash and cash equivalents at beginning of period                              1,000,269         105,854
                                                                            -----------     -----------
Cash and cash equivalents at end of period                                  $ 1,643,861     $   106,390
                                                                            ===========     ===========

SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:

  Cash paid during the three months for income taxes                        $   128,880     $        --
                                                                            ===========     ===========

SUPPLEMENTAL SCHEDULE OF NONCASH INVESTING ACTIVITY:

  Noncash purchases of property and equipment                               $    76,500     $        --
                                                                            ===========     ===========
</TABLE>

                                               See Notes to Financial Statements


                                       6
<PAGE>   7
RMS TITANIC, INC.
NOTES TO FINANCIAL STATEMENTS
(UNAUDITED)


Note 1 -    The accompanying financial statements contain all adjustments
            necessary to present fairly the financial position of the Company as
            of May 31, 1998 and its results of operations and its cash flows for
            the three months ended May 31, 1998 and 1997. Results of operations 
            for the three month period ended May 31, 1998 are not necessarily 
            indicative of the results that may be expected for the year ending 
            February 28, 1999.

Note 2 -    In February 1997, the FASB issued Statement of Financial Accounting
            Standards ("SFAS") No. 128, Earnings per Share. SFAS No. 128 
            requires dual presentation of basic earnings (loss) per share 
            ("EPS") and diluted EPS on the face of all statements of earnings 
            issued after December 15, 1997 for all entities with complex 
            capital structures. Basic EPS is computed as net earnings divided 
            by the weighted-average number of common shares outstanding
            for the period. Diluted EPS reflects the potential dilution that
            could occur from common shares issuable through stock-based
            compensation including stock options, restricted stock awards,
            warrants and other convertible securities. The adoption of SFAS No.
            128 had no effect on the restatement of the net income per common
            share for the three months ended May 31, 1997. Diluted EPS is not
            presented for the three months ended May 31, 1998 and 1997 since the
            dilutive effect of potential common shares is not material.

Note 3 -    In April 1996, the Company entered into an agreement with CRE-CO
            Finanz GmbH, a German company, for an exhibition of Titanic
            artifacts in Europe from May 8, 1997 to November 8, 1997. The
            agreement, as amended, was extended through May 10, 1998 and has
            been verbally further extended through September 30, 1998. Pursuant
            to the agreement, as amended, the Company received two-thirds of the
            net profits, after recoupment of certain project expenses through
            February 28, 1998 and $2.00 per visitor until May 1, 1998, as
            defined. For the period subsequent to May 1, 1998, the Company
            receives two-thirds of net profits, after recoupment of certain
            project expenses, plus a percentage of merchandise revenues, as
            amended.

            In December 1996, the Company entered into an agreement with Florida
            International Museum, Inc. for an exhibition of Titanic 


                                       7
<PAGE>   8
RMS TITANIC, INC.
NOTES TO FINANCIAL STATEMENTS
(UNAUDITED)

            artifacts in St. Petersburg, Florida, from November 15, 1997 to May
            15, 1998 and further extended the exhibition to May 31, 1998.
            Pursuant to the agreement, the Company will receive exhibition
            revenue from attendance fees ranging from $0.34 to $3.10 per
            attendee, based upon the total number of attendees during the
            exhibition term, as defined. In addition, the Company will receive
            10% of gross revenue, as defined, from the sale of merchandise at
            the exhibition.

            In May 1997, the Company entered into an agreement with the RMS
            Foundation, Inc. for the exhibition of artifacts, expedition
            equipment, photographs and film footage from the 1996 Titanic
            expedition aboard the Queen Mary in Long Beach, California (the
            "Queen Mary") from June 1, 1997 through January 5, 1998 (the
            "Initial Term"). In January 1998, the agreement was amended and the
            exhibition was extended through February 5, 1998 and further
            extended to September 7, 1998 in April 1998 (the "Extension
            Term"). Pursuant to the Queen Mary exhibition agreement, the Company
            will receive, from the sale up to 150,000 tickets, $2.00 per ticket
            during the Initial Term and $2.50 per ticket during the Extension
            Term, and $3.00 per ticket from the sale of more than 150,000
            tickets. In addition, the Company will receive fifty (50%) percent
            of net profits, as defined, from the sale of merchandise at the
            Queen Mary exhibition, and fifty (50%) of any sponsorship revenues.

ITEM 2.     MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
            RESULTS OF OPERATIONS

         The following discussion provides information to assist in the
understanding of the Company's financial condition and results of operations,
and should be read in conjunction with the financial statements and related
notes appearing elsewhere herein.

                              RESULTS OF OPERATIONS

FOR THE QUARTER ENDED MAY 31, 1998 VERSUS THE QUARTER ENDED MAY 31, 1997
------------------------------------------------------------------------

      During the first quarter of its 1999 fiscal year (the "1999 fiscal year"),
the Company's 


                                       8
<PAGE>   9
revenues increased approximately 532%, as compared to the first quarter of its
1998 fiscal year (the "1998 fiscal year"). This increase was principally
attributable to a 456% increase in revenue from exhibitions and related
merchandise sales during the first quarter of the 1999 fiscal year as compared
to the first quarter of the 1998 fiscal year. This increase was primarily
attributable to exhibitions of the Company's Titanic artifacts having been
presented in St. Petersburg, Florida, Hamburg, Germany and Long Beach,
California throughout the first quarter of the 1999 fiscal year, while
exhibitions were presented for portions of the first quarter of the 1998 fiscal
year in Memphis, Tennessee, Hamburg, Germany and Norfolk, Virginia. Revenue from
licensing fees was $115,941 during the first quarter of the 1999 fiscal year, as
compared to zero revenue from licensing fees during the first quarter of the
1988 fiscal year. The Company's revenue from the sale of merchandise, books and
other sources increased approximately 859% during the first quarter of the 1999
fiscal year as compared to the first quarter of the 1998 fiscal year, primarily
as a result of the receipt of revenues during the 1999 quarter from a book
published in conjunction with unrelated third parties and revenues derived from
the sale of merchandise through the Company's web site
(http://wwww.titanic-online.com) and through the Company's 1-800-TITANIC
telephone number. Additionally, the Company recognized, as other revenue during
the first quarter of its 1999 fiscal year, $76,500 from the rental of exhibitry
to the Florida International Museum, Inc. The Company's revenue from the sale
of coal was $77,339 during the first quarter of the 1999 fiscal year as
compared to zero during the first quarter of the 1998 fiscal year, primarily as
a result of sales of coal made through the Company's web site and in the
merchandise shops of the Company's United States exhibitions.       

      The Company's cost of coal sold amounted to $2,630 during the first
quarter of the 1999 fiscal year as compared to zero during the first quarter of
the 1998 fiscal year, with such cost relating to the volume of sales in the
respective periods. General and administrative expenses of the Company increased
approximately 12% during the first quarter of the 1999 fiscal year as compared
to the first quarter of the 1998 fiscal year, primarily as a result of an
increase in professional fees related to protecting the Company's rights as
salvor-in-possession of the Titanic. The Company's depreciation expense
increased approximately 1,279% during the first quarter of its 1999 fiscal year
as compared to the first quarter of its 1998 fiscal year, primarily as a result
of depreciation of exhibitry and equipment used at the Hamburg, Germany
exhibition.

                         LIQUIDITY AND CAPITAL RESOURCES

      In connection with its 1994 expedition to the wreck site of the Titanic,
the Company entered into an agreement with IFREMER to charter equipment and crew
necessary to conduct research and recovery efforts. Pursuant to the terms of
such charter agreement, the Company has paid IFREMER the sum of $300,000 and was
obligated to pay an additional $700,000 in two installments of $350,000 each
payable on September 30 and December 1, 1994. The installment due to IFREMER on
September 30, 1994 was paid during the first quarter of the Company's 1996
fiscal year, payment of the final $350,000 installment was extended to October
1, 1995. During the 1996 fiscal year, the Company paid $70,000 on account of
such obligation, with the $280,000 balance thereof having been paid subsequent
to February 29, 1996. The source of such $280,000 payment was from an
unaffiliated entity with which the Company entered into an agreement for the
marketing of coal and the sale of cabins of cruise ships which accompanied 


                                       9
<PAGE>   10
the Company on its 1996 research and recovery expedition, and this payment was
made as an advance against the Company's share of profits from Titanic coal
sales and sales of such cruise ship cabins. The $280,000 advance was reduced by
approximately $127,000 from the sale of coal during the 1998, 1997 and 1996
fiscal years, resulting in an unpaid balance of $153,168 as of February 28,
1998. Such unpaid balance, which was not further reduced during the first
quarter of the 1999 fiscal year, does not bear interest. There were no profits
from sale of cruise ship cabins for the 1996 expedition.

      The Company entered into an agreement with IFREMER to charter equipment
and crew necessary to conduct a research and recovery expedition to the wreck
site of the Titanic in the Summer, 1996. Pursuant to the terms of such charter
agreement, the Company agreed to pay IFREMER 2,000,000 French francs
(approximately $400,000 U.S. Dollars) on or before June 20, 1996; 2,100,000
French francs (approximately $420,000 U.S. Dollars) on or before July 15, 1996;
and the sum of $980,000, payable as follows: (a) remittance of fifty (50%) of
the wholesale price of any products sold by the Company involving the 1996
expedition, up to a maximum of $480,000; and (b) up to a maximum of $500,000
payable from the following sources: (i) $.50 per visitor to any exhibition
organized by the Company; (ii) a lump sum of $250,000 for the Memphis
exhibition, payable prior to March 1, 1997; and (iii) one-third of the Company's
revenues received from any exhibition of artifacts organized by a third party,
as described. The agreement further provides that in the event the payments from
these sources do not amount to $980,000 within three (3) years after September
1, 1996, any remaining balance shall be paid from the Company's exhibition
revenues, as defined above. The Company has satisfied its obligations to pay
$500,000 of its exhibition revenue to IFREMER, as described above, and has not
received any income from the sale of products involving the 1996 expedition.
Accordingly, as of May 31, 1998, the unpaid balance owed to IFREMER under the
1996 charter agreement is $480,000. The Company and IFREMER have been pursuing
negotiations for the re-structuring of the Company's obligations under the 1996
charter agreement so as to provide for the payment of a percentage of revenues
in installments that correspond to the Company's future receipt of revenues from
exhibitions. All objects recovered during the 1996 expedition are the subject of
a lien granted to IFREMER until the Company pays all sums due and owing to
IFREMER for the 1996 expedition.

      The Company's capital commitments during its 1999 fiscal year also include
lease payments for principal offices in the base amount of $61,000 per annum
(which lease expires in September 1998), and compensation to its executive
officer. Additionally, the Company is planning its 1998 expedition to the
Titanic wreck site, and has entered into a preliminary agreement for the
charter of vessels from IFREMER for an expedition of approximately one (1)
month for $1,460,000, of which $200,000 has been paid to date as a downpayment.
The Company is in the final stages of negotiations of an agreement for the
license of audio-visual rights relative to the 1998 expedition to an unrelated
third party, and expects that substantially all of the costs for chartering the
IFREMER vessels and any other vessels or equipment required for the 1998
expedition will be paid by such third-party. In the event that these
negotiations are not successfully consummated or if the Company is unable to
license such rights to another third-party on terms satisfactory to the
Company, the Company intends to pay the costs of chartering vessels and
equipment for the 1998 expedition                                              


                                       10
<PAGE>   11
from available cash resources or payments made from future exhibition revenues,
or a combination of both. The Company may also reduce the length of the
expedition and correspondingly the cost of chartering vessels and equipment if
audio-visual rights relative to the 1998 are not successfully licensed on
adequate terms.

      The Company's near term operating needs will be financed principally from
the distribution of revenues to the Company under its agreements for exhibitions
in St. Petersburg, Florida; Hamburg, Germany; Boston, Massachusetts; its touring
exhibition in Japan; and at the Queen Mary in Long Beach, California. The
Company is actively negotiating for the presentation of an exhibition of its
Titanic artifacts in venues after its exhibitions in Hamburg, Germany and
Boston, Massachusetts. While management expects these negotiations to be
successfully consummated, no assurances can be given that the Company will be
successful in effectuating such arrangements on terms that are acceptable or
satisfactory to the Company. In the event that cash flows are not adequate to
satisfy the Company's future operating needs, inclusive of payment of
outstanding liabilities, additional debt and/or equity financing will be
required.

      Substantially all of the Company's cash flow derives from the Company's
operating activities. None of the Company's cash flow during the first quarter
of the 1999 fiscal year derived from financing activities and only a nominal
amount of cash flow derived from investing activities.

      Except for historical information contained herein, this Periodic report
on Form 10-Q contains forward-looking statements within the meaning of the
Private Securities Reform Act of 1995 which involve certain risks and
uncertainties including, without limitation, the Company's needs, as discussed
above, to obtain additional financing in order to achieve its objectives and
plans. The Company's actual results or outcomes may differ materially from those
anticipated. Important facts that the Company believes might cause such
differences are discussed in the cautionary statements accompanying the
forward-looking statements as well as in the risk factors discussed below.
Although the Company believes that the assumptions underlying the
forward-looking statements contained herein are reasonable, any of the
assumptions could be inaccurate, and therefore, there can be no assurance that
the forward-looking statements contained in this Report will prove to be
accurate. In light of the significant uncertainties inherent in the
forward-looking statements included herein, the inclusion of such information
should not be regarded as a representation of the Company or any other such
person that the objectives and plans of the Company will be achieved. In
addition to uncertainties of ordinary business operations and the factors
discussed in the Company's Form 8-K dated June 15, 1998, the forward-looking
statements of the Company contained in this report are also subject to the
following risks and uncertainties:
                                                                               
      In order for the Company to design, construct and embark on the Waterborne
Exhibition, additional debt and/or equity financing will be required. While
management believes that such financing will be available, no assurances can be
given that the Company will be successful in its efforts to obtain additional
financing, or that such financing will be available on a satisfactory 


                                       11
<PAGE>   12
timetable. If the Company is unable to arrange income producing exhibitions
similar to its land-based exhibitions in Memphis, St. Petersburg, Boston, Japan
and Hamburg, or funding for the planned worldwide touring exhibition is not
obtained, there could be a curtailment of the Company's long-term business
activities and material delays in the implementation of its business plans.

      Until such time as the Company, if ever, presents the exhibition of its
artifacts on the Waterborne Exhibition, the Company could experience
difficulties or delays in making arrangements with third parties for the
presentation of exhibitions at land-based venues on terms that are acceptable
and satisfactory to the Company. The Company's ability to present such
exhibitions in association with third parties will be dependent upon the
agreement of such third parties to construct, market and operate the
exhibitions, or the Company having adequate financial resources to construct
and/or operate the exhibitions. Delays or difficulties in making arrangements
for the presentation of exhibitions at land-based venues could have a materially
adverse affect upon the Company's operations.

      The Company could experience difficulties or delays in obtaining financing
for the Waterborne Exhibition, and if financing is obtained on terms acceptable
to the Company, could also experience difficulties or delays in the construction
of the Waterborne Exhibition. The Waterborne Exhibition is subject to all the
delays and uncertainties associated with construction projects generally.
Additionally, the Company has not made arrangements for the presentation of the
Waterborne Exhibition in specific ports and will need to obtain permits and
approvals from local governmental authorities. While management of the Company
believes that such arrangements will be available on terms and conditions
acceptable to the Company, and that the Company will satisfy requirements for
such permits and approvals, difficulties and delays could be encountered in
securing prospective sites and/or the requisite permits and approvals, which, in
turn, could delay or otherwise adversely impact the Company's revenue producing
activities.

      The Company has been seeking and intends to continue to seek debt
financing to fund as much of the Waterborne Exhibition as may be available on
terms satisfactory to the Company. In connection with any such debt financing
that may be obtained, no assurances of which can be given, the Company expects,
among other things, to be required to pledge its assets to a lender, to be
restricted in its ability to incur additional obligations, and/or to abide by
certain financial covenants.

      The Company's strategy for presenting exhibitions of Titanic artifacts is
dependent upon making acceptable arrangements with third parties or hiring
personnel who are experienced and possess expertise in operation and marketing
exhibitions. Management of the Company believes that acceptable arrangements
with such personnel or third-parties can be made within time frames required to
implement the Company's exhibition strategies. However, no assurance can be made
that such personnel or third-parties will be available on satisfactory terms or
when needed by the Company. Delays or difficulties in engaging personnel or
third parties for the operations and marketing of exhibitions, including without
limitation the Waterborne Exhibition, could have a materially adverse affect
upon the Company's operations.


                                       12

<PAGE>   13
      The Company's future business and operating results depend in significant
part upon the continued contributions of George Tulloch, the Company's
President. The Company does not maintain a key person life insurance policy on
Mr. Tulloch. The Company's future business and operating results also depends in
significant part upon its ability to attract and retain qualified additional
management, marketing and support personnel for its operations.

      In order to protect its salvor-in-possession status and to prevent
third-parties from salvaging the Titanic wreck and wreck site, or interfering
with the Company's rights and ability to salvage the wreck and wreck site, the
Company may have to commence judicial proceedings against third-parties. Such
proceedings could be expensive and time-consuming. Additionally, the Company, in
order to maintain its salvor-in-possession status, needs to, among other things,
maintain a reasonable presence at the wreck through periodic expeditions. In
addition to the payment of the balance due to IFREMER for the Summer of 1996
Expedition, the Company will be required to incur the costs for future
expeditions so as to maintain its salvor-in-possession status. The Company's
ability to undertake future expeditions may be dependent upon the availability
of financing from the grant of licenses to produce television programming and/or
the grant of expedition sponsorship rights. No assurances can be given that such
financing will be available on satisfactory terms.

      The amount spent by consumers on discretionary items, such as
entertainment activities and the purchase of merchandise, is dependent upon
consumers' levels of discretionary income, which may be adversely affected by
general or local economic conditions. A decrease in consumer spending on such
activities could have a material adverse effect on the Company's revenues from
exhibition activities and merchandising efforts.

      The Company's sales of coal recovered from the Titanic wreck site and
other merchandise through its web site increased significantly during the period
of the initial theatre release of the motion picture "Titanic" in December 1997
without the Company incurring any significant marketing expenses. This coal is
the only object recovered from the Titanic that the Company is offering or will
offer for sale to the general public. Through the date of this report,
approximately 100,000 units of the Company's Titanic coal have been sold since
the commencement of such sales in the fall 1996, which represents approximately
one-half of the total units of coal available for sale. The Company intends to
recover additional coal during its 1998 expedition. A substantial portion of the
remaining Titanic coal supply is different in size than that which the Company
has marketed to date, and the Company's pricing and commercial presentation of
the coal is likely to change. No assurances can be given that different price
points or different presentations of the coal will be attractive to consumers.
Additionally, in the event that the Company does not recover any additional
Titanic coal, and the existing supply of coal is exhausted in the future, the
volume of the Company's merchandise sales may be materially adversely affected
in the absence of the introduction and marketing of additional products, such as
replicas of artifacts.

      To the extent that the Company has transactions outside of the United
States, the Company could be affected by nationalizations or unstable
governments or legal systems or 


                                       13
<PAGE>   14
intergovernmental disputes. These economic and political uncertainties may
affect the Company's results of operations, especially to the extent that these
matters affect the Company's exhibition plans in Europe and Japan.

      In connection with its activities outside of the United States, the
Company is exposed to the risk of currency fluctuations between the United
States dollar and certain foreign currency. If the value of the United States
dollar increases in relation to the foreign currency, the Company's potential
revenues from exhibition and merchandising activities outside of the United
States will be adversely affected. During the first quarter of the 1999 fiscal
year, there were no significant fluctuations in the exchange rates with respect
to foreign currencies in which the Company transacts business. Although the
Company's financial arrangements with IFREMER, its exhibition organizer in
Germany and other entities have been based in whole or in part upon foreign
currencies, the Company has sought and will continue to seek to base its
financial commitments and understandings upon the United States dollar in its
material business transactions so as to minimize the adverse potential effect
of currency fluctuations.                

                                     PART II

                                OTHER INFORMATION

ITEM 1.     LEGAL PROCEEDINGS.

      The Company is a named defendant in a lawsuit commenced in the United
States District Court for the Eastern District of Virginia) on or about May 4,
1998 (Haver v. RMS Titanic, Inc., Civil Action No.: 2:98cv507). The plaintiff
therein seeks a declaratory judgment permitting him to participate in a
photographic expedition to the wreck of the Titanic known as Operation Titanic.
This action does not challenge the Company's salvor-in-possession status. On or
about May 4, 1998, the Company instituted a motion for a preliminary injunction
in the United States District Court for the Eastern District of Virginia against
Deep Ocean Expeditions, Mike McDowell, Bakers World Travel, Quark Expedition,
Ralph White, Don Walsh, Alfred S. McLaren, WildWings, and Mr. Haver, all of whom
are involved in Operation Titanic, seeking an order enjoining such parties from
conducting their proposed photographic expedition. (R.M.S. Titanic, Inc. v. The
Wrecked and Abandoned Vessel, etc. believed to be the RMS Titanic, in rem, Civil
Action No. 2:93cv902). The United States District Court for the Eastern District
of Virginia has previously held, in August 1996, that RMS Titanic, Inc. had the
right to exclude others from taking photographs of the wreck and to control
entry in to the wreck site. The Court's ruling to that effect also states that
the Company has the right to exclude others from the wreck site regardless of
whether the Company is at the wreck site while other groups attempt to visit the
site. Pursuant to stipulation, the action commenced by Mr. Haver and the
Company's motion for a preliminary injunction have been consolidated. By Order
dated June 23, 1998, the Court granted the Company's motion for a preliminary
injunction enjoining certain parties from visiting the wreck site to view and
photograph the wreck. Certain of the enjoined parties have appealed the Order to
the U.S. Court of Appeals for the Fourth Circuit.  By order entered on July 17,
1998, a motion to stay the Order pending determination of the appeal was
denied by the U.S. Court of Appeals.           


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<PAGE>   15
      There has been no material change in the status of the lawsuit commenced
in the United States District Court for the Southern District of New York on or
about December 16, 1997 (Lindsay v. The Wrecked and Abandoned Vessel RMS
Titanic, et al., in rem, and RMS Titanic, Inc. et al., No. 97Civ9248) subsequent
to the filing of the report on Form 8-K dated June 15, 1998.

ITEM 2.     CHANGES IN SECURITIES.

            None.

ITEM 3.     DEFAULT UPON SENIOR SECURITIES.

            None.

ITEM 4.     SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS.

            None.

ITEM 5.     OTHER INFORMATION.

            None.

ITEM 6.     EXHIBITS AND REPORTS ON FORM 8-K.

            (a) EXHIBITS

            10.1 Agreement between the registrant and Resource Plus and Event
Management International None dated April 24, 1998.

            10.2 Agreement between the registrant and Titanic Exhibition Japan
Inc. dated May 17, 1998.

            10.3 Agreement between the registrant and CRE-CO Finanz dated April
15, 1998.

            (b) REPORTS ON FORM 8-K

            None.                         


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<PAGE>   16
                                  SIGNATURES

      Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this Report to be signed on its behalf by the
undersigned thereunto duly authorized.

                                     RMS TITANIC, INC.
                                     (Registrant)



Dated:      July 20, 1998          By: /s/ GEORGE TULLOCH
                                       ---------------------------------------
                                           George Tulloch, Principal Executive
                                            Officer and Acting Principal
                                            Accounting Officer



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