<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 August 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
October 19, 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                  12
                                                            
                                     PART II                
                                                            
                                OTHER INFORMATION           
                                                            
Item 1.  Legal Proceedings                                              19
                                                            
Item 2.  Changes in Securities                                          20
                                                            
Item 3.  Defaults Upon Senior Securities                                20
                                                            
Item 4.  Submission of Matters to a Vote of Security Holders            20
                                                            
Item 5.  Other Information                                              20
                                                            
Item 6.  Exhibits and Reports on Form 8-K                               20
                                                            
Signatures                                                              21


                                       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>
                                                                        AUGUST 31,          FEBRUARY 28,
                                                                             1998                  1998
                                                                       (UNAUDITED)
ASSETS
-------------------------------------------------------------------------------------------------------
Current Assets:
<S>                                                                    <C>                 <C>
  Cash and cash equivalents                                            $  1,763,678        $  1,000,269
  Accounts receivable                                                       957,219             640,760
  Refundable withholding tax                                                240,918              45,848
-------------------------------------------------------------------------------------------------------
      TOTAL CURRENT ASSETS                                                2,961,815           1,686,877

Artifacts Recovered, at cost                                              9,200,340           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 $158,657 and $73,207, respectively                                    1,309,719             652,599

Other Assets                                                                 40,880              38,880
-------------------------------------------------------------------------------------------------------
      TOTAL ASSETS                                                     $ 13,512,754        $ 10,078,696
=======================================================================================================
LIABILITIES AND STOCKHOLDERS' EQUITY

Current Liabilities:
  Accounts payable and accrued liabilities                             $  2,220,590        $  2,483,200
  Income taxes payable                                                      859,850             143,960
  Deferred revenue                                                          416,667              14,943
-------------------------------------------------------------------------------------------------------
      TOTAL CURRENT LIABILITIES                                           3,497,107           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                                                    (3,901,720)         (6,480,774)
-------------------------------------------------------------------------------------------------------
      STOCKHOLDERS' EQUITY                                               10,015,647           7,436,593
-------------------------------------------------------------------------------------------------------
      TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                       $ 13,512,754        $ 10,078,696
=======================================================================================================
</TABLE>


                                               See Notes to Financial Statements


                                       4
<PAGE>   5
                                                               RMS TITANIC, INC.




                                                             STATEMENT OF INCOME
                                                                     (UNAUDITED)
================================================================================

<TABLE>
<CAPTION>
                                                               THREE-MONTH        THREE-MONTH       SIX-MONTH        SIX-MONTH
                                                              PERIOD ENDED       PERIOD ENDED    PERIOD ENDED     PERIOD ENDED
                                                                 AUGUST 31,         AUGUST 31,      AUGUST 31,       AUGUST 31,
                                                                      1998               1997            1998             1997
-------------------------------------------------------------------------------------------------------------------------------
Revenue:
<S>                                                          <C>                <C>               <C>               <C>
  Exhibitions and related merchandise sales                  $  1,073,511       $  1,060,884      $  3,170,530      $  1,438,204
  Licensing fees                                                3,365,650              5,308         3,481,591            5,308
  Merchandise and other                                           157,511             15,638           429,531           43,992
  Sale of coal                                                     46,127             12,986           123,466           12,986
-------------------------------------------------------------------------------------------------------------------------------
Total revenue                                                   4,642,799          1,094,816         7,205,118        1,500,490
-------------------------------------------------------------------------------------------------------------------------------
Expenses:
  Cost of coal sold                                                 8,853              1,304            11,483             1,304
  General and administrative                                      477,384            313,605           864,779          659,521
  Depreciation and amortization                                    55,225              2,030            85,450            4,222
  Expedition costs attributable to licensing fees               1,845,000                  -         1,845,000                -
  Impairment loss on exhibitry equipment                          150,000                  -           150,000                -
-------------------------------------------------------------------------------------------------------------------------------
Total expenses                                                  2,536,462            316,939         2,956,712          665,047
-------------------------------------------------------------------------------------------------------------------------------
Income before other income                                      2,106,337            777,877         4,248,406          835,443

Other income                                                        5,000             37,600             5,000           37,600
-------------------------------------------------------------------------------------------------------------------------------
Income from operations                                          2,111,337            815,477         4,253,406          873,043

Interest income                                                    15,771              -                26,211            -
-------------------------------------------------------------------------------------------------------------------------------
Income before provision for income taxes                        2,127,108            815,477         4,279,617          873,043

Provision for income taxes                                        889,299              -             1,700,563            -
-------------------------------------------------------------------------------------------------------------------------------
Net income                                                   $  1,237,809      $     815,477      $  2,579,054     $     873,043
================================================================================================================================
Basic income per common share                            $           0.08      $        0.05      $       0.16     $       0.05
================================================================================================================================
Weighted-average number of shares outstanding                  16,187,128         16,179,519        16,187,128        16,178,324
================================================================================================================================
</TABLE>


                                               See Notes to Financial Statements


                                       5
<PAGE>   6
                                                               RMS TITANIC, INC.

                                                         STATEMENT OF CASH FLOWS
                                                                     (UNAUDITED)
================================================================================
<TABLE>
<CAPTION>
                                                                              SIX-MONTH           SIX-MONTH
                                                                           PERIOD ENDED        PERIOD ENDED
                                                                              AUGUST 31,         AUGUST 31,
                                                                                   1998              1997
----------------------------------------------------------------------------------------------------------

Cash flows from operating activities:
<S>                                                                        <C>                 <C>
  Net income                                                                  $ 2,579,054        $ 873,043
----------------------------------------------------------------------------------------------------------
  Adjustments to reconcile net income to net cash provided by operating
   activities:
    Depreciation and amortization                                                  85,450            4,222
    Impairment loss on exhibitry equipment                                        150,000             --
    Other                                                                         (76,500)            --
    Noncash exhibition revenue                                                   (333,333)            --
    Changes in operating assets and liabilities:
      Increase in accounts receivable                                            (316,459)        (373,510)
      (Increase) decrease in refundable withholding tax                          (195,070)          87,500
      (Increase) decrease in other assets                                          (2,000)           4,800
      Decrease in accounts payable and accrued liabilities                       (262,610)        (197,775)
      Increase in income taxes payable                                            715,890             --
      Decrease in deferred revenue                                                (14,943)        (301,668)
----------------------------------------------------------------------------------------------------------
        TOTAL ADJUSTMENTS                                                        (249,575)        (776,431)
----------------------------------------------------------------------------------------------------------
        NET CASH PROVIDED BY OPERATING ACTIVITIES                               2,329,479           96,612
----------------------------------------------------------------------------------------------------------
Cash flows from investing activities:
  Artifact recovery costs                                                      (1,500,000)            --
  Purchases of property and equipment                                             (66,070)          (2,302)
----------------------------------------------------------------------------------------------------------
        CASH USED IN INVESTING ACTIVITIES                                      (1,566,070)          (2,302)
----------------------------------------------------------------------------------------------------------
Cash flows used in financing activity - repayment of notes payable                   --            (64,430)
----------------------------------------------------------------------------------------------------------
Net increase in cash and cash equivalents                                         763,409           29,880

Cash and cash equivalents at beginning of period                                1,000,269          105,854
----------------------------------------------------------------------------------------------------------
Cash and cash equivalents at end of period                                    $ 1,763,678        $ 135,734
==========================================================================================================
SUPPLEMENTAL DISCLOSURE OF CASH FLOW INFORMATION:

  Cash paid during the period for income taxes                                $   964,000        $    --
=========================================================================================================
SUPPLEMENTAL SCHEDULE OF NONCASH INVESTING ACTIVITY:

  Noncash purchases of property and equipment                                 $   826,500        $    --
=========================================================================================================
</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 August 31, 1998 and its results of operations
                  and its cash flows for the three and six months ended August
                  31, 1998 and 1997. Results of operations for the three and six
                  month periods ended August 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, Statement of Financial Accounting Standards
                  ("SFAS") No. 128, Earnings per Share was issued.  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 and six months ended August 31, 1997. Diluted
                  EPS is not presented for the three and six months ended
                  August 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, extended the Exhibition 
                  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 from May 1, 1998, the Company
                  receives two-thirds of net profits, after recoupment of
                  certain project expenses, plus a percentage of merchandise
                  revenues as defined.
        
                  In December 1996, the Company entered into an agreement with
                  Florida International Museum, Inc. for an exhibition of
                  Titanic 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


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

                  agreement, the Company received 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 received 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, was further extended through September 7,
                  1998, and has been extended on a month-to-month basis
                  thereafter (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.

                  The Company has entered into an agreement with Resource Plus
                  and Event Management International ("EMI"), a division of the
                  World Trade Center Boston, for the presentation of more than
                  250 artifacts in Boston, Massachusetts from July 1, 1998
                  through on or about November 15, 1998. Pursuant to the
                  exhibition agreement, EMI is responsible for payment of all
                  costs and expenses related to the design, construction,
                  operation and marketing of the exhibition. Pursuant to the
                  exhibition agreement, the Company will receive two-thirds
                  (2/3) and EMI will receive one-third (1/3) of the net profits,
                  after recoupment of certain project expenses, as defined. The
                  agreement further provided that the ownership interest of
                  certain exhibitry and equipment aggregating $750,000 was
                  transferred to the Company as of August 31, 1998, in
                  satisfaction of the minimum exhibition fee due to the 
                  Company. 

                                       8
<PAGE>   9
RMS TITANIC, INC.
NOTES TO FINANCIAL STATEMENTS
(UNAUDITED)

                  Included in deferred revenue in the accompanying balance
                  sheet at August 31, 1998 is $416,667, which represents the 
                  unearned portion of the minimum fees.

                  The Company has entered into an agreement with Titanic
                  Exhibition Japan Inc. ("TEJI") for the exhibition of
                  approximately 200 Titanic artifacts in six (6) venues in Japan
                  commencing on or about July 20, 1998 and ending on or about
                  July 1, 1999. Pursuant to the exhibition agreement, TEJI has
                  agreed to pay the conservator of the Company's artifacts
                  $321,000 for the conservation and restoration of artifacts to
                  be displayed in the exhibition. The exhibition agreement
                  further provides that TEJI will pay to the Company the greater
                  of $3.00 per attendee or 50% of the profits, as defined.

                  The Company entered into an agreement with IFREMER for the
                  charter of equipment and crews to conduct the Company's fifth
                  expedition to the Titanic wreck site in August 1998 (the
                  "Summer of 1998 Expedition"). Pursuant to the agreement, the
                  Company agreed to pay IFREMER the sum of $1,460,000 in
                  addition to a paid deposit of $200,000. Such sum included 
                  $480,000 that was due and owing to IFREMER for the Company's
                  1996 expedition to the Titanic. The Company agreed to pay 
                  $1,260,000 of such charter costs prior to the commencement 
                  of the Summer of 1998 Expedition, with the $200,000 balance 
                  to be paid upon the conclusion of the expedition. Pursuant 
                  to the agreement between the Company and its audio-visual 
                  licensee for the Summer of 1998 Expedition, the Company's 
                  audio-visual licensee paid $1,180,000 of such charter costs 
                  on behalf of the Company. In July 1998, the Company paid the 
                  sum of $80,000 to IFREMER pursuant to the charter agreement. 
                  The balance of $200,000 payable by the Company to IFREMER 
                  under the charter agreement remains due and owing as of 
                  August 31, 1998. All objects recovered during the Summer of 
                  1998 Expedition are the subject of a lien granted to IFREMER
                  until the Company pays all sums due and owing to IFREMER for
                  the Summer of 1998 Expedition.


                                       9
<PAGE>   10
RMS TITANIC, INC.
NOTES TO FINANCIAL STATEMENTS
(UNAUDITED)

                  The Company and an unrelated television production company
                  entered into an agreement whereby the Company granted certain
                  rights to the production company for the production and
                  exploitation of audio and visual recordings with respect to
                  the Summer of 1998 Expedition (the "Productions"). In
                  consideration of the granting of such rights, the television
                  production company, among other things, agreed to pay the
                  cost for chartering equipment and crew necessary for the
                  Summer of 1998 Expedition, including, but not limited to,
                  $1,150,000 of the costs for chartering IFREMER's equipment
                  and crew and an aggregate of $2,195,000 of additional
                  equipment and crew from other unrelated third-parties, on
                  behalf of the Company. Of this $2,195,000, the Company has
                  charged to operations $1,845,000, representing costs
                  attributable to the licensing agreements. The Company has
                  retained the rights for commercial exploitation of recordings
                  made at the Titanic wreck site in a print format and
                  electronic media format, and certain royalty and other rights
                  with respect to the marketing and sale of home videos based
                  upon the Summer of 1998 Expedition as defined.

Note 4 -          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


                                       10
<PAGE>   11
RMS TITANIC, INC.
NOTES TO FINANCIAL STATEMENTS
(UNAUDITED)

                  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.

                  The Company is a named defendant in a 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), as disclosed in the Company's
                  report on Form 8-K dated June 15, 1998. The plaintiff alleges
                  therein, inter alia, that he rendered certain services to the
                  Company in connection with its 1996 expedition to the Titanic
                  wreck site and in particular connection with the alleged
                  production film, video and still images of the Titanic
                  illuminated by certain light towers. The relief sought
                  includes an accounting and a judgment declaring the plaintiff
                  a co-salvor of the 1996 expedition and awarding him, in
                  specie, the underwater, film, video and still photographs
                  allegedly obtained by plaintiff from the use of the light
                  towers. The plaintiff also seeks an award of compensatory
                  damages of up to approximately $500,000 and punitive damages
                  in excess of $2,000,000 based upon claims of breach of
                  contract, fraudulent misrepresentation, money lent, quantum
                  meruit and conversion. Management of the Company has filed an
                  answer denying the essential allegations of the complaint,
                  intends to defend itself vigorously, and to assert
                  counterclaims seeking compensatory and punitive damages
                  against the plaintiff based upon, among other things, claims
                  that the plaintiff has wrongfully removed and retained
                  property owned by the Company, has wrongfully interfered with
                  contractual relations with third parties, and has violated the
                  Company's copyright to the images obtained with the light
                  towers. In connection with this action, the parties agreed,
                  without further order of the court, coins and currency
                  recovered from the Titanic located within the Southern
                  District of New York (the "District") as of December 18, 1997
                  would not be removed from the District, and would not be sold,
                  liened or otherwise encumbered. The Company filed a motion to
                  dismiss the complaint and/or transfer it to the Eastern
                  District of Virginia. By order dated September 1, 1998, the
                  Court granted the Company's motion to dismiss the plaintiff's
                  claim for an accounting, vacated the above agreement between
                  the parties with respect to disposition of the coins and
                  currency without order of the court, and otherwise denied the
                  Company's motion to dismiss. This action is now in the stage
                  of


                                       11
<PAGE>   12
RMS TITANIC, INC.
NOTES TO FINANCIAL STATEMENTS
(UNAUDITED)

                  discovery proceedings.

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 AUGUST 31, 1998 VERSUS
THE QUARTER ENDED AUGUST 31, 1997

FOR THE SIX MONTHS ENDED AUGUST 31, 1998 VERSUS
THE SIX MONTHS ENDED AUGUST 31, 1997

         During the second quarter and the first six months of its 1999 fiscal
year (the "1999 fiscal year"), the Company's revenues increased approximately
324% and 380%, respectively, as compared to the second quarter and the first
six months of its 1998 fiscal year (the "1998 fiscal year"). This change was
principally attributable to increases in licensing fees of 63,307% and 65,491%
during the second quarter and first six months of the 1999 fiscal year,
respectively, as compared to the corresponding periods of the 1998 fiscal year.
These changes were principally attributable to the Company having earned
licensing fees of approximately $3,345,000 during the second quarter of the
1999 fiscal year related to the production and exploitation of audio and visual
recordings with respect to the Company's expedition to the Titanic wreck site
during the summer of 1998 (the "Summer of 1998 Expedition"). The Company's
revenue from exhibitions increased approximately 1% during the second quarter
of the 1999 fiscal year as compared to the second quarter of the 1998 fiscal
year, and increased approximately 120% during the first six months of the 1999
fiscal year as compared to the first six months of the 1998 fiscal year. This
change during the respective six month periods was primarily attributable to
the extent of the Company's exhibition activities during the first quarter of
the 1999 fiscal year as compared to the first quarter of the 1998 fiscal year.
Revenue from merchandise, book and other activities increased approximately
907% and approximately 876% during the second quarter and first six months of
the 1999 fiscal year, respectively, as compared with the corresponding periods
of the 1998 fiscal year. These changes resulted primarily from the recognition
of revenues during the 1999 fiscal year from a book published in conjunction
with unrelated third parties and revenue derived from the sale of merchandise
through the Company's web site (http://www.titanic-online.com). The Company's
revenue from the sale of coal increased 255% and 851% during the second quarter
and first six months of the 1999 fiscal year, respectively, as compared to the
corresponding periods of the 1998 fiscal year. These changes derived primarily
from increases in the amount of coal sold through the Company's web site and in
the merchandise shops of the Company's United States exhibitions.


                                       12
<PAGE>   13
         The Company's cost of coal sold increased approximately 579% during the
second quarter of the 1999 fiscal year as compared to the second quarter of the
1998 fiscal year, and approximately 781% during the first six months of the
1999 fiscal year as compared to the first six months of the 1998 fiscal year,
with such cost relating to the volume of sales in the respective periods. The
Company's general and administrative expenses increased approximately 52%
during the second quarter of the 1999 fiscal year as compared to the second
quarter of the 1998 fiscal year, and increased approximately 31% during the
first six months of the 1999 fiscal year as compared to the first six months of
the 1998 fiscal year. These changes were primarily the result of an increase in
professional fees. The Company's depreciation and amortization expenses
increased approximately 2,620% and 1,924% during the second quarter and first
six months of the 1999 fiscal year, respectively, as compared to the
corresponding periods of the 1998 fiscal year. During the second quarter of the
1999 fiscal year, the Company incurred $1,845,000 of costs related to vessel
and equipment chartering related to the Company's audio-visual licensee's
requirements for the Summer of 1998 Expedition. During the second quarter of
its 1999 fiscal year, the Company recorded an impairment loss of $150,000
attributable to  exhibitry equipment related to the Company's exhibition of
Titanic artifacts in Hamburg, Germany based upon the determination that certain
items of exhibitry would not be utilized in the planned re-location and
presentation of the Hamburg exhibition in Zurich, Switzerland commencing in the
middle of November 1998.                                                    

         The Company's income before provision for income taxes increased
approximately 161% during the second quarter of the 1999 fiscal year as compared
to the second quarter of the 1998 fiscal year, and increased approximately 390%
during the first six months of the 1999 fiscal year as compared to the first six
months of the 1998 fiscal year. The Company's net income increased approximately
52% during the second quarter of the 1999 fiscal year as compared to the first
quarter of the 1998 fiscal year, and increased approximately 195% during the
first six months of the 1999 fiscal year as compared to the first six months of
the 1998 fiscal year.

                         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 the Company on its 1996 research and recovery expedition,


                                       13
<PAGE>   14
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 second 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 June 1, 1998, the unpaid balance owed to IFREMER under the
1996 charter agreement is $480,000, with the sum of $200,000 paid to IFREMER
during the first quarter of the 1999 fiscal year having been applied as a
deposit for the chartering of IFREMER's vessel and crews for the Summer of
1998 Expedition.

         In connection with the Summer of 1998 Expedition, the Company entered
into an agreement with IFREMER to charter equipment and crew necessary for this
expedition, which commenced on August 3, 1998 and concluded on August 31, 1998.
Pursuant to the terms of such charter agreement, the Company agreed to pay
IFREMER, in addition to the deposit of $200,000, the sum of $1,460,000 for this
expedition, inclusive of all amounts that were due and owing to IFREMER for the
Summer of 1996 Expedition ($480,000). The Company agreed to pay $1,260,000 of
such charter costs prior to the commencement of the Summer of 1998 Expedition,
with the $200,000 balance to be paid upon the conclusion of the expedition.
Pursuant to the agreement between the Company and its audio-visual licensee for
the Summer of 1998 Expedition, the Company's audio-visual licensee paid
$1,150,000 of such charter costs on the Company's behalf. In July 1998, the
Company paid the sum of $80,000 to IFREMER pursuant to the charter agreement.
The balance of $200,000 payable by the Company to IFREMER under the charter
agreement remains due and owing as of the date of this report. All objects
recovered during the Summer of 1998 Expedition are the subject of a lien
granted to IFREMER until the Company pays all sums due and owing to IFREMER for
such expedition.


                                       14
<PAGE>   15
         In addition to the charter agreement with IFREMER, the Company also
entered into agreements with unrelated third parties for the chartering of
equipment and crews in connection with the Summer of 1998 Expedition in an
aggregate amount of $2,195,000. The Company's audio-visual licensee for the
Summer of 1998 Expedition, in addition to the $1,150,000 payment to IFREMER
discussed above, also agreed to pay all of such other charter costs on the
Company's behalf.

         The Company's capital commitments during its 1999 fiscal year includes
compensation to the Company's principal executive officer and lease payments for
its principal offices, with respect to which the Company is presently
negotiating an extension of its lease for the period commencing October 1, 1998.

         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 Hamburg, Germany; Boston, Massachusetts; its touring exhibition
in Japan; and at the Queen Mary in Long Beach, California. The Company has
entered into an agreement to move its exhibition currently presented in Boston,
Massachusetts, which is presently scheduled to end on November 15, 1998, to St.
Paul, Minnesota for a four (4) month period commencing January 1, 1998 (the "St.
Paul Exhibition"). Pursuant to its agreement for the St. Paul Exhibition, the
Company will be paid a minimum of $1,000,000 no later than February 28, 1999
(subject to withholding for a maximum period of one month an amount of up to
approximately $200,000 for agreed upon operating expenses for the month of
March 1999 in the event that cash flow needs so require). The Company will
receive two-thirds of the net profits, as defined (the "Net Profits"), derived
from ticket, merchandise and sponsorship revenues in excess of a maximum budget
of $2,000,000 (the "Budget"). The Budget includes a $300,000 payment to be made
to the Company for the lease of its exhibitry for the St. Paul Exhibition. The
$1,000,000 minimum to be paid to the Company will be credited against its share
of the Net Profits.

         The Company has also preliminarily agreed, subject to the execution of
a definitive agreement, for the re-location of its exhibition from Hamburg,
Germany, which closed on September 30, 1998, to Zurich, Switzerland for a
six-month presentation commencing on or about November 9, 1998 (the "Zurich
Exhibition"). Pursuant to the terms of the preliminary agreement, the Company
will be paid a minimum of $100,000 per month, commencing November 30, 1998,
during the term of the Zurich Exhibition. After the total of net ticket and
sponsorship revenue combined with 20% of gross merchandise sales (less sales
tax) exceed 4,600,000 Swiss Francs (the "Threshold"), the Company will receive
two-thirds of the net profits, as defined, derived from ticket and sponsorship
revenues in excess of the Threshold and 20% of all merchandise revenues from
inception of the Zurich Exhibition. The $100,000 per month payments to the
Company will be credited against its share of the net profits from the Zurich
Exhibition after the Threshold has been attained. The Company is also actively
negotiating for the presentation of an exhibition of its Titanic artifacts in
venues after its present and planned exhibitions are completed. In the event
that cash flows are not adequate to satisfy the Company's future operating
needs (inclusive of payment of outstanding liabilities), no assurances of which
can be given, additional debt and/or equity financing may be required.


                                       15
<PAGE>   16
         In view of the Company's recent purchase of new computers and the
limited impact that Year 2000 issues has upon the Company's business activities
or competitive conditions, management of the Company does not believe that Year
2000 issues will have a material adverse affect upon the Company.

         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 with
approximately $1,566,000 used in investing activities.

         Except for historical information contained herein, this Quarterly
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
timetable. If the Company is unable to arrange income producing exhibitions
similar to its land-based exhibitions in Memphis, St. Petersburg, Boston, 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


                                       16
<PAGE>   17
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.

         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 1998
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.


                                       17
<PAGE>   18
         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. 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 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 second 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 and its exhibition organizer in
Germany and Japan 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.


                                       18
<PAGE>   19
                                     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.

                  The Company is a named defendant in a 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), as disclosed in the
Company's report on Form 8-K dated June 15, 1998. The plaintiff alleges therein,
inter alia, that he rendered certain services to the Company in connection with
its 1996 expedition to the Titanic wreck site and in particular connection with
the alleged production film, video and still images of the Titanic illuminated
by certain light towers. The relief sought includes an accounting and a judgment
declaring the plaintiff a co-salvor of the 1996 expedition and awarding him, in
specie, the underwater, film, video and still photographs allegedly obtained by
plaintiff from the use of the light towers. The plaintiff also seeks an award of
compensatory damages of up to approximately $500,000 and punitive damages in
excess of $2,000,000 based upon claims of breach of contract, fraudulent
misrepresentation, money lent, quantum meruit and conversion. Management of the


                                       19
<PAGE>   20
Company has filed an answer denying the essential allegations of the complaint,
intends to defend itself vigorously, and to assert counterclaims seeking
compensatory and punitive damages against the plaintiff based upon, among other
things, claims that the plaintiff has wrongfully removed and retained property
owned by the Company, has wrongfully interfered with contractual relations with
third parties, and has violated the Company's copyright to the images obtained
with the light towers. In connection with this action, the parties agreed,
without further order of the court, coins and currency recovered from the
Titanic located within the Southern District of New York (the "District") as of
December 18, 1997 would not be removed from the District, and would not be sold,
liened or otherwise encumbered. The Company filed a motion to dismiss the
complaint and/or transfer it to the Eastern District of Virginia. By order dated
September 1, 1998, the Court granted the Company's motion to dismiss the
plaintiff's claim for an accounting, vacated the above agreement between the
parties with respect to disposition of the coins and currency without order of
the court, and otherwise denied the Company's motion to dismiss. This action is
now in the stage of discovery proceedings.

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.

                  10.1  1998 Charter Agreement with IFREMER.

                  10.2  1998 Charter Agreement with Oceaneering International,
                        Inc.

                  10.3  Agreement dated July 15, 1998 between Discovery
                        Communications and the Company.

                  10.4  1998 Charter Agreement with Aqua Plus.

                  10.5  1998 Charter Agreement with Les Abeilles International,
                        Travocean and the Company.

                  10.6  Amendment to Agreement dated August 4, 1998 between the
                        Company and CRE-CO Finanz GmbH.


                                       20
<PAGE>   21
         (b) REPORTS ON FORM 8-K

         On June 15, 1998, the Company filed a report on Form 8-K reporting on
Items 5 and 7.

                                   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:   October 20, 1998            By: /s/ George Tulloch
                                         ---------------------------------------
                                     George Tulloch, Principal Executive Officer
                                     and Principal Accounting Officer

                                       21



<PAGE>   22
                                EXHIBIT INDEX
                                -------------

      Exhibit
       Index
     
       10.1      1998 Charter Agreement with IFREMER.
      
       10.2      1998 Charter Agreement with Oceaneering International,
                 Inc.
      
       10.3      Agreement dated July 15, 1998 between Discovery
                 Communications and the Company.
      
       10.4      1998 Charter Agreement with Aqua Plus.
      
       10.5      1998 Charter Agreement with Les Abeilles International,
                 Travocean and the Company.
      
       10.6      Amendment to Agreement dated August 4, 1998 between the
                 Company and CRE-CO Finanz GmbH.
      
       27        Financial Data Schedule.