<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 September 30, 1998

                                       or

[ ]  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES 
     EXCHANGE ACT OF 1934

               For the transition period from          to 
                                              --------    --------

                           Commission File No. 0-22483
                                               -------

                            -----------------------

                            SEVEN SEAS PETROLEUM INC.
             (Exact name of registrant as specified in its charter)

              YUKON TERRITORY                                73-1468669
     (State or other jurisdiction of                      (I.R.S. Employer
      incorporation or organization)                     Identification No.)

               SUITE 1700
            5555 SAN FELIPE
             HOUSTON, TEXAS                                    77056
(Address of principal executive offices)                     (Zip Code)

       Registrant's telephone number, including area code: (713) 622-8218

                            -----------------------

         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 of 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  X   No 
                                        ---     ---

         Indicate the number of shares outstanding of each of the issuer's
classes of common stock, as of the latest practicable date.

AS OF OCTOBER 31, 1998 THERE WERE 37,588,420 SHARES OF THE REGISTRANT'S COMMON
SHARES, NO PAR VALUE PER SHARE, OUTSTANDING.


<PAGE>   2

                                      INDEX

<TABLE>
<CAPTION>
PART I.  FINANCIAL INFORMATION                                                               PAGE
         (DEVELOPMENT STAGE ENTERPRISE)
<S>                                                                                          <C>
         Item 1.  Consolidated Balance Sheets as of September 30, 1998
                  (Unaudited) and December 31, 1997...........................................2

                  Statements of Consolidated Operations and Accumulated Deficit
                  for the nine months and three months ended September 30, 1998
                  and 1997 and the Cumulative Total from Inception (February 3,
                  1995) to September 30, 1998 (Unaudited).....................................3

                  Statements of Consolidated Cash Flows for the nine months
                  ended September 30, 1998 and 1997 and the Cumulative Total
                  from Inception (February 3, 1995) to September 30, 1998 (Unaudited).........4

                  Notes to Condensed Consolidated Financial Statements (Unaudited)............5

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

         Item 3.  Quantitative and Qualitative Disclosures about Market Risk.................14

PART II. OTHER INFORMATION...................................................................14

         Item 6   Exhibits and Reports on Form 8-K...........................................14
</TABLE>


                                       1
<PAGE>   3

                   SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                        (A DEVELOPMENT STAGE ENTERPRISE)
                           CONSOLIDATED BALANCE SHEETS
                        (In thousands, except share data)

<TABLE>
<CAPTION>
                                                                                    SEPTEMBER 30,    DECEMBER 31, 
                                                                                       1998              1997
                                                                                     ----------      ----------
ASSETS                                                                              (Unaudited)
<S>                                                                                  <C>             <C>       
CURRENT
     Cash and cash equivalents                                                       $   41,709      $   18,067
     Short-term investments                                                              31,201              44
     Accounts receivable                                                                  2,457           3,865
     Interest receivable                                                                    495              --
     Prepaids and other                                                                      65             118
                                                                                     ----------      ----------
                                                                                         75,927          22,094

Note receivable from related party                                                          200             200
Long-term held-to-maturity investments                                                   24,868              --
Land                                                                                      1,591              --
Evaluated oil and gas interests, full-cost method                                        51,777          46,117
Unevaluated oil and gas interests, full-cost method                                     247,510         221,713
Fixed assets, net of accumulated depreciation of $153 at September 30, 1998
     and $43 at December 31, 1997                                                         1,344             304
Other assets, net of accumulated amortization of $309 at September 30, 1998
     and $194 at December 31, 1997                                                        4,045           1,486
                                                                                     ----------      ----------
TOTAL ASSETS                                                                         $  407,262      $  291,914
                                                                                     ==========      ==========

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT
     Accounts payable                                                                $    3,843      $    6,885
     Interest payable                                                                     5,462              --
     Accrued compensation                                                                   508           1,228
     Other accrued liabilities                                                              431              92
                                                                                     ----------      ----------
                                                                                         10,244           8,205

Long-term debt                                                                          110,000          25,000
Deferred income taxes                                                                    70,459          70,459
Minority interest                                                                         8,592           4,087

STOCKHOLDERS' EQUITY
Share capital -
     Authorized unlimited common shares without par value and
     37,588,420 and 35,071,606  issued and outstanding common shares
     at September 30, 1998 and December 31, 1997, respectively                          220,586         196,406

     Authorized unlimited Class A preferred shares without par value                         --              --

     Warrants - 1,068,044 and 0 outstanding at September 30, 1998                         3,093              --
     and December 31, 1997, respectively

Deficit accumulated during development stage                                            (15,712)        (12,243)

Treasury stock, 29 shares held at September 30, 1998 and December 31, 1997                   --              --
                                                                                     ----------      ----------

Total Stockholders' Equity                                                              207,967         184,163
                                                                                     ----------      ----------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                           $  407,262      $  291,914
                                                                                     ==========      ==========
</TABLE>



   The accompanying notes are an integral part of these financial statements.

                                       2
<PAGE>   4

                   SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                        (A DEVELOPMENT STAGE ENTERPRISE)
          STATEMENTS OF CONSOLIDATED OPERATIONS AND ACCUMULATED DEFICIT
                  (Unaudited; In thousands, except share data)

<TABLE>
<CAPTION>
                                                                                                                       CUMULATIVE
                                                                                                                       TOTAL FROM
                                                                                                                        INCEPTION
                                                      NINE MONTHS ENDED                   THREE MONTHS ENDED          (FEBRUARY 3,
                                                        SEPTEMBER 30,                        SEPTEMBER 30,               1995) TO
                                               ------------------------------      ------------------------------     SEPTEMBER 30,
                                                   1998              1997              1998              1997              1998
                                               ------------      ------------      ------------      ------------      ------------
<S>                                            <C>               <C>               <C>               <C>               <C>         
REVENUE
    Crude oil sales                            $         91      $        489      $         --      $         52      $      1,104
    Interest income                                   2,574               490             1,431               256             3,855
                                               ------------      ------------      ------------      ------------      ------------
                                                      2,665               979             1,431               308             4,959

EXPENSES
    General and administrative                        5,761             4,604             3,442             1,323            18,001
    Oil and gas operating expenses                      804               231                46                --             1,964
    Depreciation and amortization                       446                71               219                33               743
    Dry hole and abandonment costs                       --                17                --                --             1,145
    Geological and geophysical                           --                27                --                --                47
    Other (income) expense                              (32)              (32)               (2)              (32)              (57)
    Gain on sale of exploration properties             (577)               --              (577)               --              (546)
                                               ------------      ------------      ------------      ------------      ------------
                                                      6,402             4,918             3,128             1,324            21,297

NET LOSS BEFORE INCOME TAXES                         (3,737)           (3,939)           (1,697)           (1,016)          (16,338)

INCOME TAX EXPENSE                                      102                24                72                16               102

NET LOSS BEFORE MINORITY INTEREST                    (3,839)           (3,963)           (1,769)           (1,032)          (16,440)

MINORITY INTEREST                                       370               132               167                59               728
                                               ------------      ------------      ------------      ------------      ------------

NET LOSS                                       $     (3,469)     $     (3,831)     $     (1,602)     $       (973)     $    (15,712)
                                               ============      ============      ============      ============      ============

DEFICIT ACCUMULATED DURING THE DEVELOPMENT
STAGE, BEGINNING OF PERIOD                          (12,243)           (4,315)          (14,110)           (7,173)               --

DEFICIT ACCUMULATED DURING THE DEVELOPMENT
STAGE, END OF PERIOD                           $    (15,712)     $     (8,146)     $    (15,712)     $     (8,146)     $    (15,712)
                                               ============      ============      ============      ============      ============

BASIC AND DILUTED NET LOSS PER COMMON SHARE    $      (0.10)     $      (0.12)     $      (0.04)     $      (0.03)     $      (0.71)
                                               ============      ============      ============      ============      ============

WEIGHTED AVERAGE
  COMMON SHARES OUTSTANDING                      35,706,779        31,662,631        36,724,401        31,662,631        22,028,421
                                               ============      ============      ============      ============      ============
</TABLE>

   The accompanying notes are an integral part of these financial statements.


                                       3
<PAGE>   5

                   SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                        (A DEVELOPMENT STAGE ENTERPRISE)
                      STATEMENTS OF CONSOLIDATED CASH FLOWS
                            (Unaudited; In thousands)

<TABLE>
<CAPTION>
                                                                                                    CUMULATIVE 
                                                                                                    TOTAL FROM 
                                                                                                     INCEPTION 
                                                                          NINE MONTHS ENDED         (FEBRUARY 3, 
                                                                            SEPTEMBER 30,            1995) TO 
                                                                    --------------------------     SEPTEMBER 30,
                                                                        1998            1997           1998
                                                                    ----------      ----------      ----------
<S>                                                                 <C>             <C>             <C>        
OPERATING ACTIVITIES
     Net loss                                                       $   (3,469)     $   (3,831)     $  (15,712)
     Add (subtract) items not requiring (providing) cash:
     Compensation expense                                                   --              --           2,140
     Minority interest                                                    (370)           (132)           (728)
     Common stock contribution to 401(k) retirement plan                    --              --              79
     Dry hole and abandonment costs                                         --              17           1,140
     Gain on sale of marketable securities                                  (6)             --              (6)
     Gain on sale of exploration properties                               (577)             --            (546)
     Depreciation and amortization                                         449              71             746
     Changes in working capital excluding changes to cash and
     cash equivalents:
        Accounts receivable                                                867           1,174          (1,575)
        Interest receivable                                               (495)             --            (495)
        Prepaids and other, net                                             53             (11)            (65)
        Accounts payable                                                (5,299)            730          (3,807)
        Interest payable                                                    --             222              --
       Other accrued liabilities                                           339             508             431
                                                                    ----------      ----------      ----------
Cash Flow Used in Operating Activities                                  (8,508)         (1,252)        (18,398)
                                                                    ----------      ----------      ----------
INVESTING ACTIVITIES
     Exploration of oil and gas properties                             (24,324)         (8,607)        (46,690)
     Purchase of land                                                   (1,591)             --          (1,591)
     Purchase of investments                                           (56,069)             --         (56,069)
     Proceeds from acquisition                                              --              --             630
     Proceeds from sale of property                                      1,163              --           1,247
     Proceeds from sale of marketable securities                            50              --              50
     Note receivable from related party                                     --              --            (200)
     Other asset additions                                              (1,150)           (159)         (1,664)
                                                                    ----------      ----------      ----------
Cash Flow Used in Investing Activities                                 (81,921)         (8,766)       (104,287)
                                                                    ----------      ----------      ----------
FINANCING ACTIVITIES
     Proceeds from special warrants issued                                 284              --          12,393
     Proceeds from share capital issued                                  2,619           3,944          14,113
     Proceeds from additional paid-in capital contributed                   --              --               1
     Proceeds from issuance of  long-term debt                         110,000          25,000         135,000
     Costs of issuing long-term debt                                    (4,248)         (1,566)         (5,821)
     Contributions by minority interest                                  5,416           1,931           8,708
                                                                    ----------      ----------      ----------
Cash Flow Provided by Financing Activities                             114,071          29,309         164,394
                                                                    ----------      ----------      ----------
NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                    23,642          19,291          41,709
Cash and cash equivalents, beginning of period                          18,067          10,620              --
                                                                    ----------      ----------      ----------
CASH AND CASH EQUIVALENTS, END OF PERIOD                            $   41,709      $   29,911      $   41,709
                                                                    ==========      ==========      ==========
</TABLE>

Supplemental disclosures of cash flow information:

The Company incurred interest costs of $7.0 million for the nine month period
ended September 30, 1998 and $0.6 for the year ended December 31, 1997. Such
amounts were capitalized during the respective periods. Interest paid for the
nine month period ended September 30, 1998 and for the period ended 
September 31, 1997 was $.9 million and zero, respectively. 

The Company paid $30,000 for estimated income taxes during the nine month period
ended September 30, 1998.


   The accompanying notes are an integral part of these financial statements.

                                       4
<PAGE>   6

                   SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                        (A DEVELOPMENT STAGE ENTERPRISE)
              NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS
                                   (Unaudited)

1.   DEVELOPMENT STAGE OPERATIONS

     The accompanying unaudited condensed consolidated financial statements
include the accounts of Seven Seas Petroleum Inc. and its subsidiaries
(collectively referred to as "Seven Seas" or the "Company") after elimination of
intercompany balances and transactions. The unaudited condensed consolidated
financial statements of the Company for the periods indicated herein have been
prepared by the Company pursuant to the rules and regulations of the Securities
and Exchange Commission and in accordance with generally accepted accounting
principles for interim financial reporting. Accordingly, they do not include all
of the information and footnotes required by generally accepted accounting
principles for complete financial statements. In the opinion of management, all
adjustments, consisting of normal recurring accruals, necessary to present
fairly the information in the accompanying condensed consolidated financial
statements have been included. Interim period results are not necessarily
indicative of the results of operations or cash flows for a full year period.

     The Company (a Yukon Territory, Canada corporation) was formed on February
3, 1995. Seven Seas is a development stage enterprise engaging in the
acquisition, exploration, and development of interests in oil and gas projects
worldwide. The Company's primary business operations to date have been the
exploration and development of its interests in Colombia, South America.

     The Company has yet to generate any significant revenue from oil and gas
sales and has no assurance of future revenues. The Company's principal asset is
its 57.7 percent working interest in the Dindal Association Contract and Rio
Seco Association Contract (collectively, the "Association Contracts" or the
"Emerald Mountain Project"). The Association Contracts were issued by Empresa
Colombiana de Petroleos ("Ecopetrol"), the national oil company of Colombia, in
March 1993 and August 1995, respectively, and entitle the Company to engage in
exploration, development, and production activities in Colombia. To date, five
of the ten exploratory wells drilled have been completed on Emerald Mountain and
have encountered on average 303 feet of Cimarrona formation at vertical depths
between 6,000 and 7,500 feet. For the five wells where production testing has
been completed, actual per well production rates realized ranged from 3,415 to
13,123 barrels per day with an average in excess of 7,079 barrels per day. The
wells which have not been completed found the intended formation and two are
scheduled for production testing in late 1998. The Company plans to complete the
other three wells in 1999. The Company plans to rapidly and efficiently continue
its field development and delineation drilling program and to build the
production facilities and pipeline infrastructure to allow its production to
reach existing transportation lines for access to export markets.

     Seven Seas is subject to several categories of risk associated with its
development stage activities. Oil and gas exploration and development is a
speculative business and involves a high degree of risk. The Company has
expended, and plans to expend, significant amounts of capital on the acquisition
and exploration of its properties, and most of such properties have not been
fully evaluated for hydrocarbon potential. The exploration and development of
current properties and any properties acquired in the future are expected to
require substantial amounts of additional capital which the Company may be
required to raise through debt or equity financings, which might involve
encumbering properties or entering into arrangements where certain costs of
exploration will be paid by others to earn an interest in the property. Seven
Seas' success currently depends to a high degree on its activities in Colombia.
However, there are risks that result because the Company has acquired interests
in properties outside of North America, in some cases in countries that may be
considered politically and economically unstable.

2.   INVESTMENTS

     At September 30, 1998, all the Company's investments were classified as
held-to-maturity. These securities include both securities due within one year
and securities due beyond one year. The securities with a maturity date within
one year are classified as short-term investments as part of Current Assets and
are stated at amortized cost. The securities with maturity dates beyond one year
are included in Non-Current Assets classified as long-term held-to-maturity


                                       5
<PAGE>   7

investments and are stated at amortized cost. The calculation of gross
unrealized gain (loss) for the quarter and nine months ended September 30, 1998
was as follows:

<TABLE>
<CAPTION>
                                                                                       Gross Unrealized
                                                         Fair Value     Amortized Cost    Gain (Loss)
                                                         ----------     --------------    -----------
<S>                                                     <C>             <C>             <C>
SHORT-TERM INVESTMENTS
U.S. Treasury Note, face value of
$6,769,000, interest at 5.875%, due October
31, 1998                                                $ 6,775,363     $ 6,771,260     $     4,103
U.S. Treasury Note, face value of
$6,663,000, interest at 6.375%, due April
30, 1999                                                  6,729,630       6,695,192          34,438
Xerox Credit Commercial Paper, face value of
$4,850,000, interest at 5.24%, due January
20, 1999                                                  5,403,750       5,410,909          (7,159)
Prudential Fund Commercial Paper, face value
of $5,803,000, interest at 5.29%, due
January 21, 1999                                          5,695,557       5,707,401         (11,844)
American Express Credit Commercial Paper,
face value of $1,000,000, interest at
7.375%, due February 1, 1999                              1,007,003       1,005,750           1,253
Cargill Inc. Commercial Paper, face value of
5,721,000, interest at 5.21%, due February
11, 1999                                                  5,660,118       5,610,809          49,309
                                                        -----------     -----------     -----------
Total Short-term investments                            $31,271,421     $31,201,321     $    70,100
                                                        ===========     ===========     ===========

LONG-TERM INVESTMENTS
U.S. Treasury Strip, face value of
$6,875,000, due November 15, 1999                       $ 6,539,981     $ 6,473,568     $    66,413
U.S. Treasury Strip, face value of
$6,875,000, due May 15, 2000                              6,405,575       6,299,763     $   105,812
U.S. Treasury Strip, face value of
$6,875,000, due November 15, 2000                         6,270,275       6,131,077     $   139,198
U.S. Treasury Strip, face value of
$6,875,000, due May 15, 2000                              6,140,613       5,963,317     $   177,296
                                                        -----------     -----------     -----------
Total Long-term held-to-maturity
investments
                                                        $25,356,444     $24,867,725     $   488,719
                                                        ===========     ===========     ===========
</TABLE>

Net unrealized gains (losses) on held-to-maturity securities have not been
recognized in the accompanying condensed consolidated financial statements.

3.   LONG-TERM DEBT

     The Company issued $110 million aggregate principal amount of 12 1/2%
Senior Notes due 2005 (the "Notes") in a private transaction on May 7, 1998 that
was not subject to registration requirements of the Securities Act of 1933. The
Notes mature on May 15, 2005. Interest on the Notes will be payable
semi-annually, in arrears on May 15 and November 15 commencing November 15, 1998
to holders of record on the immediately preceding May 1 and November 1. On
September 23, 1998, the Company completed its exchange of registered notes for
the previously issued privately placed notes.

     On August 5, 1998, the Company's Special Notes were deemed to be exercised
for Debentures. On August 6, 1998, all Debentures were converted into Units.
Accordingly, the Trustee has since delivered to Debentureholders of record
certificates representing the Common Shares and Warrants that comprise the
Units, for a total of 2,173,901 Common Shares and 1,086,957 Warrants.



                                       6
<PAGE>   8

     The Toronto Stock Exchange granted up to a six month extension, to February
5, 1999, of the exercise period for the Warrants issued when the Debentures were
converted into Units. The Warrants will expire prior to February 5, 1999, if the
weighted average trading price of the Company's common shares on The Toronto
Stock Exchange exceeds $17.64 for a 20 day period during the extension period
("the Triggering Event"). The exercise period for the warrants will then expire
30 calendar days following the Triggering Event. The warrants potentially
represent 1.087 million common shares, with an exercise price of $15.00 per
share and originally were scheduled to expire August 7, 1998. All other terms
and conditions of the warrants remain unchanged.

     The Company currently is negotiating an agreement with Banque Paribas
providing for a $25 million senior secured revolving credit facility. The
revolving credit facility is expected to have a term of not less than three
years. The Company expects that borrowings under the facility will bear
interest, at the Company's option, at LIBOR plus a margin of 2.75% or Citibank's
base rate plus a margin of 1.00%; provided, however, that the applicable margins
for both LIBOR and base rate loans is expected to increase by 1.25% under
certain circumstances. An annual commitment fee of 0.50% is expected to be
payable on the unused available portion of the facility. In addition, the
Company expects to pay a customary underwriting fee and other expenses in
connection with the facility. The Company expects that the facility will be
secured by certain assets of the Company , including the stock of certain of the
Company's subsidiaries. The facility is expected to contain certain restrictive
covenants which impose limitations on the Company and its Subsidiaries, with
respect to, among other things, (1) the creation of liens, (ii) mergers,
acquisitions or dispositions of assets, (iii) incurrence of indebtedness, (iv)
transactions with affiliates, (v) sale-leaseback transactions and (vi) dividends
and other restricted payments. The credit facility also is expected to require
the Company to maintain a minimum current ratio, a minimum tangible net worth,
and a minimum debt coverage ratio. The credit facility is expected to contain
customary provision on events of default. While it is anticipated that the
credit facility will be completed in the fourth quarter of 1998, no assurance
can be made that the credit facility will be completed on the terms set forth
above or on terms acceptable to the Company.

4.   RECENTLY ISSUED ACCOUNTING PRONOUNCEMENTS

     In June 1998, the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 133, Accounting for Derivative Instruments
and Hedging Activities. The Statement establishes accounting and reporting
standards requiring that every derivative instrument, including certain
derivative instruments embedded in other contracts, be recorded in the balance
sheet as either an asset or liability measured at its fair value. The Statement
requires that changes in the derivative's fair value be recognized currently in
earnings unless specific hedge accounting criteria are met. Special accounting
for qualifying hedges allows a derivative's gains and losses to offset related
results on the hedged item in the income statement, and requires that a company
must formally document, designate, and assess the effectiveness of transactions
that receive hedge accounting.

     Statement No. 133 is effective for fiscal years beginning after June 15,
1999. A company may also implement the Statement as of the beginning of any
fiscal quarter after issuance. Statement No. 133 cannot be applied
retroactively. Statement No. 133 must be applied to (a) derivative instruments
and (b) certain derivative instruments embedded in hybrid contracts that were
issued, acquired, or substantively modified after December 31, 1997 and, at the
company's election, before January 1, 1998. Statement No. 133 will not currently
impact the Company's disclosure or reporting.

     In June 1997, the Financial Accounting Standards Board ("FASB") issued
Statement No. 130, "Reporting Comprehensive Income" ("Statement No. 130") and
Statement No. 131, "Disclosures About Segments of an Enterprise and Related
Information ("Statement No. 131"). In February 1998, the FASB issued Statement
No. 132 "Employers' Disclosure About Pension and Other Post-retirement Benefits"
("Statement No. 132") that revised disclosure requirements for pension and other
post-retirement benefits. Statement No. 132 does not impact the Company's
disclosure or reporting. During the first quarter of 1998, the Accounting
Standards Executive Committee of the American Institute of Certified Public
Accountants issued two Statements of Position ("SOP"), SOP 98-5 "Reporting on
the Costs of Start-up Activities and SOP 98-1 "Accounting for the Costs of
Computer Software Developed or Obtained for Internal Use".


                                       7
<PAGE>   9

     Statement No. 130 established standards for reporting and display of
comprehensive income and its components in a full set of general purpose
financial statements. This standard does not currently alter the Company's
reporting or disclosure.

     Statement No. 131 established standards for the way public enterprises
report information about operating segments in annual financial statements and
requires that those enterprises report selected information about operating
segments in interim financial reports issued to share holders. It also
established standards for related disclosure about products and services,
geographic areas and major customers. Statement No. 131 will not currently
impact the Company's disclosure or reporting.

     SOP 98-1 establishes guidance on the accounting for the costs of computer
software developed or obtained for internal use. The Company's current
accounting policies adhere to the provisions of the SOP.

5.   SUBSEQUENT EVENT

     In October 1998, the Company assigned its interest in Papua New Guinea to
ARCO Papua New Guinea Inc., retaining a $250,000 production payment from 5% of
the net proceeds of future production.


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

     The following discussion and analysis should be read in conjunction with
the unaudited condensed consolidated financial statements included elsewhere and
with the Company's Annual Report on Form 10-K/A for the year ended December 31,
1997.

     Seven Seas is an independent international energy company engaged in the
exploration, development and production of oil and natural gas in Colombia. The
Company is the operator of an oil discovery ("Emerald Mountain") defined by two
adjoining association contracts covering a total of approximately 109,000
contiguous acres in central Colombia. The Company has focused most of its
efforts to date on delineating the oil and gas potential of Emerald Mountain,
from which there has been no commercial production pending construction of a
pipeline and other infrastructure facilities. The Company also has interests in
three additional association contracts in Colombia, which, together with the
Emerald Mountain association contracts, cover over one million gross acres. The
Company has a carried interest in Papua New Guinea and is in the process of
divesting or farming out its oil and gas interests in Australia.

TERMS OF ASSOCIATION CONTRACTS AND RELATED MATTERS

     The Company has a 57.7% working interest (before Colombian government
participation) in the Association Contracts. An association contract gives the
parties to the contract a right to explore the contracted area and develop such
petroleum as may be found therein. The Colombian government receives a royalty
equal to 20% of production (after transportation costs are deducted). In the
event of commerciality, Ecopetrol has the right to acquire an initial 50%
working interest in the project. Ecopetrol's share of production and costs in
the Dindal Association Contract area will increase once a commercial field
produces in excess of 60 MMBbls, up to a maximum interest of 70% in the field
produces in excess of 150 MMBbls. In addition, Ecopetrol's share of production
and costs in the Rio Seco Association Contract area is also subject to increase
once a commercial field produces in excess of 60 MMBbls, up to a maximum
interest of 75% depending upon revenues and associated costs.

     Under the terms of the Association Contracts, if a commercially feasible
discovery is made, Ecopetrol may acquire a 50% interest in the property. If
Ecopetrol elects to acquire a 50% interest in the property, the interests of all
other parties to the contract, including the Company, will be reduced by 50%.
Ecopetrol will then bear 50% of the associated development costs and must
reimburse the other working interest owners for 50% of certain exploration
activities. The Company expects that Ecopetrol will elect to finance a
significant portion of the costs associated with its working interest from
Ecoptrol's share of future production rather than contributing its proportionate
share of development costs 


                                       8
<PAGE>   10

in cash. As a result, the Company and the other working interest owners may be
required initially to finance Ecopetrol's share of the development costs
associated with the property. While the Association Contracts do not require
Ecopetrol's participation in the pipeline and production facilities, the Company
expects that Ecopetrol will participate to the extent of 50% of the Phase I and
Phase II pipeline and infrastructure costs. No assurances can be given, however,
that an agreement will be reached on these terms and the Company may be required
to fund amounts greater than the amounts presented as the Company's net share.

     To date, all oil produced by the Company has been from production testing
on Emerald Mountain. Upon the drilling of sufficient wells to reasonably define
the hydrocarbon-producing area and acceptance by Ecopetrol that the field is
capable of commercial production, oil produced from the Dindal and Rio Seco
Association Contract areas may be sold to Ecopetrol or to third parties and
Ecopetrol may acquire their 50% working interest. In the event the production is
required to satisfy internal demand for oil in Colombia, the Company may be
required to sell some or all of its production to Ecopetrol at prevailing market
prices.

COLOMBIAN TAXES

     The Company's net income, as defined under Colombian law, from Colombian
sources is subject to Colombian corporate income tax at a rate of 35%. An
additional remittance tax is imposed upon remittance of profits abroad at a rate
of 7%.

ACCOUNTING POLICIES AND DEVELOPMENT STAGE ACCOUNTING

     The Consolidated Financial Statements and Notes thereto included herein
have been prepared in accordance with generally accepted accounting principles
in the United States.

     The Company follows the full-cost method of accounting for oil and natural
gas properties. Under this method, all costs incurred in the acquisition,
exploration and development of oil and gas properties, including unproductive
wells, are capitalized in separate cost centers for each country. Such
capitalized costs include contract and concession acquisition, geological,
geophysical and other exploration work, drilling, completing and equipping oil
and gas wells, constructing production facilities and pipelines, and other
related costs. As of December 31, 1996, unevaluated oil and gas interests
included capitalized general and administrative costs of $0.1 million. No
additional general and administrative costs were capitalized during 1997 or
1998. The Company capitalized interest of $0.6 million for the year ended
December 31, 1997 and $7.0 million for the nine month period ended September 30,
1998.

     The capitalized costs of oil and gas properties in each cost center are
amortized on the composite units of production method based on future gross
revenues from proved reserves. Sales or other dispositions of oil and gas
properties are normally accounted for as adjustments of capitalized costs. Gain
or loss is not recognized in income unless a significant portion of a cost
center's reserves is involved. Capitalized costs associated with the acquisition
and evaluation of unproved properties are excluded from amortization until it is
determined whether proved reserves can be assigned to such properties or until
the value of the properties is impaired. If the net capitalized costs of oil and
gas properties in a cost center exceed an amount equal to the sum of the present
value of estimated future net revenues from proved oil and gas reserves in the
cost center and the lower of cost or fair value or properties not being
amortized, both adjusted for income tax effects, such as excess is charged to
expense.

     The Company's exploration and development activities have generated an
insignificant amount of revenue, thus requiring the financial statements to be
presented as a development stage enterprise. Accumulated losses are presented on
the balance sheet as "Deficit accumulated during the development stage." The
income statement presents revenues and expenses for each period presented and
also a cumulative total of both amounts from the Company's inception. The
statement of cash flows shows inflows and outflows for the date and number of
shares of each class of security issued for cash or other consideration and the
dollar amount assigned. In addition, the notes to financial statements are
required to identify the enterprise as development stage. Thus, period-to-period
comparisons of such results and certain financial data may not be meaningful or
indicative of future results. In this regard, future results of the Company will
be materially dependent upon the success of the Company's Emerald Mountain
operations.


                                       9
<PAGE>   11

RESULTS OF DEVELOPMENT STAGE OPERATIONS

Three Months Ended September 30, 1998 and 1997

     To date, oil revenues and oil and gas operating expenses pertained solely
to the Company's share of crude oil produced during production testing of the
Company's wells on Emerald Mountain. Revenues from oil sales were zero and $0.1
million for the quarter ended September 30, 1998 and 1997, respectively. Oil and
gas operating expenses were $46,000 and zero for the quarter ended September 30,
1998 and 1997, respectively. The 1998 oil and gas operating expenses represent
such costs as tank rentals and other miscellaneous fixed costs.

     Interest income was $1.4 million for the quarter ended September 30, 1998
as compared to $0.3 million for the same period in 1997. The increase was the
consequence of higher cash and investment balances resulting from the issuance
of the 12 1/2% Senior Notes in May 1998.

     General and administrative costs were $3.4 million during the quarter ended
September 30, 1998 as compared to $1.3 million during the same period of 1997.
The quarter ended September 30, 1998 included $0.8 million relating to costs
incurred conducting a feasibility study for the proposed pipeline and production
facilities. The remaining $1.3 million increase in general and administrative
expenses was primarily attributable to a $1.1 million increase in personnel
costs, including salaries, benefits, rent, and insurance due to increased
personnel in both Houston and Bogota as well as the expansion of operations in
Bogota. In addition, the Company incurred $0.1 million in professional services
and consulting fees.

     Depreciation and amortization was $0.2 million and $33,000 for the quarter
ended September 30,1998 and 1997, respectively. The increase was primarily
attributable to the amortization of costs incurred in issuing the Special Notes
in August 1997 and the Senior Notes in May 1998 (see "Liquidity and Capital
Resources" below). As of September 30, 1998, the Company has not recorded
depletion of its proved oil and gas property as only insignificant quantities of
oil have been produced during its production testing plan.

     The Company incurred net losses of $1.6 million and $1.0 million for the
quarter ended September 30, 1998 and 1997, respectively.

Nine Months Ended September 30, 1998 and 1997

     To date, oil revenues and oil and gas operating expenses pertained solely
to the Company's share of crude oil produced during production testing of the
Company's wells on Emerald Mountain. Revenues from oil sales were $0.1 million,
and $0.5 million for the nine months ended September 30, 1998 and 1997,
respectively. Oil and gas operating expenses were $0.8 million and $0.2 million
for the nine months ended September 30, 1998 and 1997, respectively. Oil and gas
operating expenses represent such costs as tank rentals and other miscellaneous
fixed costs.

     Interest income was $2.6 million for the nine months ended September 30,
1998 as compared to $0.5 million for the same period in 1997. The increase was
the consequence of higher cash and investment balances resulting from the
issuance of the 12 1/2% Senior Notes in May 1998.

     General and administrative costs were $5.8 million during the nine months
ended September 30, 1998 as compared to $4.6 million during the same period of
1997. The nine months ended September 30, 1997 included costs of severance and
related compensation costs associated with the resignations of former officers.
The costs incurred during the nine months ended September 30, 1998 included $0.8
million relating to costs incurred conducting a feasibility study for the
proposed construction of pipeline and production facilities in Colombia. The
remaining $1.7 million increase in general and administrative expenses was
primarily attributable to a $1.4 million increase in personnel costs, including
salaries, benefits, rent, and insurance due to increased personnel in both
Houston and Bogota as well as the expansion of operations in Bogota. In
addition, the Company incurred $0.1 million in professional services and
consulting fees.

     Depreciation and amortization was $0.4 million and $0.1 million for the
nine months ended September 30,1998 and 1997, respectively. The increase was
primarily attributable to the amortization of costs incurred in issuing the


                                       10
<PAGE>   12

Special Notes in August 1997 and the Senior Notes in May 1998 (see "Liquidity
and Capital Resources" below). As of September 30, 1998, the Company has not
recorded depletion of its proved oil and gas property as only insignificant
quantities of oil have been produced during its production testing plan.

     The Company incurred net losses of $3.5 million and $3.8 million for the
nine months ended September 30, 1998 and 1997, respectively.

LIQUIDITY AND CAPITAL RESOURCES

     The Company's activities have been funded primarily by the proceeds from
private placements of the Company's securities from inception through September
30, 1998, resulting in aggregate cash proceeds of $155.9 million. In 1996, the
Company acquired an additional 36.7% interest in the Association Contracts in
Colombia in exchange for the issuance of the Company's securities valued at
$153.1 million in the aggregate. From inception through September 30, 1998, the
Company had capital expenditures of $46.7 million for the acquisition,
exploration, and development of its oil and gas properties, including $44.6
million with respect to its interests in Colombia and approximately $2.1
million, of which $1.1 million has been expensed, with respect to its interests
in other countries. Such expense included $0.5 million for the cost of an option
to acquire a 5% participating interest in three exploration blocks in North
Africa and $0.6 million associated with a dry hole in the San Jorge Basin,
Argentina. The Company's activities in North Africa and Argentina have been
discontinued.

     On May 7, 1998, the Company issued $110 million of 12.5% Senior Notes in a
private transaction. Net proceeds available to the Company for its capital
expenditures and other general corporate purposes were approximately $67.6
million, after deducting $37.8 million held in a separate account or in escrow 
to provide for the first three years of interest payments on the notes.

     The Company's primary capital commitments include Phases I and II of its
Emerald Mountain development program. The Company's capital expenditures
estimated for Phase I include $26.1 million for field development and
delineation and $57.7 million for pipeline and production facilities, which is
scheduled for completion in late 1999. The Company's capital expenditures
estimated for Phase II include $31.5 million for field development and
delineation and $65.7 million for pipeline and production facilities, which is
scheduled for completion in mid- 2000. The Company had working capital of $65.7
million as of September 30, 1998. The Company believes that the net proceeds of
the offering of Senior Notes, together with other sources of funds expected to
be available to it (including bank and vendor financing), will be sufficient to
finance its initial net capital expenditure requirements estimate for Phase I.
Substantial amounts of capital will be needed to finance Phase II, and no
external sources of capital have yet been identified. Certain expenditures for
Phase II are expected to occur during Phase I. In addition, the Company has
budgeted approximately $14.6 million to participate in drilling a deep
exploratory well on Emerald Mountain scheduled to commence in the first quarter
of 1999. The Company expects that additional amounts for capital expenditures
may be funded through cash from operations, joint ventures and other such
arrangements, and debt or equity financings. The Company does not expect any
significant funds from operations until scheduled completion of the initial
pipeline and production facilities in late 1999. There can be no assurances that
debt or equity financing will be available to the Company on economically
acceptable terms.

     Colombia. During the remainder of 1998, the Company plans to complete two
wells on the Dindal and Rio Seco blocks, begin construction of a 36-mile
pipeline to provide transportation capacity of 50,000 BBls/d, conduct seismic
operations, and carry out other development activities for an aggregate
estimated cost of $8.7 million. The pipeline is scheduled for completion in
late-1999.

     An exploratory well on the Company's non-operated Tapir Block in Colombia
commenced drilling in March 1998. The Company's share of budgeted costs are
approximately $0.4 million. Drilling activity on the exploratory well has been
completed; however, testing of potential production intervals were suspended due
to risk of flooding caused by heavy rain. Testing is scheduled to resume in the
fourth quarter of 1998. In addition, the Company may participate in the drilling
of two more exploratory wells on the Tapir block in 1999.

     For the nine months ended September 30, 1998 and 1997, the Company had oil
sales of $0.1 million and $0.5 million, respectively, solely from production
testing of the Company's wells on Emerald Mountain. Although the 



                                       11
<PAGE>   13

Company intends to continue to sell oil resulting from production tests,
significant commercial production is not expected until further development of
the field is completed through the drilling of additional wells and construction
of producing facilities and pipelines. The Company has received preliminary
plans for the construction of pipelines and producing facilities, and permitting
and final planning for pipelines and production facilities are now proceeding.
Completion of the first phase of these facilities is scheduled to occur in late
1999.

     Australia and Papua New Guinea. The Company is in the process of
eliminating any mandatory capital commitments outside of Colombia. In October
1998, the Company assigned its interest in Papua New Guinea to ARCO Papua New
Guinea Inc., and retained a $250,000 production payment from 5% of the net
proceeds of future production. In the Western Perth Basin in Australia, the
Company sold its 11.77% working interest to Forcenergy International Inc. for
$0.9 million. The Company retained a small overriding interest and was
reimbursed $0.3 million for certain capital expenditures. In the Bass Strait
Basin in Australia, the Company is seeking to farm-out its interests.

     Convertible Debentures. In August 1997, the Company issued $25 million of
6% exchangeable subordinated notes ("Special Notes") in a private transaction
with institutional and accredited investors. Interest on the Special Notes was
payable in arrears commencing on December 31, 1997 at a rate of 6% per annum on
December 31 and June 30 in each year until maturity on August 7, 2003.

     On August 5, 1998, the Company's Special Notes were deemed to be exercised
for Debentures. On August 6, 1998, all Debentures were converted into Units.
Accordingly, the Trustee has since delivered to Debentureholders of record
certificates representing the Common Shares and Warrants that comprise the
Units, for a total of 2,173,913 Common Shares and 1,086,957 Warrants.

     On July 23, 1998, the Toronto Stock Exchange (the "TSE") granted an
extension of the exercise period for the Warrants from August 7, 1998 to
5:00p.m. (Calgary time) on the earlier of (a) the date that is 30 calendar days
following a 20 day period during which the weighted average trading price for
the Common Shares on the TSE exceeds US$17.64 and (b) February 5, 1999.

     Senior Notes. In May 1998, the Company completed the offering of Senior
Notes and received net proceeds of approximately $106 million, of which
approximately $37.8 million has been held in a separate account or in escrow to
provide for the first three years of interest payable under the Senior Notes.
Interest on the Senior Notes is payable semi-annually on May 15 and November 15
of each year, commencing November 15, 1998. The Senior Notes mature on May 15,
2005. The Senior Notes are redeemable a the option of the Company, in whole or
in part, at any time on or after May 15, 2002, at the prescribed redemption
price, plus accrued and unpaid interest, liquidated damages and additional
amounts, if any, to the date of redemption. Notwithstanding the foregoing, at
any time prior to May 15, 2001, the Company may redeem up to 33 1/2% of the
original aggregate principal amount of the Senior Notes with a portion of the
net proceeds of an equity or strategic investor offering, provided that at least
66 2/3% of the original aggregate principal amount of the Senior Notes remains
outstanding immediately after the occurrence of such redemption. The Senior
Notes may also be redeemed at the option of the Company, in whole but not in
part, at any time at a redemption price equal to 100% of the principal amount
thereof plus accrued and unpaid interest, liquidated damages and additional
amounts, if any, to the redemption date in the event of certain changes
affecting withholding taxes applicable to certain payments on the Senior Notes.
Upon the occurrence of a change of control, (i) unless the Company redeems the
Senior Notes as provided in clause (ii) below, the Company will be required to
offer to purchase the Senior Notes at a purchase price equal to 101% of the
aggregate principal amount thereof, plus accrued and unpaid interest, liquidated
damages and additional amounts, if any, to the date of purchase, and (ii) the
Company will have the option, at any time prior to May 15, 2002, to redeem the
Senior Notes, in whole but not in part at a redemption price equal to 100% of
the principal amount thereof plus the applicable premium and accrued and unpaid
interest, liquidated damages and additional amounts, if any, to the date of
redemption. The Senior Notes are senior obligations of the Company and rank pari
passu in right and priority of payment with all existing and future senior
indebtedness of the Company.

     Proposed Credit Facility. The Company is negotiating an agreement with
Banque Paribas providing for a $25 million senior secured revolving credit
facility. The revolving credit facility is expected to have a term of not less
than three years. The Company expects that borrowings under the facility will
bear interest, at the Company's option, at LIBOR plus a margin of 2.75% or
Citibank's base rate plus a margin of 1.00%; provided, however, that the
applicable 



                                       12
<PAGE>   14
 margins for both LIBOR and base rate loans will increase by 1.25% under certain
circumstances. An annual commitment fee of 0.50% is expected to be payable on
the unused available portion of the facility. In addition, the Company expects
to pay a customary underwriting fee and other expenses in connection with the
facility. The Company expects that the facility will be secured by certain
assets of the Company, including the stock of certain of the Company's
Subsidiaries and that the facility will contain certain restrictive convenants
which impose limitations on the Company and its Subsidiaries, with respect to,
among other things, (i) the creation of liens, (ii) mergers, acquisitions or
disposition of assets, (iii) incurrence of indebtedness, (iv) transactions with
affiliates, (v) sale-leaseback transactions and (vi) dividends and other
restricted payments. The credit facility is expected also require the Company to
maintain a minimum current ratio, a minimum tangible net worth, and a minimum
debt coverage ratio. The credit facility is expected to contain customary events
of default provisions. While it is anticipated that the credit facility will be
completed in the fourth quarter of 1998, no assurance can be made that the
credit facility will be completed on the terms set forth above or on terms
acceptable to the Company.


     Year 2000 Disclosure

     The "Year 2000 Issue" is a general term used to refer to certain business
implications of the arrival of the new millennium. In simple terms, on January
1, 2000, all hardware and software systems which use the two-digit convention
could fail completely or create erroneous data as a result of the system failing
to recognize the two digit internal date "00" as representing the Year 2000.

     The Company does not believe that its internal systems and operations have
any material issues with respect to Year 2000 compliance and does not anticipate
incurring significant remediation costs, if any. The Company has only been
formed in the last three years and is engaged solely in the exploration,
development and production of oil and natural gas in Colombia. As such, the
Company engages in few transactions and relies minimally on the hardware and
software systems of third parties. Further, the Company's hardware and software
systems are all new and widely utilized and the Company has been advised that
all of these systems are Year 2000 compliant. The Company's internal dependence
on information systems and other operating equipment that could potentially
require remedial action to become Year 2000 compliant is low. Accordingly, the
risk of operation disruptions and the corresponding risk of liability for
disruptions caused by non-Year 2000 compliant systems are not of major concern
to the Company.

     One of the next phases in the development of Emerald Mountain is the
transportation and marketing of crude oil to be produced from the Company's
properties. This project will be completed in two phases, with Phase I scheduled
for completion in mid-to-late 1999 and Phase II to be commenced thereafter and
completed mid-2000. The Company is engaged in negotiations with oil pipeline,
construction and engineering firms to construct its processing, storage and
related facilities and a 36-mile pipeline from Emerald Mountain to the existing
Oleoductos Alto Magdalena ("OAM") pipeline, which terminates at Vasconia. The
Company's current Phase II pipeline construction plans would bypass the OAM
pipeline with a direct link from Emerald Mountain to Vasconia. Beyond Vasconia,
the Company's oil production may be routed through two existing pipeline
systems, Oleoducto de Colombia ("ODC") and Oleoducto Central S.A. ("OCENSA").
The Company has retained Brown & Root Energy Services and Technivance Brown &
Root S.A., subsidiaries of Halliburton Company, to conduct planning and
engineering studies for its planned pipeline and associated compression
facilities from Emerald Mountain, and intends that the technology employed in
its own delivery systems will be Year 2000 compliant. The Company has also asked
these consultants to review any Year 2000 risks associated with the planned
interconnection of its delivery systems in conjunction with the OAM, ODC and
OCENSA pipelines, and is reviewing the OAM delivery systems in conjunction with
its current negotiations with the operator of that pipeline. The Company or the
consultants will review and, where necessary, rectify, the Year 2000 risks
associated with Phase I prior to any interconnection with the OAM, ODC, and
OCENSA pipelines. The Company is not currently aware of Year 2000 limitations
affecting the computer systems that control these third party pipeline systems
that would compromise the operation of such systems. Moreover, the Company would
not be responsible for remediation costs associated with such computer systems
should any technical problems arise. However, in the event a pipeline was
rendered inoperable as a result of Year 2000 issues affecting its operating
systems, the Company may be required to rely on less efficient alternate
delivery systems, such as tanker trucks, to transport any oil production to
market.


                                       13
<PAGE>   15

     As the Company develops its infrastructure at Emerald Mountain as part of
the Phase I and Phase II programs, it will continue to monitor Year 2000
compliance issues as they relate to equipment supplied by its vendors and
contractors. Since the Company does not currently supply significant oil
production to its customers, and no supply contracts have been entered into in
respect of Emerald Mountain production, the Company is unable to assess the
significance of Year 2000 issues affecting potential customers at this stage in
its operations.


                 DISCLOSURE REGARDING FORWARD LOOKING STATEMENTS

     This Quarterly Report on Form 10-Q includes "forward-looking statements"
within the meaning of Section 27A of the Securities Act of 1934, as amended (the
"Securities Act"). All statements other than statements of historical fact
included in this Form 10-Q, including without limitation, statements under
"Management's Discussion and Analysis of Financial Condition and Results of
Operations" regarding the planned capital expenditures, drilling activities, the
Company's financial position, business strategy, and other plans and objectives
for future operations, are forward-looking statements. Although the Company
believes that the expectations reflected in such forward-looking statements are
reasonable, it can give no assurance that such expectations will prove to have
been correct.

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET RISK

     Not applicable.

PART II. OTHER INFORMATION

Item 6.  Exhibits and Reports on 8-K

     (a)  Exhibits

          27 Financial Data Schedule

     (b)  Reports on From 8-K

          None

                                            SIGNATURES

                                            Seven Seas Petroleum Inc.
Date:  November 16, 1998                By: Herbert C. Williamson, III
                                            Executive Vice President and 
                                            Chief Financial Officer

                                            Ray A. Housley
                                            Treasurer and Controller



                                       14
<PAGE>   16

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT NO.                   DESCRIPTION
-----------                   -----------
<S>                 <C>
   27               Financial Data Schedule
</TABLE>