<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 March 31, 1998

                                       or

[ ]   TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
      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 960, THREE POST OAK CENTRAL
          1990 POST OAK BOULEVARD
              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 MAY 4, 1998 THERE WERE 35,226,606 SHARES OF THE REGISTRANT'S COMMON
SHARES, NO PAR VALUE PER SHARE, OUTSTANDING.






<PAGE>   2


                                     INDEX

<TABLE>
<CAPTION>
                                                                                             PAGE
<S>      <C>                                                                                  <C>
PART I.  FINANCIAL INFORMATION
         (DEVELOPMENT STAGE ENTERPRISE)

         Item 1.  Condensed Consolidated Balance Sheets as of March 31, 1998 (unaudited)
                  and December 31, 1997....................................................... 2

                  Condensed Statements of Consolidated Operations and Accumulated Deficit
                  for the three months ended March 31, 1998 and 1997 and the Cumulative Total
                  from Inception (February 3, 1995 to March 31, 1998 (unaudited).............. 3

                  Condensed Consolidated Statements Cash Flows for the three months ended
                  March 31, 1998 and 1997 and the Cumulative Total from
                  Inception (February 3, 1995) to March 31, 1998 (unaudited).................. 4

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

         Item 2.  Management's Discussion and Analysis of Financial Condition and
                  Results of Development Stage Operations..................................... 7

         Item 3.  Quantitative and Qualitative Disclosures about Market Risk..................10

PART II. OTHER INFORMATION....................................................................10

         Item 1.  Legal Proceedings...........................................................10

         Item 2.  Changes in Securities.......................................................10

         Item 3.  Defaults upon Senior Notes..................................................10

         Item 4.  Submission of Matters to a Vote of Security Holders.........................10

         Item 5.  Other Information...........................................................10

         Item 6.  Exhibits and Reports on Form 8-K............................................10
</TABLE>



                                       1


<PAGE>   3
                     SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                          (A DEVELOPMENT STAGE ENTERPRISE)
                        CONDENSED CONSOLIDATED BALANCE SHEETS
                        (IN THOUSANDS, EXCEPT SHARE AMOUNTS)


<TABLE>
<CAPTION>
                                                                                     MARCH 31,       DECEMBER 31,
                                                                                      1998              1997
                                                                                    ----------       ------------
ASSETS                                                                             (Unaudited)
<S>                                                                                  <C>               <C>      
CURRENT
     Cash and cash equivalents                                                       $   8,725         $  18,067
     Marketable securities                                                                --                  44
     Accounts receivable                                                                 3,802             3,865
     Prepaids and other                                                                    109               118
                                                                                     ---------         ---------
                                                                                        12,636            22,094

Note receivable from related party                                                         200               200
Land                                                                                       441              --
Evaluated oil and gas interests, full-cost method                                       47,652            46,117
Unevaluated oil and gas interests, full-cost method                                    229,338           221,713
Fixed assets, net of accumulated depreciation of $61 at March 31, 1998                     333               304
     and $43 at December 31, 1997
Other assets, net of accumulated amortization of $260
     at March 31, 1998 and $194 at December 31, 1997                                     1,420             1,486
                                                                                     ---------         ---------
TOTAL ASSETS                                                                         $ 292,020         $ 291,914
                                                                                     ---------         ---------

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT
     Accounts payable                                                                $   5,497         $   6,885
     Accrued compensation                                                                  659             1,228
     Interest payable                                                                      375              --
     Other accrued liabilities                                                            --                  92
                                                                                     ---------         ---------
                                                                                         6,531             8,205

Long-term debt                                                                          25,000            25,000
Deferred income taxes                                                                   70,459            70,459
Minority interest                                                                        5,297             4,087

STOCKHOLDERS' EQUITY
Share capital -
   Authorized unlimited common shares without par value and unlimited Class A
   preferred shares without par value; 35,226,606 and 35,071,606 issued and
   outstanding common shares at March 31, 1998 and December 31, 1997, 
   respectively                                                                        198,091           196,406

Deficit accumulated during development stage                                           (13,358)          (12,243)

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

Total Stockholders' Equity                                                             184,733           184,163
                                                                                     ---------         ---------

TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                           $ 292,020         $ 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)
    CONDENSED STATEMENTS OF CONSOLIDATED OPERATIONS AND ACCUMULATED DEFICIT
                      (IN THOUSANDS, EXCEPT SHARE AMOUNTS)
                                   (Unaudited)


<TABLE>
<CAPTION>
                                                                                                                   CUMULATIVE TOTAL
                                                                                                                    FROM INCEPTION
                                                                               THREE MONTHS ENDED MARCH 31,       (FEBRUARY 3, 1995)
                                                                               ----------------------------            TO MARCH 31,
                                                                                 1998                 1997                1998
                                                                                 ----                 ----                ----
<S>                                                                        <C>                  <C>                  <C>         
REVENUE
    Crude oil sales                                                        $       --           $        319         $      1,013
    Interest income                                                                 184                  114                1,465
                                                                           ------------         ------------         ------------
                                                                                    184                  433                2,478

EXPENSES
    General and administrative                                                    1,120                  917               13,360
    Lease operating expenses                                                        188                  230                1,348
    Depreciation and amortization                                                    84                   20                  381
    Dry hole and abandonment costs                                                 --                     17                1,145
    Geological and geophysical                                                     --                      9                   47
    Other (income) expense                                                          (30)                --                    (55)
    Loss on sale of resource properties                                            --                   --                     31
                                                                           ------------         ------------         ------------
                                                                                  1,362                1,193               16,257

NET LOSS BEFORE INCOME TAXES                                                     (1,178)                (760)             (13,779)

INCOME TAX EXPENSE                                                                   15                 --                     15

NET LOSS BEFORE MINORITY INTEREST                                                (1,193)                (760)             (13,794)

MINORITY INTEREST                                                                    78                   38                  436
                                                                           ------------         ------------         ------------

NET LOSS                                                                   $     (1,115)        $       (722)        $    (13,358)
                                                                           ============         ============         ============

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

DEFICIT ACCUMULATED DURING THE DEVELOPMENT STAGE, END OF PERIOD            $    (13,358)        $     (5,037)        $    (13,358)
                                                                           ============         ============         ============

BASIC AND DILUTED NET LOSS PER COMMON SHARE                                $      (0.03)        $      (0.03)        $      (0.67)
                                                                           ============         ============         ============

WEIGHTED AVERAGE COMMON SHARES OUTSTANDING                                   35,126,162           25,245,027           19,812,121
                                                                           ============         ============         ============
</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)
                CONDENSED STATEMENTS OF CONSOLIDATED CASH FLOWS
                                (IN THOUSANDS)
                                  (Unaudited)
                                       

<TABLE>
<CAPTION>
                                                                                                       CUMULATIVE TOTAL
                                                                                                        FROM INCEPTION
                                                                        THREE MONTHS ENDED MARCH 31,  (FEBRUARY 3, 1995)
                                                                        ----------------------------      TO MARCH 31,
                                                                            1998             1997             1998
                                                                          --------         --------         --------
<S>                                                                       <C>              <C>              <C>      
OPERATING ACTIVITIES
     Net loss                                                             $ (1,115)        $   (722)        $(13,358)
     Add (subtract) items not requiring (providing) cash:
     Compensation expense                                                     --               --              2,140
     Minority interest                                                         (78)            --               (436)
     Common stock contribution to 401(k) retirement plan                      --               --                 79
     Dry hole and abandonment costs                                           --                  3            1,140
     Gain on sale of marketable securities                                      (6)            --                 (6)
     Loss on sale of resource properties                                      --               --                 31
     Depreciation and amortization                                              84               18              381
     Changes in working capital excluding changes to cash and cash
     equivalents:
        Accounts receivable                                                   (478)             (30)          (2,920)
        Prepaids and other, net                                                  9               (1)            (109)
        Accounts payable                                                      (427)            (904)           1,065
       Other accrued liabilities                                               (92)            --               --
                                                                          --------         --------         --------
Cash Flow Used in Operating Activities                                      (2,103)          (1,636)         (11,993)
                                                                          --------         --------         --------
INVESTING ACTIVITIES
     Exploration of oil and gas properties                                  (9,746)          (1,169)         (32,112)
     Purchase of land                                                         (441)            --               (441)
     Proceeds from acquisition                                                --                 12              630
     Proceeds from sale of property                                           --               --                 84
     Proceeds from sale of marketable securities                                50                                50
     Note receivable from related party                                       --               --               (200)
     Other asset additions                                                     (47)             (27)            (561)
                                                                          --------         --------         --------
Cash Flow Used in Investing Activities                                     (10,184)          (1,184)         (32,550)
                                                                          --------         --------         --------
FINANCING ACTIVITIES
     Proceeds from special warrants issued                                    --               --             12,109
     Proceeds from share capital issued                                      1,116            3,549           12,610
     Proceeds from additional paid-in capital contributed                     --               --                  1
     Proceeds from issuance of special notes                                  --               --             25,000
     Costs of issuing special notes                                           --               --             (1,573)
     Contributions by minority interest                                      1,829              288            5,121
     Purchase of treasury stock                                               --               --               --
                                                                          --------         --------         --------
Cash Flow Provided by Financing Activities                                   2,945            3,837           53,268
                                                                          --------         --------         --------
NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                        (9,342)           1,017            8,725
Cash and cash equivalents, beginning of period                              18,067           10,620             --
                                                                          --------         --------         --------
CASH AND CASH EQUIVALENTS, END OF PERIOD                                  $  8,725         $ 11,637         $  8,725
                                                                          ========         ========         ========
</TABLE>


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.    BASIS OF PRESENTATION

     The accompanying unaudited, condensed consolidated financial statements
include the accounts of Seven Seas Petroleum Inc. and it 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 the GAAP for complete financial statements. In the opinion of
management, all adjustment, 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 condensed financial statements included herein should be read
in conjunction with the audited financial statements and notes thereto included
in the Company's Annual Report on Form 10-K for the year ended December 31,
1997.

     Seven Seas Petroleum Inc. (a Yukon Territory, Canada corporation) was
formed on February 3, 1995. Seven Seas is a development stage enterprise
engaging in 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
exploratory wells have been drilled and 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.
Currently two additional wells are drilling or completing and one well has been
drilled and temporarily abandoned pending potential sidetrack operations or
re-drilling. 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, and
intends to continue to acquire, interests in properties outside of North
America, in some cases in countries that may be considered politically and
economically unstable.

2.    SUBSEQUENT EVENT

     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.


                                       5
<PAGE>   7

     The Notes will represent senior obligations of the Company, ranking pari
passu in right and priority of payment with all existing and future senior
indebtedness and senior in right and priority of payment to all indebtedness
that is expressly subordinated to the Notes.

     In accordance with the terms of the Notes, the Company purchased $13.5
million of U.S. Government Securities from the proceeds of the Notes and
deposited such securities in a segregated account in an amount that will be
sufficient to provide for payment of the first two scheduled interest payments.
Additionally, the Company purchased and pledged to the Bank of Nova Scotia Trust
Company New York, the Trustee, as security for the benefit of the holders of the
Notes, U.S. Government Securities in an amount that will be sufficient to
provide payment of the four scheduled interest payments on the Notes from
November 15, 1999 through May 15, 2001.

     Banque Paribas has provided a commitment letter (the "Commitment Letter")
pursuant to which Banque Paribas has agreed to provide a $25 million senior
secured revolving credit facility. The Commitment Letter provides that the
revolving credit facility will have a term of three years. 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%. The amount available
under the facility will be subject to periodic redetermination based on the
value of the Company's reserves. A commitment fee of 0.50% is payable on the
unused portion of the facility. In addition, the indebtedness under the credit
facility will be guaranteed, subject to funding, by certain of the Company's
Subsidiaries. The facility will be secured by certain assets of the Company and
certain of its subsidiaries, including the stock of certain of the Company's
Subsidiaries, intercompany notes, equipment, inventory, contract rights, and a
collateral account that will include proceeds of sales of production under the
Association Contracts. The facility will also contain certain restrictive
covenants which impose limitations on the Company and its Subsidiaries, with
respect to, among other things, (i) 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 will also require
the company to maintain a minimum current ratio, a minimum tangible net working
capital, and a minimum debt coverage ratio. The credit facility will contain
customary events of default. No assurance can be made that the credit facility
will be completed on the terms set forth in the Commitment Letter or on terms
acceptable to the Company prior to the time additional funds are required by
the Company.

3.    RECENTLY ISSUED ACCOUNTING PRONOUNCEMENTS

      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".

      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.

     SOP 98-5 provides guidance on the accounting for start up costs and
organization costs, and must be adopted for fiscal years beginning after
December 15, 1998. At adoption, the Company will be required to record the
cumulative effect 


                                       6
<PAGE>   8

of a change in accounting principle to write off any unamortized start up or
organization costs remaining on the balance sheet. The Company plans to adopt
the SOP in the first quarter of 1999.

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 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. 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 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 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. Until commercial production is initiated, the
Company expects that the working interest owners will fund all costs associated
with the initiation of commercial production and that, upon such initiation,
Ecopetrol's 50% share of such costs will be repaid through proceeds from their
share of production.

         To date, all oil produced has been from production testing on Emerald
Mountain. Upon Ecopetrol's acceptance of commerciality of the Company's
discovery, oil produced from the Dindal and Rio Seco contract areas may be sold
to Ecopetrol or to third parties. 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

     Accounting Principles. The Consolidated Financial Statements and Notes
thereto included herein have been prepared in accordance with generally
accepted accounting principles in the United States ("US GAAP"). As a
consequence of being a "reporting issuer" under Canadian Securities laws and
the Company's listing on the Toronto Stock Exchange, the Company is required to
file a quarterly report with the Ontario Securities Commission with its
Consolidated Interim Financial Statements, prepared in accordance with Canadian
generally accepted accounting principles ("Canadian GAAP"). The Consolidated
Interim Financial Statements prepared in accordance with Canadian GAAP do not
require certain entries discussed below or development stage presentation made
in accordance with US GAAP. The Company recorded deferred income tax
liabilities relating to the acquisitions of GHK Company Colombia, Esmeralda
LLC, and 62.963% of Cimarrona LLC in 1996 and Petrolinson, S.A. on March 5,
1997 pursuant to US GAAP. The credit to deferred income tax liabilities and the
corresponding increase in unevaluated oil and gas interests amounted to $70.5
million as of December 31, 1997. The liabilities for deferred income taxes
recorded in 1997 would not be required by Canadian GAAP. 



                                      7
<PAGE>   9

RESULTS OF DEVELOPMENT STAGE OPERATIONS

     To date, oil revenues and lease 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
$0.3 million for the quarter ended March 31, 1998 and 1997, respectively. Lease
operating expenses were $0.2 and $0.2 million for the quarter ended March 31,
1998 and 1997, respectively. The 1998 lease operating expenses represent such
costs as tank rentals and other miscellaneous fixed costs.

     Interest income was $0.2 million for the quarter ended March 31, 1998 as
compared to $0.1 million for the same period in 1997. The increase was the
consequence of higher cash balances resulting from the private placements of
the Company's securities.

     General and administrative costs under US GAAP were $1.1 million during
the three months ended March 31, 1998 as compared to $0.9 million during the
same period of 1997. The increase was primarily attributable to the expansion
of the Company's operating activities and additions to its professional staff
in the U. S. and Colombia.

     Depreciation and amortization was $0.1 and zero for the quarter ended
March 31,1998 and 1997, respectively. The increase was primarily attributable
to the amortization of costs incurred in issuing the Special Notes in August
1997 (see "Liquidity and Capital Resources" below). As of March 31, 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 $1.1 million and $0.7 million for the
three months ended March 31, 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 March 31,
1998, resulting in aggregate cash proceeds of $48.1 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 March 31, 1998, the
Company had capital expenditures of $32.6 million for the acquisition,
exploration, and development of its oil and gas properties including $30.5
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 12.5% senior notes in a
private transaction. Net proceeds available to the Company for its capital
expenditures and other general corporate purposes are approximately $68.7
million.

     The Company's primary capital commitments include Phases I and II of its
development program. The Company's capital expenditures estimated for Phase I
include $16.2 million for field development and delineation and $60.7 million
for pipeline and production facilities. The Company's capital expenditures
estimated for Phase II include $65.2 million for field development and
delineation and $89.0 million for pipeline and production facilities. The
Company has working capital of $6.1 million as of March 31, 1998. The Company
may finance its operations and investments through the issuance of public and
private debt, equity, and convertible securities, as well as through commercial
banking credit facilities. However, there can be no assurance that debt or
equity financing will be available to the Company on economically acceptable
terms. If sufficient funds are not available to meet the Company's obligations
with respect to a property, the Company may elect to forfeit its interest in
such property. The Company does not anticipate that it will forfeit its
interest in such property. The Company believes that the proceeds of the 12.5%
senior notes will enable it to fund its operations and investments attributable
to the first phase of its Emerald Mountain development program.

     Colombia. During the remainder of 1998, the Company plans to drill a total
of seven additional 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 $62.2 million. The pipeline is scheduled for
completion in mid-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. Subsequent 


                                       8
<PAGE>   10
to March 31, 1998, drilling activity on the exploratory well was completed;
however, testing of potential production intervals have been suspended due to
risk of flooding caused by heavy rain. Testing is expected to resume in the
fourth quarter of 1998.

     For the three months ended March 31, 1998 and March 31, 1997, the Company
had oil sales of zero and $0.3 million, respectively, solely from production
testing of the Company's wells on Emerald Mountain. Although the Company intends
to continue to sell oil resulting from production tests, significant production
is not expected until further evaluation and 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 is now proceeding. Completion
of the first phase of these facilities is scheduled to occur in 1999.

     Australia and Papua New Guinea. The Company is in the process of
eliminating any mandatory capital commitments outside of Colombia. In Papua New
Guinea, the Company entered into a farm-out agreement with ARCO Papua New
Guinea Inc. ("Arco") whereby Arco will fund the Company's obligation for the
twelve month period ended July 1998 for an 80% interest in the subject
exploration permit. In future periods, the Company has no obligation to expend
funds but may be subject to a forfeiture of its interest should the Company
decide not to continue to fund its remaining 20% interest. In the Western Perth
Basin in Australia, the Company has signed a purchase and sale agreement with
Forcenergy International Inc. in which the Company will exchange its 11.77%
working interest for $0.9 million. The Company will retain a small overriding
interest and will also be reimbursed $0.3 million for certain capital
expenditures. The agreement is pending its final approval by an aboriginal
council in West Australia. In the Bass Strait Basin in Australia, the Company
is seeking to farm-out its interests. The Company has no required capital
commitments for this prospect.

     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 is
payable in arrears at a rate of 6% per annum on December 31 and June 30 in each
year until maturity, commencing on December 31, 1997.

     The Special Notes are exchangeable for a like principal amount of
convertible redeemable debentures (the "Convertible Debentures") on the earlier
occurring of (i) the effectiveness of a registration statement under the
Securities Act of 1933 as Amended covering the resale of the Convertible
Debentures and compliance with certain Canadian securities requirements, or (ii)
August 7, 1998. The Convertible Debentures are convertible into Units totaling
2,173,913 common shares and warrants exercisable for 1,086,957 common shares.
Each warrant is exercisable for one common share at an exercise price of $15 and
expire on August 7, 1998. Upon exercise of all of the warrants, the Company will
receive proceeds of $16 million. The Convertible Debentures are convertible into
common shares at the option of the Company if a registration statement of the
common shares has been declared effective under the Securities Act and has been
effective during the seven day notice period required to be given by the Company
to the holders of the Convertible Debentures of its intent to exercise its
conversion rights, provided that the Company's shares have traded at or above
U.S. $14.00 per share for 20 consecutive trading days on the Toronto Stock
Exchange. The Special Notes and Debentures are secured by a pledge of shares of
certain of the subsidiaries of the Company and are guaranteed by Seven Seas
Petroleum Holdings Inc.

     The Company filed a registration statement on April 24, 1998, registering
(i) up to 2,173,913 common shares (the "Shares"), (ii) up to 1,086,957 warrants
of the Company exercisable for one common share at an exercise price of $15 per
share (the "Warrants"), and (iii) 1,086,957 common shares issuable upon exercise
of the warrants (the "Warrant Shares"). The Shares and Warrants are issuable as
a unit upon the conversion of up to $25 million aggregate principal amount of
the Convertible Debentures. Pursuant to the terms of the Offering, the Company
has agreed to keep such registration statement effective for a period of two
years.

                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 



                                    9
<PAGE>   11
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 1.  Legal Proceedings

     Petrolinson, S.A. and GHK Company Colombia (two of the Company's
subsidiaries), along with Norman Rowlinson (the former owner of Petrolinson,
S.A.) and heirs of Howard Thomas Corrigan, are defendants in a lawsuit recently
filed in the civil circuit court of Santa Fe de Bogota, Colombia by the heirs
of Nicolas Beltran Franco alleging that (i) a de facto company existed between
Nicolas Beltran Franco and the defendants with regards to the exploration and
production of the Dindal and Rio Seco contract areas and that (ii) prior to the
execution of the Dindal and Rio Seco Association Contracts the de facto company
conducted exploration works in the Dindal and Rio Seco contract areas. Despite
the fact that none of the plaintiffs is a party to the Association Contracts,
the plaintiffs are seeking 50% of the income generated by the alleged de facto
company. It is unclear from statements made in the lawsuit, however, what
percentage of the Dindal and Rio Seco contract areas might be covered by the
plaintiff's claims made through the alleged de facto company.

     As the Company has just been notified of the lawsuit, the Company's
investigation of claims made by the plaintiffs is in the early stages; however,
the Company believes that this lawsuit is without merit and intends to defend
the lawsuit vigorously. The Company believes that the outcome of this lawsuit
will not have a material adverse effect on the Company. The Company's Colombian
counsel, Raisbeck, Lara, Rodriguez & Rueda, members of the law firm of Baker &
McKenzie, based on their review of the matter to date, are of the opinion that
if the above-described claim is litigated to its conclusion it is remote that
the plaintiffs in such lawsuit would succeed on the merits of their claim.

Item 2.  Changes in Securities

     None.

Item 3.  Defaults 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 8-K

     (a) Exhibits:

  No.         Exhibit Document
  ---         ----------------




                                      10
<PAGE>   12


  (3)                Articles of Incorporation and By-laws

              *(A)   The Amalgamation Agreement effective June 29, 1995
                     by and between Seven Seas Petroleum Inc., a British
                     Columbia corporation; and Rusty Lake Resources Ltd.

              *(B)   Certificate of Continuance and Articles of Continuance into
                     the Yukon Territory

              *(C)   By-Laws

  (4)                Instruments defining the rights of security holders,
                     including indentures

              *(A)   Excerpts from the Articles of Continuance

              *(B)   Excerpts from the By-laws

              *(C)   Specimen stock certificate

              *(D)   Form of Class B Warrant

              *(E)   Class B Warrant Indenture dated as of October 15,
                     1996 by and between the Company of Canada and
                     Montreal Trust Company

  (10)               Material Contracts

              *(A)   Agreement dated August 14, 1995 by and between the
                     Company and GHK Company Colombia, as amended by
                     letter agreement dated November 30, 1995

              *(B)   The Association Contract by and between Ecopetrol, GHK
                     Company Colombia and Petrolinson, S.A. relating to the
                     Dindal block, as amended

              *(C)   The Association Contract by and between Ecopetrol and GHK 
                     Company Colombia relating to the Rio Seco block

              *(D)   Joint Operating Agreement dated as of August 1, 1994 by and
                     between GHK Company Colombia and the holders of interests 
                     in the Dindal block

              *(E)   The GHK Company Colombia Share Purchase Agreement dated as
                     of July 26, 1996 by and between Robert A. Hefner III, Seven
                     Seas Petroleum Colombia Inc. and the Company

              *(F)   The Cimarrona Purchase Agreement dated as of July 26, 1996
                     by and between the members of Cimarrona Limited Liability
                     Company, the Company, Seven Seas Petroleum Colombia Inc.,
                     and Robert A. Hefner III



                                      11
<PAGE>   13

              *(G)   The Esmeralda Purchase Agreement dated as of July 26, 1996
                     by and between the members of Esmeralda Limited Liability
                     Company, Robert A. Hefner III, the Company, Seven Seas
                     Petroleum Holdings, Inc. and Seven Seas Petroleum Colombia
                     Inc.

              *(H)   The Registration Rights Agreement dated as of July 26, 1996
                     by and between the Company and certain individuals

              *(I)   Shareholders' Voting Support Agreement dated as of July 26,
                     1996 by and between Seven Seas Petroleum  Inc. and Messrs.
                     Hefner, Kerr, Whitehead, Plewes and Stephens

              *(J)   Management Services Agreement by and among GHK Company
                     Colombia, the Company and The GHK Company LLC

              *(K)   The Escrow Agreement for a Natural Resources Company by and
                     among Montreal Trust Company as trustee, the Company and
                     certain individuals and entities

              *(L)   The Escrow Agreement for a Natural Resources Company by and
                     among Montreal Trust Company, as trustee, the Company and
                     Albert E. Whitehead

              *(M)   Amended 1996 Stock Option Plan

              *(N)   Form of Incentive Stock Option Agreement

              *(O)   Form of Directors' Stock Option Agreement

              *(P)   Form of Employment Agreement between the Company and each 
                     of Messrs. Stephens, Dorrier and DeCort

              *(Q)   Form of Agreement between the Company and each of Messrs.
                     Stephens, Dorrier and DeCort relating to a change of 
                     control

              *(R)   Form of Employment Agreement between the Company and
                     Larry A. Ray

              *(S)   Settlement Agreement between the Company and Mr. Whitehead
                     dated May 20, 1997

              *(T)   Petrolinson S.A. Share Purchase Agreement dated February 
                     14,  1997,  between Hazel Ventures LTD., Seven Seas 
                     Petroleum Colombia Inc. and Seven Seas Petroleum Inc.

              *(U)   Pledge Agreement dated March 5, 1997 among Hazel Ventures 
                     LTD., Seven Seas Petroleum Inc., Seven Seas Petroleum 
                     Colombia Inc., and Integro Trust (BVI Limited)

              *(V)   Shareholder Voting Support Agreement made as of March 5, 
                     1997 between Seven Seas Petroleum Inc. and Hazel Ventures 
                     LTD.

              *(W)   Purchase Warrant Indenture made as of August 7, 1997 
                     between Seven Seas Petroleum Inc. and Montreal Trust 
                     Company of Canada


                                      12
<PAGE>   14

              *(X)   Indenture made as of August 7, 1997 between Seven Seas 
                     Petroleum  Inc. and Montreal Trust Company of Canada

              *(Y)   Limited Recourse Guarantee, Security and Pledge Agreement  
                     made as of August 7, 1997 between Seven Seas Petroleum 
                     Holdings Inc. and Montreal Trust Company of Canada

              *(Z)   Limited Recourse Guarantee, Security and Pledge Agreement  
                     made as of August 7, 1997 between Seven Seas Petroleum 
                     Colombia Inc. and Montreal Trust Company of Canada

              *(AA)  Private Placement Subscription Agreement made as of August 
                     7, 1997 between Seven Seas Petroleum Inc. and Jasopt Pty 
                     Limited

              *(BB)  1997 Stock Option Plan

             **(CC)  English Translation of the Rosablanca Association Contract
                     between Empresa Colombiana De Petroleos and Seven Seas 
                     Petroleum Colombia

             **(DD)  English Translation of the Montecristo Association Contract
                     between Empresa Colombiana De Petroleos and Seven Seas 
                     Petroleum Colombia

*(22)  Subsidiaries of the Registrant

 (27)  Financial Data Schedule


 *   Incorporated herein by reference to Exhibit on like registration on Form 10
     (File No. 022483)

**   Incorporated  herein by reference from Annual Report on Form 10-K/A for the
     year ended  December 31, 1997 (Commission File No. 022483)

       (b)  Reports on Form 8-K

              None



                                       13
<PAGE>   15

                                   SIGNATURES


                                                 Seven Seas Petroleum Inc.
Date:  May 15, 1998                        By:   Herbert C. Williamson, III
                                                 Executive Vice President and 
                                                 Chief Financial Officer

                                                 Ray A. Housley
                                                 Treasurer and Controller



                                       14
<PAGE>   16
                                 EXHIBIT INDEX


  No.         Exhibit Document
  ---         ----------------

  (3)                Articles of Incorporation and By-laws

              *(A)   The Amalgamation Agreement effective June 29, 1995
                     by and between Seven Seas Petroleum Inc., a British
                     Columbia corporation; and Rusty Lake Resources Ltd.

              *(B)   Certificate of Continuance and Articles of Continuance into
                     the Yukon Territory

              *(C)   By-Laws

  (4)                Instruments defining the rights of security holders,
                     including indentures

              *(A)   Excerpts from the Articles of Continuance

              *(B)   Excerpts from the By-laws

              *(C)   Specimen stock certificate

              *(D)   Form of Class B Warrant

              *(E)   Class B Warrant Indenture dated as of October 15,
                     1996 by and between the Company of Canada and
                     Montreal Trust Company



<PAGE>   17


  (10)               Material Contracts

              *(A)   Agreement dated August 14, 1995 by and between the
                     Company and GHK Company Colombia, as amended by
                     letter agreement dated November 30, 1995

              *(B)   The Association Contract by  and between Ecopetrol, GHK
                     Company Colombia and Petrolinson, S.A. relating to the
                     Dindal block, as amended

              *(C)   The Association Contract by and between Ecopetrol and GHK 
                     Company Colombia relating to the Rio Seco block

              *(D)   Joint Operating Agreement dated as of August 1, 1994 by and
                     between GHK Company Colombia and the holders of interests 
                     in the Dindal block

              *(E)   The GHK Company Colombia Share Purchase Agreement dated as
                     of July 26, 1996 by and between Robert A. Hefner III, Seven
                     Seas Petroleum Colombia Inc. and the Company

              *(F)   The Cimarrona Purchase Agreement dated as of July 26, 1996
                     by and between the members of Cimarrona Limited Liability
                     Company, the Company, Seven Seas Petroleum Colombia Inc.,
                     and Robert A. Hefner III

              *(G)   The Esmeralda Purchase Agreement dated as of July 26, 1996
                     by and between the members of Esmeralda Limited Liability
                     Company, Robert A. Hefner III, the Company, Seven Seas
                     Petroleum Holdings, Inc. and Seven Seas Petroleum Colombia
                     Inc.

              *(H)   The Registration Rights Agreement dated as of July 26, 1996
                     by and between the Company and certain individuals

              *(I)   Shareholders' Voting Support Agreement dated as of July 26,
                     1996 by and between Seven Seas Petroleum  Inc. and Messrs.
                     Hefner, Kerr, Whitehead, Plewes and Stephens

              *(J)   Management Services Agreement by and among GHK Company
                     Colombia, the Company and The GHK Company LLC

              *(K)   The Escrow Agreement for a Natural Resources Company by and
                     among Montreal Trust Company as trustee, the Company and
                     certain individuals and entities

              *(L)   The Escrow Agreement for a Natural Resources Company by and
                     among Montreal Trust Company, as trustee, the Company and
                     Albert E. Whitehead
<PAGE>   18

              *(M)   Amended 1996 Stock Option Plan

              *(N)   Form of Incentive Stock Option Agreement

              *(O)   Form of Directors' Stock Option Agreement

              *(P)   Form of Employment Agreement between the Company and each 
                     of Messrs. Stephens, Dorrier and DeCort

              *(Q)   Form of Agreement between the Company and each of Messrs.
                     Stephens, Dorrier and DeCort relating to a change of 
                     control

              *(R)   Form of Employment Agreement between the Company and
                     Larry A. Ray

              *(S)   Settlement Agreement between the Company and Mr. Whitehead
                     dated May 20, 1997

              *(T)   Petrolinson S.A. Share Purchase Agreement dated February 
                     14,  1997,  between Hazel Ventures LTD., Seven Seas 
                     Petroleum Colombia Inc. and Seven Seas Petroleum Inc.

              *(U)   Pledge Agreement dated March 5, 1997 among Hazel Ventures 
                     LTD., Seven Seas Petroleum Inc., Seven Seas Petroleum 
                     Colombia Inc., and Integro Trust (BVI Limited)

              *(V)   Shareholder Voting Support Agreement made as of March 5, 
                     1997 between Seven Seas Petroleum Inc. and Hazel Ventures 
                     LTD.

              *(W)   Purchase Warrant Indenture made as of August 7, 1997 
                     between Seven Seas Petroleum Inc. and Montreal Trust 
                     Company of Canada

              *(X)   Indenture made as of August 7, 1997 between Seven Seas 
                     Petroleum  Inc. and Montreal Trust Company of Canada

              *(Y)   Limited Recourse Guarantee, Security and Pledge Agreement  
                     made as of August 7, 1997 between Seven Seas Petroleum 
                     Holdings Inc. and Montreal Trust Company of Canada

              *(Z)   Limited Recourse Guarantee, Security and Pledge Agreement  
                     made as of August 7, 1997 between Seven Seas Petroleum 
                     Colombia Inc. and Montreal Trust Company of Canada

              *(AA)  Private Placement Subscription Agreement made as of August 
                     7, 1997 between Seven Seas Petroleum Inc. and Jasopt Pty 
                     Limited

              *(BB)  1997 Stock Option Plan

             **(CC)  English Translation of the Rosablanca Association Contract
                     between Empresa Colombiana De Petroleos and Seven Seas 
                     Petroleum Colombia

             **(DD)  English Translation of the Montecristo Association Contract
                     between Empresa Colombiana De Petroleos and Seven Seas 
                     Petroleum Colombia



<PAGE>   19

 *(22)               Subsidiaries of the Registrant

  (27)               Financial Data Schedule


 *   Incorporated herein by reference to Exhibit on like registration on Form 10
     (File No. 022483)

**   Incorporated  herein by reference like Exhibit from Annual Report on Form 
     10-K/A for the year ended  December 31, 1997 (Commission File No. 022483)