<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, 1999

                                       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 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

     Yes  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 APRIL 30, 1998 THERE WERE 37,833,420 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 March 31, 1999
                (Unaudited) and December 31, 1998...................................     2

                Statements of Consolidated Operations and Accumulated Deficit
                for the three months ended March 31, 1999 and 1998 and the               
                Cumulative Total from Inception (February 3, 1995) to March 31,
                1999 (Unaudited)....................................................     3

                Statements of Consolidated Cash Flows for the three months
                ended March 31, 1999 and 1998 and the Cumulative Total from
                Inception (February 3, 1995) to March 31, 1999 (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.......     13

    PART II. OTHER INFORMATION......................................................     13

           Item 6  Exhibits and Reports on Form 8-K.................................     13
</TABLE>


                                       1

<PAGE>   3
               SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                    (A Development Stage Enterprise)
                       CONSOLIDATED BALANCE SHEETS
                    (In thousands, except share data)

<TABLE>
<CAPTION>
                                                                                    March 31, 1999   December 31, 1998
                                                                                    --------------   -----------------
<S>                                                                                 <C>               <C>         
ASSETS

CURRENT
     Cash and cash equivalents                                                       $     26,011      $     38,147
     Short-term investments                                                                 6,025             6,399
     Restricted short-term investments                                                     13,319            13,244
     Accounts receivable                                                                    8,261             6,562
     Interest receivable                                                                      409               532
     Inventory                                                                              1,289             1,316
     Prepaids and other                                                                       154               225
                                                                                     ------------      ------------
                                                                                           55,468            66,425

Note receivable from related party                                                            200               200
Restricted long-term investments                                                           18,916            18,658
Land                                                                                        1,278             1,257
Evaluated oil and gas interests, full-cost method                                          82,933            74,993
Unevaluated oil and gas interests, full-cost method                                       113,582           113,116
Fixed assets, net of accumulated depreciation of $335 at March 31, 1999
     and $232 at December 31, 1998                                                          1,394             1,357
Other assets, net of accumulated amortization of $612 at March 31, 1999
     and $461 at December 31, 1998                                                          3,742             3,894
                                                                                     ------------      ------------
TOTAL ASSETS                                                                         $    277,513      $    279,900
                                                                                     ============      ============

LIABILITIES AND STOCKHOLDERS' EQUITY

CURRENT
     Accounts payable                                                                $      3,792      $     10,058
     Interest payable                                                                       5,156             1,719
     Accrued compensation                                                                      --
     Other accrued liabilities                                                                534               580
                                                                                     ------------      ------------
                                                                                            9,482            12,357

Long-term debt                                                                            110,000           110,000
Deferred income taxes                                                                      24,732            24,732
Minority interest                                                                          11,305             9,713

COMMITMENTS AND CONTINGENCIES

STOCKHOLDERS' EQUITY
Share capital -
     Authorized unlimited common shares without par value and
     37,778,420 and 37,778,420  issued and outstanding common shares
     at March 31, 1999 and December 31, 1998, respectively                                225,540           222,447

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

     Warrants - none and 1,068,044 outstanding at March 31, 1999                               --             3,093
     and December 31, 1998, respectively

Deficit accumulated during development stage                                             (103,546)         (102,442)

Treasury stock, 29 shares held at March 31, 1999 and December 31, 1998                         --                --
                                                                                     ------------      ------------
Total Stockholders' Equity                                                                121,994           123,098
                                                                                     ------------      ------------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                           $    277,513      $    279,900
                                                                                     ============      ============
</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
                        (In thousands, except share data)

<TABLE>
<CAPTION>
                                                                                             Cumulative
                                                                                             Total from
                                                                                             Inception
                                                                                            (February 3,
                                                                                              1995) to
                                                        Three Months Ended March 31,          March 31,
                                                          1999               1998              1999
                                                       ------------      ------------      ------------
<S>                                                    <C>               <C>               <C>         
REVENUE
  Crude oil sales                                      $         90      $         --      $      1,119
  Interest income                                               906               184             5,968
                                                       ------------      ------------      ------------
                                                                996               184             7,087

EXPENSES
  General and administrative                                  1,791             1,120            23,792
  Oil and gas operating expenses                                145               188             2,247
  Depreciation and amortization                                 255                84             1,226
  Writedown of proved oil & gas properties                       --                --           129,789
  Gain on sale of exploration properties                         --                --              (546)
  Dry hole and abandonment costs                                 --                --             1,145
  Geological and geophysical                                     --                --                47
  Other (income) expense                                         16               (30)             (106)
                                                       ------------      ------------      ------------
                                                              2,207             1,362           157,594

NET LOSS BEFORE INCOME TAXES
  AND MINORITY INTEREST                                      (1,211)           (1,178)         (150,507)
                                                       ------------      ------------      ------------

INCOME TAX EXPENSE                                                6                15           (45,712)

NET LOSS BEFORE MINORITY INTEREST                            (1,217)           (1,193)         (104,795)
                                                       ------------      ------------      ------------

MINORITY INTEREST                                               113                78             1,249
                                                       ------------      ------------      ------------

NET LOSS                                               $     (1,104)     $     (1,115)     $   (103,546)
                                                       ============      ============      ============

DEFICIT ACCUMULATED DURING THE DEVELOPMENT
  STAGE , beginning of period                              (102,442)          (12,243)               -- 

DEFICIT ACCUMULATED DURING THE DEVELOPMENT
  STAGE , end of period                                $   (103,546)     $    (13,358)     $   (103,546)
                                                       ============      ============      ============

BASIC AND DILUTED NET LOSS PER COMMON SHARE            $      (0.03)     $      (0.03)     $      (4.33)
                                                       ============      ============      ============

WEIGHTED AVERAGE
  COMMON SHARES OUTSTANDING                              37,778,420        35,126,162        23,910,694
                                                       ============      ============      ============
</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
                           (In thousands)

<TABLE>
<CAPTION>
                                                                                                              Cumulative   
                                                                                                             Total from  
                                                                                                              inception   
                                                                                                             February 3,  
                                                                          Three Months Ended March 31,         1995) to    
                                                                         ------------------------------      December 31, 
                                                                             1999               1998              1998   
                                                                         ------------      ------------      ------------
<S>                                                                      <C>               <C>               <C>
OPERATING ACTIVITIES
     Net loss                                                            $     (1,104)     $     (1,115)     $   (103,546)
     Add (subtract) items not requiring (providing) cash:
     Compensation expense                                                          --                --             2,140
     Minority interest                                                           (113)              (78)           (1,249)
     Common stock contribution to 401(k) retirement plan                           --                79
     Depreciation and amortization                                                255                84             1,231
     Writedown of proved oil & gas properties                                      --                --           129,789
     Gain on sale of exploration properties                                        --                --              (546)
     Dry hole and abandonment costs                                                --                --             1,140
     Gain on sale of marketable securities                                         --                (6)               (6)
     Deferred income taxes benefit                                                 --                --           (45,727)
     Amortization of discount on investments                                       41                --                41
     Changes in working capital excluding changes to cash and 
       cash equivalents:
        Accounts receivable                                                    (1,372)             (478)           (7,052)
        Interest receivable                                                       123                --              (409)
        Inventory                                                                  27                --            (1,289)
        Prepaids and other, net                                                    71                 9              (154)
        Accounts payable                                                      (10,030)             (427)           (4,320)
       Other accrued liabilities                                                  (46)              (92)              533
                                                                         ------------      ------------      ------------
Cash Flow Used in Operating Activities                                        (12,148)           (2,103)          (29,345)
                                                                         ------------      ------------      ------------

INVESTING ACTIVITIES
     Exploration of oil and gas properties                                     (1,205)           (9,746)          (73,550)
     Purchase of land                                                             (21)             (441)           (1,278)
     Purchase of investments                                                       --                --           (38,301)
     Proceeds from acquisition                                                     --                --               630
     Proceeds from sale of property                                                --                --             1,247
     Proceeds from sale of marketable securities                                   --                50                50
     Note receivable from related party                                            --                --              (200)
     Other asset additions                                                       (140)              (47)           (1,896)
                                                                         ------------      ------------      ------------
Cash Flow Used in Investing Activities                                         (1,366)          (10,184)         (113,298)
                                                                         ------------      ------------      ------------

FINANCING ACTIVITIES
     Proceeds from special warrants issued                                         --                --            12,393
     Proceeds from share capital issued                                            --             1,116            15,466
     Proceeds from additional paid-in capital contributed                          --                --                 1
     Proceeds from issuance of  long-term debt                                     --                --           135,000
     Costs of issuing long-term debt                                               --                --            (5,821)
     Contributions by minority interest                                         1,378             1,829            11,615
                                                                         ------------      ------------      ------------
Cash Flow Provided by Financing Activities                                      1,378             2,945           168,654
                                                                         ------------      ------------      ------------

NET INCREASE (DECREASE) IN CASH AND CASH EQUIVALENTS                          (12,136)           (9,342)           26,011
Cash and cash equivalents, beginning of period                                 38,147            18,067                -- 
                                                                         ------------      ------------      ------------
CASH AND CASH EQUIVALENTS, END OF PERIOD                                 $     26,011      $      8,725      $     26,011
                                                                         ============      ============      ============
</TABLE>

Supplemental disclosures of cash flow information:

The Company incurred interest costs of $3.4 million for the three month period
   ended March 31, 1999 and $9.8 million for the year ended December 31, 1998.
   Such amounts were capitalized during the respective periods.

Cash paid for interest for the three month period ended March 31, 1999 and for
   the year ended December 31, 1998 was zero and $8.1 million, respectively.

The Company paid zero for estimated income taxes during the three months ended
   March 31, 1999.


   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

    Seven Seas Petroleum Inc. (a Yukon Territory, Canada corporation) was formed
on February 3, 1995. Seven Seas Petroleum Inc. and its subsidiaries
(collectively referred to as "Seven Seas" or the "Company") are collectively a
development stage enterprise engaged in the exploration, development and
production of oil and natural gas, primarily in Colombia. The Company is the
operator of an oil discovery, known as the "Guaduas Field" (formerly known as
"Emerald Mountain"), which is on the Emerald Mountain structure and located in
an area defined by the Rio Seco and Dindal Association Contracts (the
"Association Contracts"), which cover a total of approximately 109,000
contiguous acres in central Colombia. The Company owns a 57.7% working interest
in the two Association Contracts before participation by Empresa Colombiana de
Petroleos ("Ecopetrol"), the Colombian state oil company. The Company has no
significant income producing properties and its principal assets, its interests
in the Association Contracts, are in the early stage of exploration and
development. Since inception through March 31, 1999, the Company incurred
cumulative losses of $103.5 million and, because of its continued exploration
and development activities, expects that it will continue to incur losses and
that its accumulated deficit will increase until commencement of production from
the Association Contracts occurs in quantities sufficient to cover operating
expenses.

    As of March 31, 1999, the Company has spent $242.2 million to acquire and
$67.9 million to delineate the reserve potential of the Guaduas Field. The
Company has drilled twelve exploratory wells within the Association Contracts,
of which six have been production tested and have achieved maximum actual oil
production rates ranging from 1,666 to 13,123 Bbls per day. Four of the twelve
did not produce commercial amounts of oil and gas during testing and two remain
to be tested. As of March 31, 1999, the Guaduas Field had produced a cumulative
volume of approximately 350,000 barrels of oil during various testing
procedures. Except for additional production testing and further reservoir
evaluation, continuous production of the Guaduas Field will not commence prior
to installation of the infrastructure necessary to produce and transport
continuous oil production.

    The Company anticipates exploring and developing the Guaduas Field in
increments designed to optimize cash flows that can be reinvested into further
delineation and development of the field. These planned increments, starting
with an approximate 5,000 Bbls/d portable trucking facility (expected to be in
operation in early-2000) followed by an approximate 25,000 Bbls/d pipeline
facility (expected to be operational by year-end 2000) and culminating with an
approximate 250,000 Bbls/d pipeline facility (expected to be in operation in
early-2005) would be phased in as capital is available to fund the necessary
delineation and development drilling, production facility and transportation
facility expenditures.

    These plans are further dependent upon the timing of a global operating
license allowing development in the Association Contract areas; environmental
and rights-of-way permits for production and transportation facilities; cost and
timeliness of construction activities; availability of transportation on third
party pipeline systems; and the timing of a commerciality agreement with
Ecopetrol. Approval of commerciality by Ecopetrol is a critical part of the
Company's strategy as Ecopetrol will bear fifty percent of all costs for
development and production subsequent to the date commerciality is declared.
Although the Company has reason to believe that a commerciality agreement can be
reached with Ecopetrol, if the commerciality agreement is not in place before
December 1999 the Company will not be able to proceed as planned.

    As of March 31, 1999, the Company had cash and cash equivalents of $26.0
million and commitments under existing oil and gas agreements of $4.8 million in
1999. Based on available capital resources, the Company believes that it will be
able to make its commitments and fund its exploration and development plan
through 1999. To the extent the Company experiences delays or cost overruns in
the development plan, the Company will be required to seek additional financing
to meet its commitments and to carry out its exploration and development plan
through 2000. The continued exploration and development of the Company's current
properties is expected to require substantial amounts of additional capital
which the Company may be required to raise through debt or equity financing,
encumbering properties or entering into arrangements whereby certain costs will
be paid by others to earn an interest in the property. If the Company is
unsuccessful in constructing production and transportation facilities,
increasing its proved reserves or realizing future production from its
properties, the Company may be unable to pay existing or future debt.

    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. Among the factors that
have a direct bearing on Seven Seas' prospects are uncertainties inherent in
estimating oil and gas reserves and future hydrocarbon production and cash
flows, particularly


                                       5
<PAGE>   7

with respect to wells that have not been fully tested and with wells having
limited production testing histories; access to additional capital; changes in
the price of oil and natural gas, services and equipment; the limited
exploration of the concessions; the status of existing and future contractual
relationships with Ecopetrol; foreign currency fluctuation risks; Seven Seas'
substantial indebtedness, the presence of competitors with greater financial
resources and capacity; difficulties and risks associated with operating in
Colombia.

2.  BASIS OF PRESENTATION

    The accompanying unaudited, condensed consolidated financial statements
include the accounts of Sevens Seas Petroleum Inc. and its subsidiaries 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 (GAAP) for interim
financial reporting. Accordingly, they do not include all of the information and
footnotes required by GAAP 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 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 10K for the year ended December 31, 1998.

3.  STOCKHOLDERS' EQUITY

    Exchangeable Notes. In August 1997, the Company issued $25 million of
Exchangeable Notes in a private transaction with institutional and accredited
investors. The Exchangeable Notes accrued interest at a rate of 6% per annum and
were payable on December 31 and June 30 in each year, commencing December 31,
1997. The Exchangeable Notes were scheduled to mature on August 7, 2003.

    The Exchangeable Notes were exchanged for a like principal amount of
Convertible Debentures on August 5, 1998. The Convertible Debentures were
converted on August 6, 1998 into Units consisting of a total of 2,173,901 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 will expire on
the earlier of (i) the date that is 30 calendar days following a 20-day period
during which the weighted average trading price for the common shares of the
Company on the Toronto Stock Exchange exceeds US$17.64 or (ii) February 5, 1999.

    On February 5, 1999, purchase warrants for 1.1 million Common Shares of
Seven Seas Petroleum Inc. expired without exercise. These purchase warrants had
been issued in association with the exchange and conversion of the Company's
previously outstanding $25 million issue of 6% Exchangeable Notes.

4.  OPERATIONS BY GEOGRAPHIC AREA:

    The Company has one operating and reporting segment. Information about the
Company's operations for the quarters ended March 31, 1999 and 1998 and by
geographic area is shown below (In thousands):

<TABLE>
<CAPTION>
                                                                                        Other   
                                                        United                         Foreign  
                                        Canada          States         Colombia         Areas            Total
                                      ----------      ----------      ----------      ----------      ----------
<S>                                   <C>             <C>             <C>             <C>             <C>       
Quarter ended March 31, 1999
  Revenues ......................     $      895      $        3      $       98      $       --      $      996
  Operating Income (Loss) .......            507            (949)           (754)            (15)         (1,211)
  Capital Expenditures ..........             --              34           5,070              --           5,104
  Identifiable Assets ...........         82,073           1,207         193,732             501         277,513
  Depreciation and Amortization .            152              83              20              --             255

Quarter ended March 31, 1998
  Revenues ......................     $      161      $        3      $       20      $       --      $      184
  Operating Income (Loss) .......            (12)           (737)           (419)            (10)         (1,178)
  Capital Expenditures ..........             --              17           9,226              19           9,262
  Identifiable Assets ...........          9,758             383         280,866           1,013         292,020
  Depreciation and Amortization .             65               9              10              --              84

</TABLE>


                                       6
<PAGE>   8
5.  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.

6.  CONTINGENCIES

    The Company is, from time to time, party to certain legal actions and claims
arising in the ordinary course of business. While the outcome of these events
cannot be predicted with certainty, management does not expect these matters to
have a material adverse effect on the financial position or results of
operations or cash flows of the Company.

    The Ministry of Environment by resolution has decided to open a list of
charges against GHK Company Columbia based on alleged environmental damages,
originating from the location that has been constructed for the proposed El
Segundo 7-E well. The Company has experienced difficulty trying to stabilize the
slopes of this location, and as a result, sediments from the location were
entering a creek. At this time, remediation efforts are underway and should be
completed soon. The Company has been notified that it will likely be assessed a
fine for the alleged environmental damages at the El Segundo 7-E location. The
Company believes that the amount accrued will be sufficient to cover remediation
costs and potential fines assessed as a result of El Segundo 7-E operations.

    Commercial relations between the Company and International Technical
Solutions Inc. (ITS), a consulting engineering firm, were terminated by the
Company's operating subsidiary, GHKCC as of January 1999. ITS states that there
were unfair causes for termination and has demanded that the Company pay $3.2
million to ITS. The Company and ITS are currently negotiating this claim. In the
event that an agreement is not reached, however, ITS has declared that it
intends to initiate an Ordinary Lawsuit before a Judge in Colombia against the
Company to prove that it has the right to receive the amounts claimed. The
Company has no written contract with ITS and believes the claims are
substantially without merit. The Company's Colombian legal counsel is of the
opinion that the likelihood of any substantial payments other than valid,
existing accounts payable to ITS as a result of an Ordinary Lawsuit are remote.

    The Dindal Association Contract was issued in March 1993 and provides for a
maximum six-year exploration period followed by a maximum 22-year production
period, with partial relinquishment of acreage, excluding commercial fields,
required commencing at the end of the sixth year of the Association Contract.
The exploration period had previously been extended and, unless further extended
by Ecopetrol, the exploration period under the Dindal Association Contract will
expire in September 1999, at which time the Company must relinquish 50% of the
contract area or all lands that fall outside a five kilometer buffer zone around
the area designated to be the commercial field. The Company has requested an
extension of the exploration period.

7.  SUBSEQUENT EVENTS

    Effective April 5, 1999, the Company appointed Robert M.D. Cross to its
Board of Directors to replace Mr. James Scarlett, who resigned. In addition,
Herbert C. Williamson III, Executive Vice President and Chief Financial Officer,
resigned from his position with the Company and all of its affiliated entities
and as a Director of the Company. Larry A. Ray, Executive Vice President, Chief
Operating Officer, and Director of the Company was appointed as Chief Financial
Officer on an interim basis.

    The Company has initiated the following actions to reduce overhead and
increase efficiency. First, the Company's exploration office in Denver, Colorado
is being moved to the Company's headquarters in Houston, Texas. In addition, the
Bogota staff has been downsized and restructured to conform the organization to
the project. The staff has been reduced through the implementation of a
voluntary separation program.

    The lawsuit filed by Timothy Stephens against Seven Seas Petroleum Inc. and
Mr. Robert A. Hefner III was settled in April 1999.

                                       7
<PAGE>   9

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

Introduction

    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 for the year ended December 31,
1998.

    From time to time, Seven Seas may make certain statements that provide
stockholders and the investing public with "forward-looking" information (as
defined in the Private Securities Litigation Reform Act of 1995). Words such as
"anticipate," "assume," "believe," "estimate," "project," and similar
expressions are intended to identify such forward-looking statements.
Forward-looking statements may be made by management orally or in writing,
including, but not limited to, in press releases, as part of this "Management's
Discussion and Analysis of Financial Condition and Results of Operations"
section and as part of other sections of the Company's filings with the SEC
under the Securities Act and the Securities Exchange Act. Such forward-looking
statements may include, but not be limited to, statements concerning estimates
of current and future results of operations, financial position, reserves, the
timing and commencement of wells and development plans, drilling results as
indicated by log analysis, core samples, examination of cuttings, hydrocarbons
shows while drilling and production estimates from wells drilled based upon
drill stem tests and other test data, future capacity under credit arrangements,
future capital expenditures, liquidity requirements, liquidity sufficiency and
year 2000 compliance.

    Such forward-looking statements are subject to certain risks, uncertainties
and assumptions, including without limitation, those defined below. Should one
or more of these risks or uncertainties materialize, or should any of the
underlying assumptions prove incorrect, actual results of current and future
operations may vary materially from those anticipated, estimated or projected.

    Among the factors that have a direct bearing on Seven Seas' results of
operations and the oil and gas industry in which it operates are uncertainties
inherent in estimating oil and gas reserves and future hydrocarbon production
and cash flows, particularly with respect to wells that have not been fully
tested and with wells having limited production testing histories; access to
additional capital; changes in the price of oil and natural gas, services and
equipment; the limited exploration of the concessions; the status of existing
and future contractual relationships with Ecopetrol; foreign currency
fluctuation risks; Seven Seas' substantial indebtedness, the presence of
competitors with greater financial resources and capacity; and difficulties and
risks associated with operating in Colombia.

Overview

    Seven Seas' principal asset is a 57.7% interest (before participation by
Ecopetrol, the Colombian state oil company) in the Dindal and Rio Seco
Association Contracts. As of December 31, 1998, Ryder Scott Company Petroleum
Engineers ("Ryder Scott") estimated total proved recoverable reserves for the
Guaduas Field of 163,303,000 Bbls, of which 38,719,235 Bbls were attributable to
the Company's interest.

    The Company currently plans to focus its resources on placing the Guaduas
Field on production by increments in order to achieve cash flow as soon as
possible and to take advantage of the expected low equipment, service and
construction cost resulting from the oil and gas industry's current depressed
state. First production from the Guaduas Field, Increment I, should be achieved
through the construction of a Portable Trucking Facility ("PTF" -- subsequently
to become part of the permanent facilities) for the trucking of between 4,000
Bbls/d and 6,000 Bbls/d to a local refinery located approximately 80 miles from
the Guaduas Field. The estimated net capital cost to the Company for these
facilities is approximately $9.4 million. The Company estimates that it can
commence PTF production in early 2000. Increment II, Early Pipeline Production,
includes the construction of facilities for the production of 20,000 Bbls/d to
30,000 Bbls/d and is scheduled to go on line by year-end-2000. Increment II
facilities will include the construction of a 36-mile pipeline that will connect
with the existing regional OAM pipeline. Contemporaneously, the Company will
drill additional development wells and one gas injection well. The Company
estimates that the net capital cost of the pipeline, the production facilities
and drilling the necessary wells will be approximately $14 million. The net cost
of the pipeline is approximately $6.1 million.


                                       8
<PAGE>   10

    The Company's unrestricted cash resources, including short-term investments,
as of March 31, 1999 were $32.0 million and the Company has obligatory capital
expenditure commitments of $4.8 million through year end 1999 (see "-- Liquidity
and Capital Resources"). Whether the Company can achieve the Increment I and II
objectives on schedule and with the Company's existing capital resources is
dependant upon a number of factors, many of which are not within its control,
such as timely environmental permitting, securing pipeline rights-of-way,
obtaining Ecopetrol's agreement to commerciality under the Association Contracts
and timely payments by the co-participants of their share of these costs as well
as the market price of oil field equipment and services. If the Company
experiences delays or cost overruns, which must be considered possible, the
Company will seek other sources of financing, including project financing,
industry joint ventures or like arrangements with industry service companies,
commercial bank borrowings and traditional debt and equity financing. The
Company's expenditures for Increment II, Early Pipeline Production, may be
substantially reduced by the formation of a separate company to construct the
Guaduas pipeline (connecting to the OAM regional pipeline) to be owned and
financed by third parties and in which the Company may have little or no equity,
thereby obligating the Company to pay only a per barrel tariff on its oil
transported through the pipeline and none of the capital expenditures that are
currently budgeted by the Company for the construction of the pipeline.

    Furthermore, the Company will be required to obtain additional sources of
financing to meet its other, multiple objectives of accelerating incremental
production from the Guaduas Field beyond Increment II and delineation and
exploratory drilling. Each additional increment of field production (Increments
III through V) will require additional production facilities, a pipeline
expansion, and the expansion of proved oil reserves through successful
development and delineation drilling of the shallow Cimarrona reservoir. If
external financing is obtained, the Company would anticipate drilling a
delineation well on the west flank of the Guaduas structure and an exploration
well to test the deep Guaduas Field structure, depending on certain actions by
Ecopetrol.

    The Company also plans to participate in the drilling of an exploratory well
on the Tapir block and to conduct seismic operations on the Rosablanca and
Montecristo blocks during 1999 at an aggregate cost of $3.1 million.

Liquidity and Capital Resources

    The Company had working capital of $32.7 million, net of restricted
investments, and unrestricted cash resources, including short-term investments,
of $32.0 million as of March 31, 1999. The Company's non-discretionary capital
commitments for the remainder of 1999 as of April 30, 1999 are approximately
$4.8 million.

    The Company's activities from its inception through March 31, 1999 were
funded primarily by the proceeds from private placements of the Company's
securities, including the Company's common shares, warrants and notes, resulting
in aggregate cash proceeds of $157.0 million. Such funding transactions are as
follows:

    (i) Exchangeable Notes. In August 1997, the Company issued $25 million of 6%
Exchangeable Notes (the "Exchangeable Notes") in a private transaction with
institutional and accredited investors. The Exchangeable Notes accrued interest
at a rate of per annum and were payable on December 31 and June 30 in each year,
commencing December 31, 1997. The Exchangeable Notes were scheduled to mature on
August 7, 2003.

    The Exchangeable Notes were exchanged for a like principal amount of 6%
Convertible Debentures on August 5, 1998. The 6% Convertible Debentures were
converted on August 6, 1998 into Units consisting of 2,173,901 common shares and
warrants exercisable for 1,086,957 common shares. The warrants expired on
February 5, 1999. The Company received proceeds of $0.3 million from the
exercise of 18,913 warrants.

    (ii) Senior Notes. In May 1998, the Company completed the offering of $110
million of 12 1/2% Senior Notes due May 15, 2005 (the "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 at 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 1/3% 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


                                       9
<PAGE>   11

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.

    Colombia. In 1995, the Company acquired a 15% interest in the Dindal and Rio
Seco Association Contracts through its participation in El Segundo 1-E, the
Guaduas Field discovery well. In 1996, the Company acquired an additional 36.7%
in the Dindal and Rio Seco Association Contracts in Colombia in exchange for the
issuance of the Company's common shares valued at $153.1 million in the
aggregate at that time. In 1997, the Company acquired an additional 6% in the
Dindal and Rio Seco Association Contracts in Colombia in exchange for the
issuance of the Company's common shares valued at $18.6 million in the aggregate
at that time. From inception through March 31, 1999, the Company had capital
expenditures of $70.9 million for the acquisition, exploration, and development
of its oil and gas properties including $69.8 million with respect to its
interests in Colombia.

    The Company's estimated capital expenditures assume in each case that each
of the associates in the Association Contracts approves and pays its
proportionate share of capital expenditures. Under the terms of the Association
Contracts, if a commercially feasible discovery is made, the Colombian national
oil company ("Ecopetrol") may acquire a 50% interest in the property, and the
interests of all other parties to the contract, including the Company, will be
reduced by 50%. Ecopetrol will bear 50% of the associated development costs and
will reimburse the other associates for 50% of certain exploration activities.
The Association Contracts require Ecopetrol's participation in the production
facilities. The Company expects that Ecopetrol will participate to the extent of
50% of the 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. Ecopetrol retains the right not to participate initially in the
development. In this case, the associates can develop the Guaduas Field under a
sole risk provision, and will be required to invest 100% of the development
costs. After the associates have recovered 200% of the costs invested for
development plus 50% of certain exploration costs, Ecopetrol will become a
participant in the project at a 50% interest.

    Total 1999 capital expenditures on the Company's non-operated Tapir
Association Contract area are estimated to be $0.6 million. Such expenditures
will be made to complete the Mateguafa 1 well, which was drilled in 1998, and to
drill the Caporal 1 exploratory well on the block. The Caporal 1 well was
plugged and abandoned in April 1999.

    To date, all oil revenues have been due to the Company's share of crude oil
produced during production testing of the Company's wells on the Guaduas Field.
Although the Company intends to continue to sell oil resulting from production
tests, significant commercial production is not expected until further
development of the field through the drilling, well operations and construction
of production and pipeline transportation facilities. The Company has completed
plans for the construction of pipeline and production facilities at the Guaduas
Field. Permitting and the purchasing of equipment and supplies for pipeline and
production facilities is in process. Anticipated completion of Increment II at
20,000 Bbls/d to 30,000 Bbls/d is year-end 2000.

    The Company plans to conduct seismic operations on the Montecristo and
Rosablanca Association Contract areas in 1999 for an estimated cost of $2.5
million. The Company is considering acquisition of outside funding via farm-out
or forming an alliance with a seismic contractor to complete this work. Either
of these events will result in a reduction of the Company's interest.

    Australia. The Company is in the process of eliminating any mandatory
capital commitments outside of Colombia. In the Bass Strait Basin offshore
southeast Australia, the Company is seeking to farm out its interests. If the
Company does not farm-out its interests in this prospect and an exploratory well
is drilled during 1999, the Company will have an estimated $2.2 million capital
commitment for this prospect during 1999.

    In 1998, the Company completed the sale of its 11.77% working interest in
the Perth Basin in Western Australia for approximately $0.9 million in cash and
the reimbursement of approximately $0.3 million for certain capital
expenditures.


                                       10
<PAGE>   12

    Papua New Guinea. The Company entered into an Agreement with ARCO Papua New
Guinea Inc. ("ARCO") for a farm out of its interest whereby ARCO funded the
Company's obligation for the twelve-month period ended July 1998 for an 80%
interest in the subject exploration permit. Subsequently, the Company
relinquished its rights in the property to ARCO, retaining a small production
payment. The Company has no remaining required capital expenditures.

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 of America.

    The Company's exploration and development activities have not generated a
substantial 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 each period presented and
from the Company's inception. The statement of stockholders' equity presents 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
Consolidated Financial Statements are required to identify the enterprise as
development stage.

    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 and
1998. The Company capitalized interest of $9.8 million for the year ended
December 31 1998 and $3.4 million for the three month period ended March 31,
1999.

    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 are 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 of properties not being amortized, both adjusted for income tax effects,
such excess is charged to expense.

    As of March 31, 1999, the Company's exploration and development activities
have not generated significant revenues. As a result, the Company's historical
results of operations have been presented as a development stage company; 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 highly dependent upon the success of the Company's Guaduas
Field operations.

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 in the Guaduas Field. Revenues from oil sales were $.1 million and zero
for the quarter ended March 31 1999 and 1998, respectively. Lease operating
expenses were $0.1 million and $0.2 million for the quarter ended March 31, 1999
and 1998, respectively. The 1998 oil and gas operating expenses represent such
costs as tank rentals and other miscellaneous fixed costs.

    Oil production in Colombia (net to the Company, including minority interest)
of 11,623 barrels and zero for the quarter ended March 31, 1999 and 1998,
respectively, pertaining solely to the Company's share of oil produced from
production testing, was sold to Ecopetrol at an average price of $7.75 per
barrel in 1999. In January 1999, production testing began from the Tres Pasos
1-W Horizontal and anticipate completion of the testing at the end of the second
quarter of 1999. Later in 1999 the Company plans additional production testing.

    Interest income was $0.9 million and $0.2 million for the quarter ended
March 31, 1999 and 1998, respectively. The increase from 1998 to 1999 was the
consequence of higher cash and investment balances resulting from the issuance
of the Senior Notes in May 1998.


                                       11
<PAGE>   13

    General and administrative costs were $1.8 million and $1.1 million for the
quarter ended March 31, 1999 and 1998, respectively. The $0.7 million increase
in general and administrative expenses from the three month period ended March
31, 1998 to the three month period ended March 31, 1999 was primarily
attributable to a $0.6 million increase in personnel costs, including salaries,
benefits, travel, rents, and insurance due to increased personnel in both US and
Colombia.

    Depreciation and amortization was $0.3 million and $0.1 million for the
quarter ended March 31, 1999 and 1998, respectively. The increase from 1998 to
1999 was primarily attributable to the amortization of costs incurred on the
issue of the Senior Notes in May 1998 (see "Liquidity and Capital Resources").
The remaining increase resulted from higher depreciation costs relating to the
increase in fixed assets. As of March 31, 1999, 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.

    As required under the full cost method of accounting, capitalized costs are
limited to the sum of the present value of future net revenues using current
unescalated pricing discounted at 10% related to estimated production of proved
reserves and the lower of cost or estimated fair value of unevaluated
properties, all net of expected income tax effects.

    The Company incurred net losses of $1.1 million and $1.1 million for the
quarter ended March 31, 1999 and 1998, respectively.

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%.

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 year
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 a limited
operating history 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 has minimum reliance on the hardware and software systems
of third parties. Further, the Company's hardware and software systems are
relatively new, 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 the Guaduas Field is the
transportation and marketing of crude oil to be produced from the Company's
properties. 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 the Guaduas Field to the existing
Oleoducto Alto Magdalena ("OAM") pipeline, which terminates at Vasconia. Beyond
Vasconia, the Company's oil production may be transported to the export terminal
at Covenas via the existing pipeline system, Oleducto de Colombia ("ODC"). The
Company has employed Brown & Root Energy Services and Technivance Brown & Root
S.A. to conduct certain planning and engineering studies for its planned
pipeline and associated compression facilities from the Guaduas Field 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
with the OAM and ODC 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 interconnections to the OAM and ODC 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.



                                       12
<PAGE>   14

    As the Company develops its infrastructure at the Guaduas Field, 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 the Guaduas Field production, the Company is
unable to assess the significance of Year 2000 issues affecting potential
customers at this stage in its operations.

ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET RISK

    Seven Seas is exposed to market risk, including adverse changes in commodity
prices, interest rates and foreign currency exchange rates as discussed below.

    Commodity Risk. The Company's exposure in the commodity pricing applicable
to its oil and natural gas production is currently minimal due to the small
amounts of oil and gas produced to date. Realized commodity prices received for
such production are primarily driven by the prevailing worldwide price for crude
oil and spot prices applicable to natural gas. The effects of such pricing are
expected to be minor until such time as the Company produces commercial
quantities of oil and gas.

    Interest Rate Risk. The Company considers its interest rate risk exposure to
be minimal as a result of a fixed interest rate on the $110 million 12 1/2%
Senior Notes. The Company currently has no open interest rate swaps agreements.

    Foreign Currency Exchange Rate Risk. The Company conducts business in
several foreign currencies and is subject to foreign currency exchange rate risk
on cash flows related to sales, expenses and capital expenditures. However,
because predominately all transactions in Seven Seas' existing foreign
operations are denominated in U.S. dollars, the U.S. dollar is the functional
currency for all operations. Exposure from transactions in currencies other than
the U.S. dollars is not material.


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:

    May 14, 1998           By:  Larry A. Ray Executive Vice President, Chief 
                                Operating Officer and Chief Financial Officer

                                Ray A. Housley Treasurer and Controller


                                       13
<PAGE>   15
                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
Exhibit 
Number           Description
-------          -----------
<S>              <C>
  27             Financial Data Schedule
</TABLE>