<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 June 30, 1998

                                       or

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

               For the transition period from _______ to ________

                           Commision File No. 0-22483

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

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

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

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

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

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

         Indicate by check mark whether the registrant (1) has filed all reports
required to be filed by Section 13 of 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.

                                    Yes X    No
                                       ---      
         Indicate the number of shares outstanding of each of the issuer's
classes of common stock, as of the latest practicable date.

AS OF JULY 31, 1998 THERE WERE 35,380,606 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>                                                                 <C>
          Item 1. Condensed Consolidated Balance Sheets as of June 30, 1998
                  (Unaudited) and December 31, 1997..........................2

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

                  Condensed Consolidated Statements Cash Flows for the six
                  months ended June 30, 1998 and 1997 and the Cumulative
                  Total from Inception (February 3, 1995) to June 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 Operations........................8

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

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

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

          Item 6 Exhibits and Reports on Form 8-K...........................15
</TABLE>


                                     1
<PAGE>   3
                   SEVEN SEAS PETROLEUM INC. AND SUBSIDIARIES
                        (A DEVELOPMENT STAGE ENTERPRISE)
                     CONDENSED CONSOLIDATED BALANCE SHEETS
                  (Unaudited; In thousands, except share data)


<TABLE>
<CAPTION>
                                                                                JUNE 30, 1998   DECEMBER 31, 1997
                                                                                -------------   -----------------
ASSETS                                                                           (Unaudited)
<S>                                                                                <C>             <C>
CURRENT
     Cash and cash equivalents                                                      $  67,849       $  18,067
     Short-term investments                                                            13,487              44
     Accounts receivable                                                                2,069           3,865
     Interest receivable                                                                  343               -
     Prepaids and other                                                                   107             118
                                                                                    ---------       ---------
                                                                                       83,855          22,094





Note receivable from related party                                                        200             200
Long-term held-to-maturity investments                                                 24,514               -
Land                                                                                    1,139               -
Evaluated oil and gas interests, full-cost method                                      49,473          46,117
Unevaluated oil and gas interests, full-cost method                                   238,374         221,713
Fixed assets, net of accumulated depreciation of $89 at June 30, 1998
     and $43 at December 31, 1997                                                         394             304
Other assets, net of accumulated amortization of $375 at June 30, 1998
     and $194 at December 31, 1997                                                      5,499           1,486
                                                                                    ---------       ---------
TOTAL ASSETS                                                                        $ 403,448       $ 291,914
                                                                                    =========       =========

LIABILITIES AND STOCKHOLDERS' EQUITY


CURRENT
     Accounts payable                                                                 $ 2,678         $ 6,885
     Interest payable                                                                   2,025               -
     Accrued compensation                                                                 508           1,228
     Other accrued liabilities                                                              -              92
                                                                                    ---------       ---------
                                                                                        5,211           8,205

Long-term debt                                                                        135,000          25,000
Deferred income taxes                                                                  70,459          70,459
Minority interest                                                                       7,483           4,087


STOCKHOLDERS' EQUITY
Share capital -
     Authorized unlimited common shares without par value and
     unlimited Class A preferred shares without par value;
     35,350,606 and 35,071,606  issued and outstanding common shares
     at June 30, 1998 and December 31, 1997, respectively                             199,405         196,406

Deficit accumulated during development stage                                          (14,110)        (12,243)

Treasury stock, 29 shares held at June 30, 1998 and December 31, 1997                       -               -
                                                                                    ---------       ---------
Total Stockholders' Equity                                                            185,295         184,163
                                                                                    ---------       ---------
TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                                          $ 403,448       $ 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
                  (Unaudited; In thousands, except share data)

<TABLE>
<CAPTION>

                                                                                                                   
                                                                                                                     CUMULATIVE
                                                                                                                     TOTAL FROM
                                                                                                                      INCEPTION
                                                SIX MONTHS ENDED JUNE 30,          THREE MONTHS ENDED JUNE 30,       (FEBRUARY 3,
                                             ------------------------------      ------------------------------    1995) TO JUNE 30,
                                                 1998              1997              1998               1997             1998
                                             ------------      ------------      ------------      ------------    -----------------

<S>                                                   <C>               <C>               <C>               <C>               <C>
REVENUE
    Crude oil sales                          $         91      $        436      $         91      $        117      $      1,104
    Interest income                                 1,143               235               959               120             2,424
                                             ------------      ------------      ------------      ------------      ------------
                                                    1,234               671             1,050               237             3,528

EXPENSES
    General and administrative                      2,319             3,281             1,199             2,372            14,559
    Lease operating expenses                          758               231               570                 1             1,918
    Depreciation and amortization                     227                38               143                17               524
    Dry hole and abandonment costs                     --                17                --                --             1,145
    Geological and geophysical                         --                27                --                18                47
    Other (income) expense                            (30)               --                --                --               (55)
    Loss on sale of resource properties                --                --                --                --                31
                                             ------------      ------------      ------------      ------------      ------------
                                                    3,274             3,594             1,912             2,408            18,169

NET LOSS BEFORE INCOME TAXES                       (2,040)           (2,923)             (862)           (2,171)          (14,641)

INCOME TAX EXPENSE                                     30                 8                15                --                30

NET LOSS BEFORE MINORITY INTEREST                  (2,070)           (2,931)             (877)           (2,171)          (14,671)

MINORITY INTEREST                                     203                73               125                35               561
                                             ------------      ------------      ------------      ------------      ------------

NET LOSS                                     $     (1,867)     $     (2,858)     $       (752)     $     (2,136)     $    (14,110)
                                             ============      ============      ============      ============      ============
DEFICIT ACCUMULATED DURING THE
DEVELOPMENT STAGE , beginning of period           (12,243)           (4,315)          (12,243)           (5,037)               -- 

DEFICIT ACCUMULATED DURING THE
DEVELOPMENT STAGE , end of period            $    (14,110)     $     (7,173)     $    (12,995)     $     (7,173)     $    (14,110)
                                             ============      ============      ============      ============      ============

BASIC AND DILUTED NET LOSS PER COMMON        
SHARE                                        $      (0.05)     $      (0.10)     $      (0.02)     $      (0.07)     $      (0.67)
                                             ============      ============      ============      ============      ============

WEIGHTED AVERAGE
  COMMON SHARES OUTSTANDING                    35,189,534        30,033,434        35,189,534        30,033,434        20,941,581
                                             ============      ============      ============      ============      ============
</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
                           (Unaudited; In thousands)

<TABLE>
<CAPTION>
                                                                                           CUMULATIVE 
                                                                                           TOTAL FROM
                                                                                           INCEPTION 
                                                            SIX MONTHS ENDED JUNE 30,     (FEBRUARY 3, 
                                                            -------------------------   1995) TO JUNE 30,
                                                               1998           1997           1998
                                                            -----------   -----------   -----------------
<S>                                                         <C>            <C>            <C>         
OPERATING ACTIVITIES

    Net loss                                                 $  (1,867)     $  (2,858)     $ (14,110)
    Add (subtract) items not requiring (providing) cash:
    Compensation expense                                            --             --          2,140
    Accretion of interest on zero coupon bonds                    (175)            --           (175)
    Minority interest                                             (203)           (73)          (561)
    Common stock contribution to 401(k) retirement plan             --             --             79
    Dry hole and abandonment costs                                  --             17          1,140
    Gain on sale of marketable securities                           (6)            --             (6)
    Loss on sale of resource properties                             --             --             31
    Depreciation and amortization                                  227             38            524
    Changes in working capital excluding changes to cash
    and cash equivalents:
       Accounts receivable                                       1,255          1,139         (1,187)
       Interest receivable                                        (343)            --           (343)
       Prepaids and other, net                                      11            (10)          (107)
       Accounts payable                                         (1,439)        (1,732)            53
       Accrued compensation                                         --             --             -- 
      Other accrued liabilities                                    (92)           264             -- 
                                                             ---------      ---------      ---------
Cash Flow Used in Operating Activities                          (2,632)        (3,215)       (12,522)
                                                             ---------      ---------      ---------

INVESTING ACTIVITIES
    Exploration of oil and gas properties                      (20,759)        (3,297)       (43,125)
    Purchase of land                                            (1,139)            --         (1,139)
    Purchase of investments                                    (37,827)            --
    Proceeds from acquisition                                       --             --            630
    Proceeds from sale of property                                  --             --             84
    Proceeds from sale of marketable securities                     50             --
    Note receivable from related party                              --             --           (200)
    Other asset additions                                         (135)           (29)          (649)
                                                             ---------      ---------      ---------
Cash Flow Used in Investing Activities                         (59,810)        (3,326)       (82,176)
                                                             ---------      ---------      ---------

FINANCING ACTIVITIES
    Proceeds from special warrants issued                           --             --         12,109
    Proceeds from share capital issued                           2,279          3,734         13,773
    Proceeds from additional paid-in capital contributed            --             --              1
    Proceeds from issuance of special notes                         --             --         25,000
    Costs of issuing special notes                                  --             --         (1,573)
    Proceeds from issuance of Senior Notes                     110,000             --        110,000
    Costs of issuing Senior Notes                               (4,195)            --         (4,195)
    Contributions by minority interest                           4,140          1,136          7,432
    Purchase of treasury stock                                      --             --             --
                                                             ---------      ---------      ---------
Cash Flow Provided by Financing Activities                     112,224          4,870        162,547
                                                             ---------      ---------      ---------

NET INCREASE (DECREASE) IN CASH AND CASH
EQUIVALENTS                                                     49,782         (1,671)        67,849

Cash and cash equivalents, beginning of period                  18,067         10,620             --
                                                             ---------      ---------      ---------
CASH AND CASH EQUIVALENTS, END OF PERIOD                     $  67,849      $   8,949      $  67,849
                                                             =========      =========      =========
</TABLE>

Supplemental disclosures of cash flow information:

The Company incurred interest costs of $2.8 million for the six month period
ended June 30, 1998 and $0.6 for the year ended December 31, 1997. Such amounts
were capitalized during the respective periods. Interest paid for the six month
period ended June 30, 1998 and for the year ended December 31, 1997 was $.8
million and $.6 million, respectively.

The Company paid $30,000 for the six month period ended June 30, 1998 for
estimated income taxes.


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



                                       4
<PAGE>   6

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

1.    DEVELOPMENT STAGE OPERATIONS

     The accompanying unaudited condensed consolidated financial statements
include the accounts of Seven Seas Petroleum Inc. and its subsidiaries
(collectively referred to as "Seven Seas" or the "Company") after elimination of
intercompany balances and transactions.

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

     The Company (a Yukon Territory, Canada corporation) was formed on February
3, 1995. Seven Seas is a development stage enterprise engaging in 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 four 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.    INVESTMENTS

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



                                     5
<PAGE>   7

The securities with maturity dates beyond one year are included in Non-Current
Assets classified as long term held-to-maturity investments and are stated at
amortized cost. The calculation of gross unrealized gain (loss) for the quarter
and six months ended June 30, 1998 was as follows (In thousands):

<TABLE>
<CAPTION>
                                                                  Amortized   Gross Unrealized
                                                  Fair Value        Cost        Gain (Loss)
                                                  ----------     -----------  ----------------
<S>                                             <C>             <C>              <C>
SHORT-TERM INVESTMENTS
U.S. Treasury Note, face value of
$6,769,000, interest at 5.875%, due October
31, 1998                                             $ 6,780         $ 6,778         $     2
U.S. Treasury Note, face value of
$6,663,000, interest at 6.375%, due April
30, 1999                                               6,709           6,709              --
                                                 -----------     -----------      ----------
Total Short-term investments                         $13,489         $13,487         $     2
                                                 ===========     ===========      ==========

LONG-TERM INVESTMENTS
U.S. Treasury Strip, face value of
$6,875,000, due November 15, 1999                    $ 6,379         $ 6,384         $    (5)
U.S. Treasury Strip, face value of
$6,875,000, due May 15, 2000                           6,210           6,210         $    --
U.S. Treasury Strip, face value of
$6,875,000, due November 15, 2000                      6,042           6,043         $    (1)
U.S. Treasury Strip, face value of
$6,875,000, due May 15, 2000                           5,877           5,877         $    --
                                                 -----------     -----------
Total Long-term held-to-maturity investments         $24,508         $24,514         $    (6)
                                                 ===========     ===========     ===========
</TABLE>

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

3.    LONG TERM DEBT

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

     The Notes 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 in 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.

     The Company currently is negotiating an agreement with Banque Paribas
providing for a $25 million senior secured revolving credit facility. The
revolving credit facility will have a term of not less than three years. The
Company expects that borrowings under the facility will bear interest, at the
Company's option, at LIBOR plus a margin of 2.75% or Citibank's base rate plus a
margin of 1.00%; provided, however, that the applicable margins for both LIBOR
and base rate loans will increase by 1.25% under certain circumstances. As
annual commitment fee of 0.50% is expected to be payable on the unused 


                                     6
<PAGE>   8
available portion of the facility. In addition, the Company expects to pay a
customary underwriting fee and other expenses in connection with the facility.
The Company expects that the facility will be secured by certain assets of the
Company , including the stock of certain of the Company's subsidiaries and that
the facility will contain certain restrictive covenants which impose limitations
on the Company and its Subsidiaries, with respect to, among other things, (1)
the creation of liens, (ii) mergers, acquisitions or dispositions of assets,
(iii) incurrence of indebtedness, (iv) transactions with affiliates, (v)
sale-leaseback transactions and (vi) dividends and other restricted payments.
The covenants are not expected to restrict the Company's ability to divest its
interests in Papua New Guinea or in Australia. The credit facility will also
require the Company to maintain a minimum current ratio, a minimum tangible net
worth, and a minimum debt coverage ratio. The credit facility will contain
customary events of default. While it is anticipated that the credit facility
will be completed in the third quarter of 1998, no assurance can be made that
the credit facility will be completed on the terms set forth above or on terms
acceptable to the Company.

4.    RECENTLY ISSUED ACCOUNTING PRONOUNCEMENTS

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

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

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

     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 


                                     7
<PAGE>   9

effect 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.

5.    SUBSEQUENT EVENT

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

         The Toronto Stock Exchange granted up to a six month extension, to
     February 5, 1999, of the exercise period for the purchase warrants issuable
     upon the exercise of exchange and conversion rights attached to the
     Company's outstanding $25 million issue of 6% Exchangeable Subordinated
     Notes. The warrants will expire prior to February 5, 1999, if the weighted
     average trading price of the Company's common shares on The Toronto Stock
     Exchange exceeds $17.64 for a 20 day period during the extension period
     ("the Triggering Event"). The exercise period for the warrants will then
     expire 30 calendar days following the Triggering Event. The warrants
     potentially represent 1.087 million common shares, with a strike price of
     $15.00 per share and originally were scheduled to expire August 7, 1998.
     All other terms and conditions regarding the subject purchase warrants
     remain unchanged.

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

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

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

TERMS OF ASSOCIATION CONTRACTS AND RELATED MATTERS

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

     Under the terms of the Association Contracts, if a commercially feasible
discovery is made, Ecopetrol may acquire a 50% interest in the property. If
Ecopetrol elects to acquire a 50% interest in the property, the interests of
all other parties to the contract, including the Company, will be reduced by
50%. Ecopetrol will then bear 50% of the associated development costs and must
reimburse the other working interest owners for 50% of certain exploration
activities. The Company expects that Ecopetrol will elect to finance a
significant portion of the costs associated with its working interest from
Ecopetrol's share of future production rather than contributing its 
proportionate share of development costs in cash. As a result, the Company and
the other working interest owners may be required initially to finance
Ecopetrol's share of the development costs associated with the property. As a
result, the Company and the other working interest owners may be required
initially to finance Ecopetrol's share of the development costs associated with
the property. While the Association Contracts do not require Ecopetrol's
participation in the pipeline and production facilities, the Company expects
that Ecopetrol will participate to the extent of 50% of the Phase I and Phase
II pipeline and infrastructure costs. No assurances can be given, however, that
an agreement will be reached on these terms and the Company may be required to
fund amounts greater than the amounts presented as the Company's net share. 


                                     8
<PAGE>   10

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

COLOMBIAN TAXES

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

ACCOUNTING POLICIES AND DEVELOPMENT STAGE ACCOUNTING

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

     The Company's exploration and development activities have generated an
insignificant amount of revenue, thus requiring the financial statements to be
presented as a development stage enterprise. Accumulated losses are presented on
the balance sheet as "Deficit accumulated during the development stage." The
income statement presents revenues and expenses for each period presented and
also a cumulative total of both amounts from the Company's inception. The
statement of cash flows shows inflows and outflows for the date and number of
shares of each class of security issued for cash or other consideration and the
dollar amount assigned. In addition, the notes to financial statements are
required to identify the enterprise as development stage.

     The Company follows the full-cost method of accounting for oil and natural
gas properties. Under this method, all costs incurred in the acquisition,
exploration and development of oil and gas properties, including unproductive
wells, are capitalized in separate cost centers for each country. Such
capitalized costs include contract and concession acquisition, geological,
geophysical and other exploration work, drilling, completing and equipping oil
and gas wells, constructing production facilities and pipelines, and other
related costs. As of December 31, 1996, unevaluated oil and gas interests
included capitalized general and administrative costs of $0.1 million. No
additional general and administrative costs were capitalized during 1997 or
1998. The Company capitalized interest of $0.6 million for the year ended
December 31, 1997 and $3.4 million for the six month period ended June 30, 1998.

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

     As of June 30, 1998, 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 materially dependent upon the success of the Company's
Emerald Mountain operations.


                                        9
<PAGE>   11
RESULTS OF DEVELOPMENT STAGE OPERATIONS

Three Months Ended June 30, 1998 and 1997

     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 $0.1 million, and $0.1
million for the quarter ended June 30, 1998 and 1997, respectively. Lease
operating expenses were $0.6 million and $1,000 for the quarter ended June 30,
1998 and 1997, respectively. The 1998 lease operating expenses represent such
costs as tank rentals and other miscellaneous fixed costs.

     Interest income was $1.0 million for the quarter ended June 30, 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 were $1.2 million during the quarter ended
June 30, 1998 as compared to $2.4 million during the same period of 1997. The
quarter ended June 30, 1997 includes costs of severance and related compensation
costs associated with the resignations of former officers.

     Depreciation and amortization was $0.1 and $17,000 for the quarter ended
June 30,1998 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 June 30, 1998, the Company
has not recorded depletion of its proved oil and gas property as only
insignificant quantities of oil have been produced during its production testing
plan.

     The Company incurred net losses of $0.7 million and $2.1 million for the
quarter ended June 30, 1998 and 1997, respectively.

Six Months Ended June 30, 1998 and 1997

     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 $0.1 million, and $0.4
million for the six months ended June 30, 1998 and 1997, respectively. Lease
operating expenses were $0.8 million and $0.2 million for the six months ended
June 30, 1998 and 1997, respectively. Lease operating expenses represent such
costs as tank rentals and other miscellaneous fixed costs.

     Interest income was $1.1 million for the six months ended June 30, 1998 as
compared to $0.2 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 were $2.3 million during the six months
ended June 30, 1998 as compared to $3.3 million during the same period of 1997.
The six month period ended June 30, 1997 includes costs of severance and related
compensation costs associated with the resignations of former officers. However,
the costs incurred during the six months ended June 30, 1998 reflect increases
in personnel costs as well as expansion of operations in Colombia.

     Depreciation and amortization was $0.2 million and $38,000 for the six
months ended June 30,1998 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 June 30,
1998, the Company has not recorded depletion of its proved oil and gas property
as only insignificant quantities of oil have been produced during its production
testing plan.

     The Company incurred net losses of $1.9 million and $2.9 million for the
six months ended June 30, 1998 and 1997, respectively.


                                     10
<PAGE>   12

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 June 30,
1998, resulting in aggregate cash proceeds of $155.1 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 June 30, 1998, the
Company had capital expenditures of $43.1 million for the acquisition,
exploration, and development of its oil and gas properties including $41.0
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 were approximately $67.6
million.

     The Company's primary capital commitments include Phases I and II of its
Emerald Mountain development program. The Company's capital expenditures
estimated for Phase I include $18.1 million for field development and
delineation and $51.9 million for pipeline and production facilities, which is
scheduled for completion in mid- to late 1999. The Company's capital
expenditures estimated for Phase II include $114.7 million for field development
and delineation and $83.5 million for pipeline and production facilities, which
is scheduled for completion in mid- 2000. The Company had working capital of
$78.7 million as of June 30, 1998. The Company believes that the net proceeds of
the offering of Senior Notes, together with other sources of funds expected to
be available to it (including bank financing and proceeds from the exercise of
warrants), will be sufficient to finance its initial net capital expenditure
requirements estimate for Phase I. Substantial amounts of capital will be needed
to finance Phase II, and no external sources of capital have yet been
identified. Certain expenditures for Phase II are expected to occur during Phase
I. In addition, the Company has budgeted approximately $14.3 million to
participate in drilling a deep exploratory well on Emerald Mountain scheduled to
be commenced in the first quarter of 1999. The Company expects that additional
amounts for capital expenditures may be funded through cash from operations,
joint ventures and other such arrangements, and debt or equity financings. The
Company does not expect any significant funds from operations until scheduled
completion of the initial pipeline and production facilities in mid- to late
1999. There can be no assurances that debt or equity financing will be available
to the Company on economically acceptable terms.

     Colombia. During the remainder of 1998, the Company plans to drill a total
of four 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 $37.6 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. Drilling activity on the
exploratory well has been completed; however, testing of potential production
intervals were suspended due to risk of flooding caused by heavy rain. Testing
is expected to resume in the fourth quarter of 1998.

     For the six months ended June 30, 1998 and June 30, 1997, the Company had
oil sales of $0.1 million and $0.4 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 commercial
production is not expected until further development of the field is completed
through the drilling of additional wells and construction of producing
facilities and pipelines. The Company has received preliminary plans for the
construction of pipelines and producing facilities, and permitting and final
planning for pipelines and production facilities are now proceeding. Completion
of the first phase of these facilities is scheduled to occur in mid- to late
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 


                                     11
<PAGE>   13

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 commencing on December 31, 1997 at a rate of 6% per annum on
December 31 and June 30 in each year until maturity on August 7, 2003.

     The Exchangeable Notes are exchangeable for a like principal amount of
Convertible Debentures at any time prior to the date (the "Exchange Date") that
is the earlier to occur of (i) the third business day following (a) the
effectiveness of a registration statement under the Securities Act covering the
registration for resale of the Common Shares and Warrants issuable upon
conversion of the Convertible Debentures and (b) the issuance by certain
Canadian securities commissions of receipts for a final prospectus in compliance
with Canadian securities law requirements and (ii) August 7, 1998. The
Convertible Debentures are convertible into Units at a rate of $11.50 per Unit,
each Unit consisting of one Common Share and one-half of one Warrant, for a
total of 2,173,913 Common Shares and 1,086,957 Warrants. Each Warrant is
exercisable for one Common Share at an exercise price of $15.00.
 
     On July 23, 1998, the Toronto Stock Exchange (the "TSE") granted an
extension of the exercise period for the Warrants from August 7, 1998 to 5:00
p.m. (Calgary time) 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 on the TSE exceeds US$17.64; and
 
          (ii) February 5, 1999.
 
     After the Exchange Date, the Convertible Debentures are convertible into
Units at the option of the Company, and provided that the Company's registration
statement filed with the SEC has been effective during the seven-day notice
period prior to the Company's exercise of its conversion rights, and provided
further that the Company's Common Shares have traded at or above $14.00 per
share for 20 consecutive trading days on The Toronto Stock Exchange. The
Exchangeable Notes are, and the Convertible Debentures will be, secured by a
pledge of shares of certain of the subsidiaries of the Company and are
guaranteed by Seven Seas Petroleum Holdings Inc.

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

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

     The Senior Notes are senior obligations of the Company and rank pari passu
in right and priority of payment with all existing and future senior
indebtedness of the Company.

     Proposed Credit Facility. The Company is negotiating an agreement with
Banque Paribas providing for a $25 million senior secured revolving credit
facility. The revolving credit facility will have a term of not less than three
years. 


                                     12
<PAGE>   14
The Company expects that borrowings under the facility will bear interest, at
the Company's option, at LIBOR plus a margin of 2.75% or Citibank's base rate
plus a margin of 1.00%; provided, however, that the applicable margins for both
LIBOR and base rate loans will increase by 1.25% under certain circumstances. An
annual commitment fee of 0.50% is expected to be payable on the unused available
portion of the facility. In addition, the Company expects to pay a customary
underwriting fee and other expenses in connection with the facility. The Company
expects that the facility will be secured by certain assets of the Company,
including the stock of certain of the Company's Subsidiaries and that the
facility will contain certain restrictive 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 disposition of assets, (iii)
incurrence of indebtedness, (iv) transactions with affiliates, (v)
sale-leaseback transactions and (vi) dividends and other restricted payments.
The covenants are not expected to restrict the Company's ability to divest its
interests in Papua New Guinea or in Australia. The credit facility will also
require the Company to maintain a minimum current ratio, a minimum tangible net
worth, and a minimum debt coverage ratio. The credit facility will contain
customary events of default. While it is anticipated that the credit facility
will be completed in the third quarter of 1998, no assurance can be made that
the credit facility will be completed on the terms set forth above or on terms
acceptable to the Company.

     Year 2000 Disclosure

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

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

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


                                     13
<PAGE>   15

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

                 DISCLOSURE REGARDING FORWARD LOOKING STATEMENTS

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

ITEM 3.  QUANTITATIVE AND QUALITATIVE DISCLOSURE ABOUT MARKET RISK

     Not applicable.

PART II. OTHER INFORMATION



                                     14
<PAGE>   16
Item 4.   Submission of Matters to a Vote of Security Holders

     The 1998 annual meeting (the "Annual Meeting") of the shareholders of the
     Company was held on June 4, 1998. The purpose of the Annual Meeting was to
     consider and vote upon the following proposals:

     1.   to elect directors to hold office until the next annual meeting of the
          Company's shareholders;

     2.   to appoint the auditors of the Company for the ensuing year and to
          authorize the directors to fix the remuneration to be paid to such
          auditors;

     3.   to approve the Seven Seas Petroleum Inc. 1997 Stock Option Plan; and

     4.   to approve an extension of the exercise period applicable to certain
          options granted under the Seven Seas Petroleum Inc. 1996 Stock Option
          Plan.

     The Company's Board of Directors is comprised of nine members. At the
     Annual Meeting, each of the following individuals was re-elected to serve
     as a director of the Company by proxy, with a total of 24,857,754 votes for
     the directors as a group and 134,317 votes withheld: Robert A. Hefner III;
     Breene M. Kerr; Brian F. Egolf; Sir Mark Thomson BT; Robert B. Panero; Gary
     F. Fuller; James D. Scarlett; Larry A. Ray; Herbert C. Williamson III.

     The following votes were cast by proxy with respect to the ratification of
     the selection of Arthur Andersen LLP as independent auditors of the Company
     for the fiscal year ending December 31, 1998:

          For:            24,961,721
          Withheld:           30,350

     The following votes were cast by ballot with respect to the ratification of
     the Seven Seas Petroleum Inc. 1997 Stock Option Plan:

          For:                14,462,359
          Against/Withheld:    2,252,670

     The following votes were cast by ballot with respect to the ratification of
     the extension of the exercise period applicable to certain options granted
     under the Seven Seas Petroleum Inc. 1996 Stock Option Plan:

          For:                13,718,965
          Against/Withheld:    2,989,320


Item 6.  Exhibits and Reports on 8-K

     (a) Exhibits:


<TABLE>
<S>               <C>
 (27)             Financial Data Schedule

</TABLE>

       (b)  Reports on Form 8-K

              None




                                     15
<PAGE>   17

                                   SIGNATURES

                                   Seven Seas Petroleum Inc.
Date:  August 14, 1998       By:   Herbert C. Williamson, III
                                   Executive Vice President and Chief Financial 
                                   Officer

                                   /s/ RAY A. HOUSLEY

                                   Ray A. Housley
                                   Treasurer and Controller




                                     16
<PAGE>   18
                               INDEX TO EXHIBITS


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

</TABLE>