<PAGE>   1
 
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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549
 
                            ------------------------
                                   FORM 10-Q
                            ------------------------
 
              [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
 
             [ ] TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(D)
                   OF THE SECURITIES EXCHANGE ACT OF 1934
 
                         COMMISSION FILE NUMBER 1-14521
 
                                  CONOCO INC.
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                            <C>
                  DELAWARE                                 (51-0370352)
(State or other jurisdiction of incorporation  (I.R.S. Employer Identification No.)
              or organization)
</TABLE>
 
                          600 NORTH DAIRY ASHFORD ROAD
                              HOUSTON, TEXAS 77079
                    (Address of principal executive offices)
 
                                 (281) 293-1000
              (Registrant's telephone number, including area code)
 
     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
 
     190,683,943 shares of Class A Common Stock, $0.01 par value, and
436,543,573 shares of Class B Common Stock, $0.01 par value, were outstanding as
of May 11, 1999.
 
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<PAGE>   2
 
                                  CONOCO INC.
 
                               TABLE OF CONTENTS
 
<TABLE>
<CAPTION>
                                                               PAGE(S)
                                                               -------
<S>                                                            <C>
Part I -- Financial Information
  Item 1. Financial Statements
     Consolidated Statement of Income.......................      1
     Consolidated Balance Sheet.............................      2
     Consolidated Statement of Cash Flows...................      3
     Notes to Consolidated Financial Statements.............      4
  Item 2. Management's Discussion and Analysis of Financial
     Condition and Results of Operations
     (a) Financial Condition................................     12
     (b) Results of Operations..............................     15
  Item 3. Quantitative and Qualitative Disclosures About
     Market Risk............................................     21
Part II -- Other Information
  Item 1. Legal Proceedings.................................     24
  Item 4. Submission of Matters to Vote of Security
     Holders................................................     24
  Item 5. Other Information
     (a) Disclosure Regarding Forward-Looking Information...     25
     (b) Split-Off of Conoco from DuPont....................     26
  Item 6. Exhibits and Reports on Form 8-K..................     26
Signature...................................................     27
Exhibit Index...............................................     28
</TABLE>
 
                                        i
<PAGE>   3
 
                                     PART I
 
                             FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS
 
                                  CONOCO INC.
 
                CONSOLIDATED STATEMENT OF INCOME (NOTES 1 AND 3)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   MARCH 31
                                                              ------------------
                                                               1999        1998
                                                              ------      ------
                                                                (IN MILLIONS,
                                                              EXCEPT PER SHARE)
<S>                                                           <C>         <C>
Revenues
  Sales and Other Operating Revenues*.......................  $5,311      $5,736
  Other Income..............................................      24          98
                                                              ------      ------
          Total Revenues....................................   5,335       5,834
                                                              ------      ------
Cost and Expenses
  Cost of Goods Sold and Other Operating Expenses...........   3,005       3,393
  Selling, General and Administrative Expenses..............     186         183
  Exploration Expenses......................................      46          67
  Depreciation, Depletion and Amortization..................     302         267
  Taxes Other Than on Income*...............................   1,591       1,417
  Interest and Debt Expense.................................      71           1
                                                              ------      ------
          Total Cost and Expenses...........................   5,201       5,328
                                                              ------      ------
Income Before Income Taxes..................................     134         506
Provision for Income Taxes..................................      51         190
                                                              ------      ------
Net Income (Note 10)........................................  $   83      $  316
                                                              ======      ======
Earnings Per Share (Note 4)
  Basic.....................................................  $  .13      $  .72
  Diluted...................................................  $  .13      $  .72
Weighted Average Shares Outstanding (Note 4)
  Class A**.................................................     191          --
  Class B...................................................     437         437
                                                              ------      ------
          Total Basic.......................................     628         437
  Stock Options**...........................................       7          --
                                                              ------      ------
          Total Diluted.....................................     635         437
Dividends Per Share of Common Stock (Note 5)................  $  .14      $   --
</TABLE>
 
---------------
 
<TABLE>
<S>                                                           <C>         <C>
 * Includes petroleum excise taxes..........................  $1,546      $1,373
</TABLE>
 
** Earnings Per Share for the period prior to the Offerings was calculated using
   only Class B Common Stock as required by SFAS 128 (See Note 4).
 
                 See Notes to Consolidated Financial Statements
 
                                        1
<PAGE>   4
 
                                  CONOCO INC.
 
                   CONSOLIDATED BALANCE SHEET (NOTES 1 AND 3)
                                  (UNAUDITED)
 
                                     ASSETS
 
<TABLE>
<CAPTION>
                                                              MARCH 31,   DECEMBER 31,
                                                                1999          1998
                                                              ---------   ------------
                                                                   (IN MILLIONS)
<S>                                                           <C>         <C>
Current Assets
  Cash and Cash Equivalents.................................   $   425      $   394
  Accounts and Notes Receivable.............................     1,228        1,191
  Inventories (Note 6)......................................       899          807
  Prepaid Expenses..........................................       305          378
                                                               -------      -------
          Total Current Assets..............................     2,857        2,770
Property, Plant and Equipment...............................    22,031       22,094
Less: Accumulated Depreciation, Depletion and
  Amortization..............................................   (10,801)     (10,681)
                                                               -------      -------
Net Property, Plant and Equipment...........................    11,230       11,413
                                                               -------      -------
Investment in Affiliates....................................     1,445        1,363
Other Assets................................................       548          529
                                                               -------      -------
          Total.............................................   $16,080      $16,075
                                                               =======      =======
 
                         LIABILITIES AND STOCKHOLDERS' EQUITY
 
Current Liabilities
  Accounts Payable..........................................   $ 1,355      $ 1,312
  Short-Term Borrowings -- Related Parties..................       926           --
  Other Short-Term Borrowings and Capital Lease
     Obligations............................................        29           52
  Income Taxes..............................................       171          199
  Other Accrued Liabilities (Note 7)........................     1,082        1,162
                                                               -------      -------
          Total Current Liabilities.........................     3,563        2,725
Long-Term Borrowings -- Related Parties.....................     3,970        4,596
Other Long-Term Borrowings and Capital Lease Obligations....        93           93
Deferred Income Taxes.......................................     1,658        1,714
Other Liabilities and Deferred Credits......................     2,144        2,200
                                                               -------      -------
          Total Liabilities.................................    11,428       11,328
                                                               -------      -------
Commitments and Contingent Liabilities (Note 8)
Minority Interests..........................................       310          309
Stockholders' Equity
  Preferred Stock, $.01 par value:
  250,000,000 shares authorized; none issued................        --           --
  Class A Common Stock, $.01 par value:
  3,000,000,000 shares authorized; 191,497,821 shares
     issued.................................................         2            2
  Class B Common Stock, $.01 par value:
  1,600,000,000 shares authorized; 436,543,573 shares issued
     and outstanding........................................         4            4
  Additional Paid-In Capital................................     4,975        4,955
  Accumulated Deficit.......................................      (250)        (244)
  Accumulated Other Comprehensive Loss (Note 9).............      (367)        (274)
  Treasury Stock, at cost (1,032,607 and 249,863 Class A
     shares at March 31, 1999 and December 31, 1998,
     respectively)..........................................       (22)          (5)
                                                               -------      -------
          Total Stockholders' Equity........................     4,342        4,438
                                                               -------      -------
          Total.............................................   $16,080      $16,075
                                                               =======      =======
</TABLE>
 
                 See Notes to Consolidated Financial Statements
 
                                        2
<PAGE>   5
 
                                  CONOCO INC.
 
              CONSOLIDATED STATEMENT OF CASH FLOWS (NOTES 1 AND 3)
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                     MARCH 31
                                                                -------------------
                                                                 1999        1998
                                                                ------      -------
                                                                   (IN MILLIONS)
<S>                                                             <C>         <C>
Cash Provided by Operations
  Net Income................................................    $  83       $  316
  Adjustments to Reconcile Net Income to Cash Provided by
     Operations:
     Depreciation, Depletion and Amortization...............      302          267
     Dry Hole Costs and Impairment of Unproved Properties...       17           22
     Deferred Income Taxes..................................      (42)          48
     Income Applicable to Minority Interest.................        5            5
     Other Noncash Charges and Credits -- Net...............        8          (51)
     Decrease (Increase) in Operating Assets:
       Accounts and Notes Receivable........................      (52)         178
       Inventories..........................................     (107)        (192)
       Other Operating Assets...............................       25          (98)
     Increase (Decrease) in Operating Liabilities:
       Accounts Payable and Other Operating Liabilities.....      113         (379)
       Accrued Interest and Income Taxes....................       41         (104)
                                                                -----       ------
          Cash Provided by Operations.......................      393           12
                                                                -----       ------
Investment Activities
  Purchases of Property, Plant and Equipment................     (457)        (389)
  Investments in Affiliates.................................     (100)         (42)
  Proceeds from Sales of Assets and Subsidiaries............       18          275
  Net Decrease (Increase) in Short-Term Financial
     Instruments............................................       (8)          (9)
                                                                -----       ------
          Cash Used for Investment Activities...............     (547)        (165)
                                                                -----       ------
Financing Activities
  Cash Dividends (Note 5)...................................      (88)          --
  Short-Term Borrowings -- Receipts.........................       --            2
                            -- Payments.....................       (1)         (21)
  Other Long-Term Borrowings -- Payments....................      (19)          (3)
  Treasury Stock Purchases..................................      (18)          --
  Transactions with Related Parties:
       Notes Receivable -- Receipts.........................       --           48
                          -- Payments.......................       --         (162)
       Borrowings -- Receipts...............................      710          137
                   -- Payments..............................     (410)          --
       Net Cash Contribution From (To) Owner................       19         (258)
  Increase (Decrease) in Minority Interests.................       (5)          (5)
                                                                -----       ------
          Cash Provided by (Used for) Financing
            Activities......................................      188         (262)
                                                                -----       ------
Effect of Exchange Rate Changes on Cash.....................       (3)          (3)
                                                                -----       ------
Increase (Decrease) in Cash and Cash Equivalents............       31         (418)
Cash and Cash Equivalents at Beginning of Year..............      394        1,147
                                                                -----       ------
Cash and Cash Equivalents at March 31.......................    $ 425       $  729
                                                                =====       ======
</TABLE>
 
                 See Notes to Consolidated Financial Statements
 
                                        3
<PAGE>   6
 
                                  CONOCO INC.
 
                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
1. BASIS OF PRESENTATION
 
     Conoco Inc., including its consolidated subsidiaries ("Conoco"), is an
integrated, global energy company that is involved in the Upstream and
Downstream operating segments of the petroleum industry. Activities of the
Upstream operating segment include exploring for, and developing, producing and
selling crude oil, natural gas and natural gas liquids. Activities of the
Downstream operating segment include refining crude oil and other feedstocks
into petroleum products, buying and selling crude oil and refined products, and
transporting, distributing and marketing petroleum products. Conoco has four
reporting segments for its Upstream and Downstream businesses, reflecting
geographic division between the United States and International. Corporate and
other includes general corporate expenses, financing costs and other
non-operating items, and results for electric power and related-party insurance
operations.
 
     The initial public offerings (the "Offerings") of the Class A Common Stock
of Conoco commenced on October 21, 1998, and the Class A Common Stock began
trading on the New York Stock Exchange on October 22, 1998. The Offerings
consisted of 191,456,427 shares of Class A Common Stock issued at a price of $23
per share, and represented E.I. du Pont de Nemours and Company's ("DuPont")
first step in the planned divestiture of Conoco. Through its ownership of 100
percent of Conoco's Class B Common Stock (436,543,573 shares), DuPont owned
approximately 70 percent of Conoco's common stock representing approximately 92
percent of the combined voting power of all classes of voting stock of Conoco at
March 31, 1999. The holders of Class A Common Stock and Class B Common Stock
generally have identical rights, except that holders of Class A Common Stock are
entitled to one vote per share while holders of Class B Common Stock are
entitled to five votes per share on matters to be voted on by stockholders.
 
     Prior to the date of the Offerings, operations were conducted by Conoco
Inc., subsidiaries of Conoco Inc. and, in some cases, subsidiaries of DuPont.
The accompanying consolidated financial statements for this period are presented
on a carve-out basis prepared from DuPont's historical accounting records, and
include the historical operations of both entities owned by Conoco and
operations transferred to Conoco by DuPont at the time of the Offerings. In this
context, no direct ownership relationship existed among all the various units
comprising Conoco. Accordingly, net cash contributions from/to owner prior to
the Offerings included funds transferred between Conoco and DuPont for operating
needs, cash dividends paid and other equity transactions.
 
     Effective at the time of the Offerings, Conoco's capital structure was
established and the transfer to Conoco of certain subsidiaries previously owned
by DuPont was substantially complete, resulting in direct ownership of those
subsidiaries. Accordingly, for periods subsequent to the Offerings, financial
information is presented on a consolidated basis.
 
     On March 22, 1999, Conoco filed a registration statement with the
Securities and Exchange Commission ("SEC") outlining a "split-off" plan to
establish Conoco as a fully independent company. This filing is the next step in
DuPont's planned divestiture of Conoco. The tax-free split-off will be achieved
through an exchange offer in which DuPont stockholders will be given an
opportunity to exchange DuPont common stock for shares of Conoco Class B Common
Stock currently held by DuPont. DuPont announced on April 28, 1999 that its
board of directors had approved the split-off plan. Following a review by the
SEC, and depending on market conditions, the split-off is expected to be
completed in the third quarter of 1999.
 
     These consolidated interim financial statements are unaudited, but reflect
all adjustments that, in the opinion of management, are necessary to provide a
fair presentation of the financial position, results of operations and cash
flows for the dates and periods covered. All such adjustments are of a normal
recurring nature. Interim period results are not necessarily indicative of
results of operations or cash flows for a full-year
 
                                        4
<PAGE>   7
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
period. These interim financial statements should be read in conjunction with
the consolidated financial statements and notes thereto included in Conoco's
1998 Annual Report on Form 10-K as amended.
 
2. RECENTLY ISSUED STATEMENTS OF FINANCIAL ACCOUNTING STANDARDS
 
     Effective January 1, 1999, Conoco adopted Statement of Position 98-5,
"Reporting on the Costs of Start-Up Activities," issued by the American
Institute of Certified Public Accountants. This Statement requires that costs
related to start-up activities, including organization costs, be expensed as
incurred. Conoco's policy has been one of expensing organization and other
similar costs of start-up operations. Accordingly, we have no cumulative charge
to earnings from a write-off of deferred start-up costs as a result of adoption
of this accounting standard.
 
     In June 1998, the Financial Accounting Standards Board ("FASB") issued
Statement on Financial Accounting Standards ("SFAS") No. 133, "Accounting for
Derivative Instruments and Hedging Activities", which requires that companies
recognize all derivatives as either assets or liabilities in the balance sheet
and measure those instruments at fair value. SFAS No. 133 provides, if certain
conditions are met, that a derivative may be specifically designated as (1) a
hedge of the exposure to changes in the fair value of a recognized asset or
liability or an unrecognized firm commitment (fair value hedge), (2) a hedge of
the exposure to variable cash flows of a forecasted transaction (cash flow
hedge), or (3) a hedge of the foreign currency exposure of a net investment in a
foreign operation, an unrecognized firm commitment, an available-for-sale
security or a foreign-currency-denominated forecasted transaction (foreign
currency hedge). Under SFAS No. 133, the accounting for changes in fair value of
a derivative depends on its intended use and designation. For a fair value
hedge, the gain or loss is recognized in earnings in the period of change
together with the offsetting loss or gain on the hedged item. For a cash flow
hedge, the effective portion of the derivative's gain or loss is initially
reported as a component of other comprehensive income and subsequently
reclassified into earnings when the forecasted transaction affects earnings. For
a foreign currency hedge, the gain or loss is reported in other comprehensive
income as part of the cumulative translation adjustment. For all other items not
designated as hedging instruments, the gain or loss is recognized in earnings in
the period of change. Conoco is required to adopt this Statement by the first
quarter of 2000 and is currently assessing its effect on the consolidated
financial statements.
 
3. RELATED PARTY TRANSACTIONS
 
     The consolidated financial statements include significant transactions with
DuPont involving services (such as cash management, other financial services,
purchasing, legal, computer and corporate aviation) and general corporate
expenses that were provided between Conoco and DuPont organizations. For periods
prior to the Offerings, the costs of services were directly charged or allocated
between Conoco and DuPont using methods management believes are reasonable.
These methods included negotiated usage rates, dedicated asset assignment and
proportionate corporate formulas involving assets, revenues and employees. Such
charges and allocations were not necessarily indicative of what would have been
incurred if Conoco had been a separate entity.
 
     Amounts charged and allocated to Conoco for these services were $7 and $34
for the first quarter of 1999 and 1998, respectively, and are principally
included in selling, general and administrative expenses. Conoco provided DuPont
services such as computer, legal and purchasing, as well as certain technical
and plant operating services, which amounted to $7 and $14 for the first quarter
of 1999 and 1998, respectively. These charges to DuPont were treated as
reductions, as appropriate, of cost of goods sold and other operating expenses
and selling, general and administrative expenses.
 
     Interest expense charged by DuPont was $72 and $27 for the first quarter of
1999 and 1998, respectively, and reflects market-based interest rates. A portion
of historical related party interest cost and other interest
 
                                        5
<PAGE>   8
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
expense of $2 and $28 for the first quarter of 1999 and 1998, respectively, was
capitalized as costs associated with major construction projects. Interest
income from DuPont was $16 for the first quarter of 1998 and also reflects
market-based interest rates.
 
     Sales and other operating revenues include sales of products from Conoco to
DuPont, principally natural gas and gas liquids to supply several DuPont plant
sites. These sales totaled $91 and $110 in the first quarter of 1999 and 1998,
respectively. Also included, for the first quarter of 1998, are revenues of $5
from insurance premiums charged to DuPont for property and casualty coverage
outside the United States. Purchases of products from DuPont during these
periods were not material. Subsequent to the Offerings, these intercompany
arrangements between DuPont and Conoco, excluding insurance coverage provided to
DuPont, are provided under transition service agreements or other long-term
agreements. It is not anticipated that a change, if any, in these costs and
revenues would have a material effect on Conoco's results of operations or
consolidated financial position.
 
     Accounts and notes receivable include amounts due from DuPont of $48 and
$80 at March 31, 1999, and December 31, 1998, respectively, representing current
month balances of transactions between Conoco and DuPont, mainly product sales
and certain charges billed annually. Accounts payable include amounts due DuPont
of $35 and $52 at March 31, 1999, and December 31, 1998, respectively. Other
liabilities include accrued interest of $122 and $51 due DuPont at March 31,
1999 and December 31, 1998, respectively.
 
     Amounts representing notes receivable or borrowings from DuPont, including
its subsidiary organizations, are identified as related parties and presented
separately in the consolidated balance sheet. At December 31, 1998, Conoco had
long-term borrowings from related parties of $4,596, representing the balance
under two promissory notes due on or before January 2, 2000. At March 31, 1999,
Conoco had aggregate related parties borrowings of $4,896 consisting of
short-term borrowings of $926 and long-term borrowings of $3,970. The short-term
borrowings consisted of $300 under a revolving credit agreement and $626 under
two promissory notes due on or before January 2, 2000. Subsequent to March 31,
1999, the long-term borrowings were refinanced with proceeds from placement of
public debt as described below. Consequently, the senior borrowings have been
classified as long-term pursuant to SFAS 6.
 
     On April 20, 1999, Conoco completed the public offering and sale of $4,000
of senior debt securities. The senior debt securities consisted of three
tranches as follows:
 
     - $1,350 in five-year notes due 2004 with a coupon of 5.90 percent, offered
       to the public at 99.856 percent.
 
     - $750 in ten-year notes due 2009 with a coupon of 6.35 percent, offered to
       the public at par.
 
     - $1,900 in 30-year notes due 2029 with a coupon of 6.95 percent, offered
       to the public at par.
 
     Conoco achieved a weighted average interest rate of 6.49 percent in this
financing. After deducting the note discount and underwriting discounts, the net
proceeds of $3,970 received from the senior debt offerings were used to repay a
portion of the outstanding principal and accrued interest owed to DuPont under
one of the promissory notes. It is expected that the remaining debt owed to
DuPont will be repaid in May 1999 with proceeds from a commercial paper program.
 
     The program provides Conoco with up to $2,000 of borrowing capacity and
gives Conoco the ability to issue commercial paper at any time with various
maturities not to exceed 270 days. As of May 13, 1999, the outstanding balance
borrowed under this program was $400, bearing a weighted average interest rate
of 4.99 percent, and was used to repay debt owed to DuPont.
 
                                        6
<PAGE>   9
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
4. EARNINGS PER SHARE
 
     Basic earnings per share ("EPS") is computed by dividing net income (the
numerator) by the weighted average number of common shares outstanding plus the
effects of award and fee deferrals that are invested in Conoco stock units by
certain employees and directors of Conoco (the denominator). Diluted EPS is
similarly computed, except that the denominator is increased to include the
dilutive effects of outstanding stock options awarded under Conoco's
compensation plans.
 
     As described in Note 1, Conoco's capital structure was established at the
time of the Offerings. In accordance with SEC Staff Accounting Bulletin No. 98,
the capitalization of Class B Common Stock has been retroactively reflected for
the purposes of presenting earnings per share for the first quarter of 1998. For
the first quarter of 1999, basic EPS reflects the Class B Common Stock plus the
weighted average number of shares of Class A Common Stock and deferred award
units outstanding at March 31, 1999. Corresponding diluted EPS for the first
quarter of 1999 includes an additional 7,347,178 shares representing the
weighted average dilutive effect of outstanding stock options that resulted from
the concurrent cancellation of DuPont stock options at the date of the Offerings
and issuance of options with respect to Class A Common Stock.
 
     The denominator is based on the following weighted average number of common
shares outstanding:
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                     MARCH 31
                                                             -------------------------
                                                                1999          1998
                                                             -----------   -----------
<S>                                                          <C>           <C>
Basic......................................................  627,633,168   436,543,573
Diluted....................................................  634,980,346   436,543,573
</TABLE>
 
     Variable stock options for 1,724,146 shares of common stock were
outstanding at March 31, 1999, but were not included in the computation of
diluted EPS since the threshold price of $32.88 required for these options to be
vested had not been reached.
 
     Common shares held as treasury stock are deducted in determining the number
of shares outstanding.
 
     For the three months ended March 31, 1999, stock options for 12,736,261
shares of Class A Common Stock are antidilutive and therefore are not included
in the diluted earnings per share calculation because the exercise price is
greater than the average market price.
 
PRO FORMA EPS
 
     Pro forma EPS for the first quarter of 1998 include the shares of Conoco
Class A and Class B Common Stock and deferred award units outstanding
immediately after the Offerings as if the Offerings had been completed at the
beginning of the period presented. Pro forma basic EPS is based on pro forma net
income for the first quarter of 1998 divided by the total Class A and Class B
Common Stock plus deferred award units outstanding immediately after the
Offerings (basic shares). For pro forma diluted EPS, basic shares have been
adjusted to reflect the effect of outstanding stock options immediately after
the Offerings as though outstanding for the period presented. Pro forma net
income reflects historical income for the period adjusted to give effect to the
transactions substantially completed in October 1998 directly associated with
the Offerings and separation from DuPont.
 
                                        7
<PAGE>   10
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
     The reconciliation of historical net income to pro forma net income with
pro forma adjustments separately identified is as follows:
 
<TABLE>
<CAPTION>
                                                                 THREE MONTHS ENDED
                                                                      MARCH 31
                                                     ------------------------------------------
                                                         1999           1998           1998
                                                        ACTUAL       PRO FORMA        ACTUAL
                                                     ------------   ------------   ------------
<S>                                                  <C>            <C>            <C>
Historical net income..............................  $         83   $        316   $        316
  Lower interest income(1).........................            --            (32)            --
  Incremental interest expense(2)..................            --            (46)            --
  Related tax effects(3)...........................            --             25             --
                                                     ------------   ------------   ------------
Net income.........................................  $         83   $        263   $        316
                                                     ============   ============   ============
Earnings per share:
  Basic............................................  $        .13   $        .42   $        .72
  Diluted..........................................  $        .13   $        .41   $        .72
Weighted average shares outstanding:
  Basic............................................   627,633,168    628,195,100    436,543,573
  Diluted..........................................   634,980,346    636,746,186    436,543,573
</TABLE>
 
---------------
 
(1) Lower interest income due to settlement of related party notes receivable
    and the impact of currency exchange rates on certain intercompany loans
    purchased by Conoco from DuPont.
 
(2) Incremental interest expense resulting from Conoco's new debt structure.
 
(3) Tax effects associated with adjustments in (1) and (2), and the impact of
    the calculation of income taxes on a separate return basis.
 
5. DIVIDENDS
 
     Conoco declared a first quarter cash dividend on January 27, 1999, of $.14
per share on each outstanding share of Class A Common Stock and Class B Common
Stock, payable March 12, 1999, to shareholders of record as of February 12,
1999. This initial dividend was determined on a pro rata basis covering the
period from October 27, 1998 to December 31, 1998, and is equivalent to $.19 per
share for a full quarter.
 
     On April 28, 1999, Conoco declared a quarterly cash dividend of $.19 per
share on each outstanding share of Class A and Class B Common Stock, payable on
June 12, 1999, to stockholders of record on May 14, 1999.
 
6. INVENTORIES
 
<TABLE>
<CAPTION>
                                                              MARCH 31,   DECEMBER 31,
                                                                1999          1998
                                                              ---------   ------------
<S>                                                           <C>         <C>
Crude oil and petroleum products............................    $757          $661
Other merchandise...........................................      22            22
Materials and supplies......................................     120           124
                                                                ----          ----
                                                                $899          $807
                                                                ====          ====
</TABLE>
 
7. RESTRUCTURING
 
     In December 1998, Conoco announced, that as a result of a comprehensive
review of its assets and long-term strategy, Conoco was making organizational
realignments consistent with furthering the efficiency of operations and taking
advantage of synergies created by the upgrading of its asset portfolio. The
announced
 
                                        8
<PAGE>   11
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
plans are being implemented in 1999 and will result in a reduction of
approximately 775 Upstream positions and 200 Downstream positions worldwide.
About three quarters of the Upstream positions and about half of the Downstream
positions affected will be in the United States. These reductions largely
reflect the elimination of redundancies at all levels resulting from past and
ongoing consolidation of assets into operations requiring less employee support
as well as better sharing of common services and functions across regions.
Associated with these announcements, Conoco recorded a charge in the fourth
quarter 1998 of $82 pretax ($52 after-tax), nearly all of which represents
termination payments and related employee benefits to be made to persons
affected. During the first quarter, approximately 134 persons in Upstream and 28
persons in Downstream left Conoco under implementation of these realignment
plans. The following table shows the status of, and changes to, the
restructuring reserve for the first quarter of 1999.
 
<TABLE>
<CAPTION>
                                                          UPSTREAM              DOWNSTREAM
                                                    --------------------   --------------------
                                                    U.S.   INTERNATIONAL   U.S.   INTERNATIONAL   TOTAL
                                                    ----   -------------   ----   -------------   -----
<S>                                                 <C>    <C>             <C>    <C>             <C>
Reserve at December 31, 1998......................  $31         $36         $8         $7          $82
  Expenditures....................................   (3)         (1)        --         --           (4)
  New accruals....................................   --          --         --         --           --
                                                    ---         ---         --         --          ---
Reserve at March 31, 1999.........................  $28         $35         $8         $7          $78
                                                    ===         ===         ==         ==          ===
</TABLE>
 
     We expect the restructuring efforts provided for in December 1998 will be
completed by year-end 1999.
 
8. COMMITMENTS AND CONTINGENT LIABILITIES
 
     Conoco has various purchase commitments for materials, supplies, services
and items of permanent investment incident to the ordinary conduct of business.
In the aggregate, such commitments are not at prices in excess of current
market. In addition, at March 31, 1999, Conoco had obligations under
international contracts to purchase, over periods up to 20 years, natural gas at
prices that were in excess of market prices at March 31, 1999. No material
annual loss is expected from these long-term commitments.
 
     Conoco is subject to various lawsuits and claims involving a variety of
matters including, along with other oil companies, actions challenging oil and
gas royalty and severance tax payments based on posted prices, and claims for
damages resulting from leaking underground storage tanks. As a result of the
separation agreement with DuPont, Conoco has also assumed responsibility for
current and future claims related to certain discontinued chemicals and
agricultural chemicals businesses operated by Conoco in the past. In general,
the effect on future financial results is not subject to reasonable estimation
because considerable uncertainty exists. Conoco believes the ultimate
liabilities resulting from such lawsuits and claims may be material to results
of operations in the period in which they are recognized but will not materially
affect the consolidated financial position of Conoco.
 
     Conoco is also subject to contingencies pursuant to environmental laws and
regulations that in the future may require further action to correct the effects
on the environment of prior disposal practices or releases of petroleum
substances by Conoco or other parties. Conoco has accrued for certain
environmental remediation activities consistent with the policy set forth in
Note 2 to the consolidated financial statements presented in Conoco's 1998 Form
10-K as amended. Conoco has assumed environmental remediation liabilities from
DuPont related to certain discontinued chemicals and agricultural chemicals
businesses operated by Conoco in the past, which are included in the
environmental accrual. At March 31, 1999, such accrual amounted to $130 and, in
management's opinion, was appropriate based on existing facts and circumstances.
Under adverse changes in circumstances, potential liability may exceed amounts
accrued. In the event future monitoring and remediation expenditures are in
excess of amounts accrued, they may be significant to results of operations in
the period recognized but management does not anticipate they will have a
material adverse effect on the consolidated financial position of Conoco.
                                        9
<PAGE>   12
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
     Conoco has indirectly guaranteed various debt obligations under agreements
with certain affiliated and other companies to provide specified minimum
revenues from shipments or purchases of products. At March 31, 1999, these
indirect guarantees totaled $18 and Conoco or DuPont, on behalf of and
indemnified by Conoco, had directly guaranteed $1,120 of the obligations of
certain affiliated companies and others. Conoco has a multiparty banking
agreement that provides for the indirect guarantee of bank account overdrafts
for itself and its subsidiaries. No material loss is anticipated by reason of
such agreements and guarantees.
 
9. COMPREHENSIVE (LOSS) INCOME
 
     The following sets forth Conoco's comprehensive income (loss) for the
periods shown:
 
<TABLE>
<CAPTION>
                                                               THREE MONTHS ENDED
                                                                    MARCH 31
                                                               ------------------
                                                                1999        1998
                                                               ------      ------
<S>                                                            <C>         <C>
Net Income..................................................    $ 83        $316
Other Comprehensive Loss:
  Foreign Currency Translation Adjustment...................     (93)        (18)
                                                                ----        ----
Comprehensive (Loss) Income.................................    $(10)       $298
                                                                ====        ====
</TABLE>
 
                                       10
<PAGE>   13
           NOTES TO CONSOLIDATED FINANCIAL STATEMENTS -- (CONTINUED)
                                  (UNAUDITED)
                    (DOLLARS IN MILLIONS, EXCEPT PER SHARE)
 
10. OPERATING SEGMENT AND GEOGRAPHIC INFORMATION
 
     Conoco is involved in both the Upstream and Downstream operating segments
of the petroleum industry. Activities of the Upstream operating segment include
exploring for, and developing, producing and selling, crude oil, natural gas and
natural gas liquids. Activities of the Downstream operating segment include
refining crude oil and other feedstocks into petroleum products, buying and
selling crude oil and refined products, and transporting, distributing and
marketing petroleum products. Conoco has four reporting segments for its
Upstream and Downstream businesses, reflecting geographic division between the
United States and International. Corporate and other includes general corporate
expenses, financing costs and other non-operating items, and results for
electric power and related-party insurance operations. Conoco sells its products
worldwide. Major products include crude oil, natural gas and refined products
that are sold primarily in the energy and transportation markets. Conoco's sales
are not materially dependent on a single customer or small group of customers.
Transfers between segments are on the basis of estimated market values.
 
<TABLE>
<CAPTION>
                                             UPSTREAM                DOWNSTREAM
                                      ----------------------   ----------------------
                                      UNITED                   UNITED                   CORPORATE
        SEGMENT INFORMATION           STATES   INTERNATIONAL   STATES   INTERNATIONAL   AND OTHER   CONSOLIDATED
        -------------------           ------   -------------   ------   -------------   ---------   ------------
<S>                                   <C>      <C>             <C>      <C>             <C>         <C>
THREE MONTHS ENDED MARCH 31, 1999
Sales and Other Operating
  Revenues..........................   $706        $479        $1,962      $2,143         $ 21         $5,311
Transfers Between Segments..........     74          79            18          43           --             --
                                       ----        ----        ------      ------         ----         ------
          Total Operating
            Revenues................   $780        $558        $1,980      $2,186         $ 21         $5,311
                                       ====        ====        ======      ======         ====         ======
Net Income (Loss)...................   $ 40        $ 68        $   17      $   23         $(65)        $   83
THREE MONTHS ENDED MARCH 31, 1998
Sales and Other Operating
  Revenues..........................   $863        $456        $2,185      $2,028         $204         $5,736
Transfers Between Segments..........     89         107            21          47           --             --
                                       ----        ----        ------      ------         ----         ------
          Total Operating
            Revenues................   $952        $563        $2,206      $2,075         $204         $5,736
                                       ====        ====        ======      ======         ====         ======
Net Income (Loss)(1)................   $ 88        $143        $   34      $   57         $ (6)        $  316
</TABLE>
 
---------------
 
(1) Includes After-Tax Benefits from Special Items:
 
<TABLE>
<S>                                   <C>      <C>             <C>      <C>             <C>         <C>
THREE MONTHS ENDED MARCH 31, 1999...   $ --        $ --        $   --      $   --         $ --         $   --
THREE MONTHS ENDED MARCH 31, 1998
  Asset Sales.......................   $ --        $ 23        $   --      $   --         $ --         $   23
</TABLE>
 
                                       11
<PAGE>   14
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS
 
(A) FINANCIAL CONDITION
 
LIQUIDITY AND CAPITAL RESOURCES
 
  CASH PROVIDED BY OPERATIONS
 
     Cash provided by operations in the first three months of 1999 increased
$381 million to $393 million versus $12 million in the first three months of
1998. Cash provided by operations before changes in operating assets and
liabilities decreased $234 million compared to the first three months of 1998,
primarily due to lower net realized crude oil and natural gas prices, weaker
refined product margins and increased interest expense resulting from
separation-related debt to DuPont incurred in the second half of 1998, partly
offset by higher volumes. Positive changes to net operating assets and
liabilities of $615 million were due to timing of payments on other operating
liabilities, lower 1999 tax payments and higher 1999 accrued interest, offset by
an increase in accounts receivable due to higher crude oil prices late in the
first quarter of 1999.
 
INVESTMENT ACTIVITIES
 
  CAPITAL EXPENDITURES AND INVESTMENTS
 
<TABLE>
<CAPTION>
                                                               THREE MONTHS ENDED
                                                                    MARCH 31
                                                               -------------------
                                                                1999         1998
                                                               ------       ------
                                                                  (IN MILLIONS)
<S>                                                            <C>          <C>
Upstream:
  United States.............................................    $113         $149
  International.............................................     198          187
                                                                ----         ----
          Total Upstream....................................    $311         $336
Downstream:
  United States.............................................    $ 32         $ 30
  International.............................................      70           65
                                                                ----         ----
          Total Downstream..................................    $102         $ 95
Corporate and Other.........................................       2            0
                                                                ----         ----
          Total Capital Expenditures and Investments........    $415         $431
                                                                ====         ====
  United States.............................................    $147         $179
  International.............................................     268          252
                                                                ----         ----
          Total.............................................    $415         $431
                                                                ====         ====
</TABLE>
 
     Total capital expenditures and investments (excluding amounts paid in the
first quarter of 1999 for the completion of 1998 acquisitions) were $415
million, a decrease of $16 million, or four percent, versus the first quarter of
1998 of $431 million. The decrease is primarily due to lower spending on
Upstream capital projects in the United States. Described below is a more
detailed analysis of capital expenditures and investments by operating segments
within the United States and International. Capital expenditures and investments
do not include expensed exploration costs.
 
     Upstream
 
     Upstream capital expenditures and investments (excluding amounts paid in
the first quarter of 1999 for the completion of 1998 acquisitions) totaled $311
million in the first three months of 1999. The decrease was $25 million, or
approximately seven percent, compared to $336 million for the first three months
of 1998, primarily a result of an overall reduction in the 1999 capital
expenditure program, including exploration, partly offset by 1999 investments in
Petrozuata, a joint venture in Venezuela.
 
                                       12
<PAGE>   15
 
     United States
 
     During the first three months of 1999, Conoco spent $113 million on capital
projects in the United States, a decrease of $36 million, or 24 percent from
$149 million in the first three months of 1998. Expenditures in the first three
months of 1999 focused on the continued development of the Lobo field in South
Texas and the completion of the Ursa field in the deepwater Gulf of Mexico.
 
     International
 
     International capital expenditures and investments totaled $198 million in
the first three months of 1999, an increase of $11 million, or six percent, from
$187 million in the first three months of 1998. The 1999 expenditures include
investment in Petrozuata, as well as continued development of various fields in
the U.K. and the Norwegian sector of the North Sea.
 
     Downstream
 
     Downstream capital expenditures and investments totaled $102 million in the
first three months of 1999, an increase of $7 million, or seven percent, versus
$95 million in the first three months of 1998, primarily reflecting increased
expenditures for European and Asia-Pacific refining operations.
 
     United States
 
     During the first three months of 1999, Conoco spent $32 million on
Downstream capital projects in the United States, up $2 million, or seven
percent, from $30 million in the first three months of 1998. The majority of the
funds spent were used to support continuing refining operations.
 
     International
 
     During the first three months of 1999, Conoco spent $70 million on
Downstream international capital expenditures and investments, up $5 million, or
eight percent, from $65 million in the first three months of 1998. Expenditures
in the first three months of 1999 focused on strengthening Conoco's retail
marketing position, as well as investment in the Melaka Refinery in Malaysia and
the Humber Refinery in the U.K.
 
     Corporate and Other
 
     Corporate and other capital expenditures totaled $2 million in the first
three months of 1999, and were associated with the capitalization of new
computer software.
 
  PROCEEDS FROM SALES OF ASSETS AND SUBSIDIARIES
 
     Conoco's investment activities also include proceeds of $18 million for the
first three months of 1999, a decrease of $257 million from the first three
months of 1998, which included $54 million from the sale of North Sea producing
and non-producing properties and $156 million from the sale of various
Downstream assets in the U.S. These proceeds are a result of Conoco's ongoing
strategic portfolio realignment.
 
FINANCING ACTIVITIES
 
     Conoco's ability to maintain and grow its operating income and cash flow is
dependent upon continued capital spending to replace depleting assets. Conoco
believes its future cash flow from operations and its borrowing capacity should
be sufficient to fund its dividends, if any, capital expenditures and working
capital requirements and to service debt.
 
     Total indebtedness owed to DuPont was $4,896 million as of March 31, 1999,
consisting of $926 million in short-term borrowings and $3,970 million in
long-term borrowings. The short-term borrowings consisted of $300 million due on
the revolving credit agreement discussed below and $626 million representing the
short-term portion of the $4,596 million promissory notes to DuPont.
 
                                       13
<PAGE>   16
 
     On October 27, 1998, Conoco and DuPont entered into a revolving credit
agreement under which DuPont provides Conoco with a revolving credit facility in
principal amount of up to $500 million. Loans under the revolving credit
agreement are subject to mandatory prepayment to the extent Conoco's cash and
cash equivalents exceed $325 million or such higher amount as Conoco and DuPont
may agree. Loans under this facility bear interest at a rate equal to 30-day
LIBOR plus 0.20 percent per annum and may be voluntarily prepaid without penalty
or premium. At March 31, 1999, the outstanding balance under the revolving
credit agreement was $300 million.
 
     On April 20, 1999, Conoco completed the public offering and sale of $4,000
million of senior debt securities. The senior debt securities consisted of three
tranches as follows:
 
     - $1,350 million in five-year notes due 2004 with a coupon of 5.90 percent,
       offered to the public at 99.856 percent.
 
     - $750 million in ten-year notes due 2009 with a coupon of 6.35 percent,
       offered to the public at par.
 
     - $1,900 million in 30-year notes due 2029 with a coupon of 6.95 percent,
       offered to the public at par.
 
     Conoco achieved a weighted average interest rate of 6.49 percent in this
financing. After deducting the note discount and underwriting discounts, the net
proceeds of $3,970 million received from the senior debt offerings were used to
repay a portion of the outstanding principal and accrued interest owed to DuPont
under one of the promissory notes. It is expected that the remaining debt owed
to DuPont will be repaid in May 1999 with proceeds from a commercial paper
program.
 
     The program provides Conoco with up to $2,000 million of borrowing capacity
and gives Conoco the ability to issue commercial paper at any time with various
maturities not to exceed 270 days. As of May 13, 1999, the outstanding balance
borrowed under this program was $400 million, bearing a weighted average
interest rate of 4.99 percent, and was used to repay debt owed to DuPont.
 
                                       14
<PAGE>   17
 
(B) RESULTS OF OPERATIONS
 
  CONSOLIDATED RESULTS
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   MARCH 31
                                                              ------------------
                                                               1999        1998
                                                              ------      ------
                                                                (IN MILLIONS)
<S>                                                           <C>         <C>
SALES AND OTHER OPERATING REVENUES..........................
  Upstream
     United States..........................................  $  706      $  863
     International..........................................     479         456
                                                              ------      ------
          Total Upstream....................................  $1,185      $1,319
  Downstream
     United States..........................................  $1,962      $2,185
     International..........................................   2,143       2,028
                                                              ------      ------
          Total Downstream..................................  $4,105      $4,213
  Corporate and Other.......................................      21         204
                                                              ------      ------
          Total Sales and Other Operating Revenues..........  $5,311      $5,736
                                                              ======      ======
AFTER-TAX OPERATING INCOME
  Upstream
     United States..........................................  $   40      $   88
     International..........................................      68         143
                                                              ------      ------
          Total Upstream....................................  $  108      $  231
  Downstream
     United States..........................................  $   17      $   34
     International..........................................      23          57
                                                              ------      ------
          Total Downstream..................................  $   40      $   91
  Corporate and Other Operating.............................     (15)        (20)
                                                              ------      ------
          Total After-Tax Operating Income..................  $  133      $  302
  Interest and Other Non-Operating Income (Expenses) Net of
     Tax....................................................     (50)         14
                                                              ------      ------
CONSOLIDATED NET INCOME.....................................  $   83      $  316
                                                              ======      ======
</TABLE>
 
  SPECIAL ITEMS
 
     Consolidated net income includes the following non-recurring items
("Special Items") on an after-tax basis:
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   MARCH 31
                                                              -------------------
                                                              1999          1998
                                                              -----         -----
                                                                 (IN MILLIONS)
<S>                                                           <C>           <C>
UPSTREAM
Asset sales.................................................   $--           $23
                                                               ---           ---
          Total Upstream Special Items......................   $--           $23
                                                               ===           ===
          Total.............................................   $--           $23
                                                               ===           ===
</TABLE>
 
     There were no Special Items for the first three months of 1999. Special
Items for the first three months of 1998 reflect a $23 million gain from the
sale of certain properties in the North Sea.
 
  First Quarter 1999 versus First Quarter 1998
 
     Conoco had first quarter consolidated net income of $83 million in 1999,
down 74 percent from $316 million in the first quarter of 1998. Conoco had
earnings before special items of $83 million in the first quarter of 1999, down
72 percent from $293 million in the first quarter of 1998. Lower earnings
primarily reflect lower net realized crude oil and natural gas prices, weaker
refined product margins and higher interest
                                       15
<PAGE>   18
 
expenses related to Conoco's debt owed to DuPont, partly offset by higher crude
oil and natural gas volumes, higher refinery throughputs and lower exploration
costs.
 
     Sales and other operating revenues for the first quarter of 1999 were
$5,311 million, down seven percent from $5,736 million in the first quarter of
1998, primarily due to lower crude oil and natural gas prices, lower refined
product prices and reduced power trading revenues, all of which were partly
offset by increased production volumes and refinery throughputs. Conoco's
worldwide net realized crude oil price was $11.00 per barrel for the quarter,
down $2.70 per barrel, or 20 percent, from $13.70 per barrel in the first
quarter of 1998. Worldwide net realized natural gas prices averaged $2.08 per
thousand cubic feet (mcf) for the quarter, compared with $2.64 per mcf in the
same period in 1998, a reduction of 21 percent. Worldwide crude oil and
condensate production in the first quarter of 1999 was 326,000 barrels per day
versus 321,000 barrels per day in the first quarter of 1998, a two percent
increase primarily attributable to new production of condensate from the
Britannia field, crude oil from the Banff field and crude oil from Petrozuata.
Worldwide natural gas deliveries in the first quarter of 1999 were up 40 percent
to 1,816 million cubic feet per day from 1,298 million cubic feet per day in the
first quarter of 1998. U.S. natural gas deliveries were up 20 percent, primarily
as a result of continued development drilling in the Lobo field of South Texas.
International natural gas deliveries were up 71 percent due to the new
production from the Britannia and Viking Phoenix gas fields in the U.K.
Worldwide refined product sales were 1,093,000 barrels per day, up 12 percent
versus 1998. Crude oil and refined product buy/sell and natural gas and electric
power resale activities in the first quarter of 1999 totaled $957 million, down
20 percent compared to $1,200 million in the first quarter of 1998, primarily
due to lower crude oil prices and a reduction in power trading revenues.
 
     Cost of goods sold and other operating expenses for the first quarter of
1999 totaled $3,005 million, a decrease of $388 million, or 11 percent, compared
to $3,393 million in the first quarter of 1998, primarily due to the reduction
in power trading activities and lower refinery feedstock costs.
 
     Exploration expenses for the first quarter of 1999 totaled $46 million, a
decline of $21 million, or 31 percent, compared to $67 million in the first
quarter of 1998, due to lower dry hole costs and lower seismic expenditures.
 
     Depreciation, depletion and amortization for the first quarter of 1999
totaled $302 million, an increase of $35 million, or 13 percent, compared to
$267 million in the first quarter of 1998, primarily due to increased production
volumes.
 
UPSTREAM SEGMENT RESULTS
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   MARCH 31
                                                              -------------------
                                                               1999         1998
                                                              ------       ------
                                                                 (IN MILLIONS)
<S>                                                           <C>          <C>
After-Tax Operating Income
  United States.............................................   $ 40         $ 88
  International.............................................     68          143
                                                               ----         ----
     After-Tax Operating Income.............................   $108         $231
Special Items
  United States.............................................   $ --         $ --
  International.............................................     --          (23)
                                                               ----         ----
     Special Items..........................................   $ --         $(23)
Earnings Before Special Items
  United States.............................................   $ 40         $ 88
  International.............................................     68          120
                                                               ----         ----
     Earnings Before Special Items..........................   $108         $208
                                                               ====         ====
</TABLE>
 
                                       16
<PAGE>   19
 
  First Quarter 1999 versus First Quarter 1998
 
     Upstream earnings before special items were $108 million in the first
quarter of 1999, down 48 percent from $208 million in the first quarter of 1998.
U.S. Upstream earnings before special items totaled $40 million in the first
quarter of 1999, down 55 percent from $88 million in the comparable period of
1998. Lower U.S. Upstream earnings were due to lower crude oil and natural gas
prices and lower crude oil volumes due to natural declines and the sale of
various small, non-strategic properties in 1998. These factors more than offset
increased natural gas production and lower exploration expenses. Natural gas
volumes in the United States were up 20 percent, as production from the South
Texas fields increased more than production declined elsewhere. International
Upstream earnings before special items were $68 million, down 43 percent, from
$120 million in the comparable period in 1998, primarily attributable to lower
prices for crude oil and natural gas, partly offset by increased natural gas and
condensate production from the Britannia field.
 
DOWNSTREAM SEGMENT RESULTS
 
<TABLE>
<CAPTION>
                                                              THREE MONTHS ENDED
                                                                   MARCH 31
                                                              -------------------
                                                              1999          1998
                                                              -----         -----
                                                                 (IN MILLIONS)
<S>                                                           <C>           <C>
After-Tax Operating Income
  United States.............................................   $17           $34
  International.............................................    23            57
                                                               ---           ---
     After-Tax Operating Income.............................   $40           $91
Special Items
  United States.............................................   $--           $--
  International.............................................    --            --
                                                               ---           ---
     Special Items..........................................   $--           $--
Earnings Before Special Items
  United States.............................................   $17           $34
  International.............................................    23            57
                                                               ---           ---
     Earnings Before Special Items..........................   $40           $91
                                                               ===           ===
</TABLE>
 
  First Quarter 1999 versus First Quarter 1998
 
     Downstream earnings before special items were $40 million for the first
three months of 1999, down 56 percent from $91 million in the comparable period
in 1998. U.S. Downstream earnings before special items were $17 million for the
first three months of 1999, down 50 percent from $34 million for the first three
months of 1998, due to weaker refined product margins, partly offset by higher
refinery volumes. International Downstream earnings before special items were
$23 million for the first three months of 1999, down 60 percent from $57 million
in the comparable period in 1998, reflecting significantly lower refinery and
marketing margins that were only partly offset by higher refining volumes.
 
CORPORATE AND OTHER SEGMENT RESULTS
 
  CORPORATE AND OTHER OPERATING
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                     MARCH 31
                                                                -------------------
                                                                 1999         1998
                                                                ------       ------
                                                                   (IN MILLIONS)
<S>                                                             <C>          <C>
After-Tax Operating Income (Loss)...........................     $(15)        $(20)
Special Items...............................................       --           --
                                                                 ----         ----
Earnings (Losses) Before Special Items......................     $(15)        $(20)
                                                                 ====         ====
</TABLE>
 
                                       17
<PAGE>   20
 
  First Quarter 1999 versus First Quarter 1998
 
     Corporate and other operating losses were $15 million for the first quarter
of 1999, improved 25 percent from a loss of $20 million for the comparable
period in 1998, resulting from lower administrative costs.
 
  INTEREST AND OTHER CORPORATE NON-OPERATING INCOME (EXPENSES) NET OF TAX
 
<TABLE>
<CAPTION>
                                                                THREE MONTHS ENDED
                                                                     MARCH 31
                                                                -------------------
                                                                 1999         1998
                                                                ------       ------
                                                                   (IN MILLIONS)
<S>                                                             <C>          <C>
  Interest Expense on Debt..................................     $(47)        $ --
  Interest Income...........................................        5           19
  Exchange Gains (Losses)...................................        2            7
  Other Corporate Expenses(1)...............................      (10)         (12)
                                                                 ----         ----
          Total.............................................     $(50)        $ 14
                                                                 ====         ====
</TABLE>
 
---------------
 
(1) Includes other non-operating items.
 
  First Quarter 1999 versus First Quarter 1998
 
     Interest and other corporate non-operating expenses for the first quarter
of 1999 were a loss of $50 million compared to income of $14 million in the
comparable period in 1998, primarily reflecting an increase in interest expense
resulting from separation-related debt to DuPont incurred in the second half of
1998 and lower interest income.
 
TAX MATTERS
 
     As a result of the separation and the Offerings, Conoco is no longer able
to combine the results of its operations with those of DuPont in reporting
income for U.S. federal income tax purposes and for state and non-U.S. income
tax purposes in certain states and countries. Conoco believes this will not have
a material adverse effect on its earnings.
 
     In late March 1999, the Internal Revenue Service ruled DuPont's proposed
split-off of Conoco Inc. would be a tax-free transaction. Under the proposed
split-off, DuPont shareholders will be allowed to exchange DuPont stock for
shares of Conoco Class B Common Stock held by DuPont. The IRS ruling was a key
condition of the split-off that is discussed in more detail in Part II, Item
5(b).
 
     During the period ended March 31, 1999, Conoco's net deferred tax assets
increased, primarily as a result of the recognition of $62 million of
carryforwards related to foreign tax credits, alternative fuels tax credits and
the U.S. alternative minimum tax. Conoco believes it is more likely than not
that the additional deferred tax assets related to these foreign tax credits and
alternative fuels tax credits will be realized in the current year. Further,
Conoco believes it is more likely than not that the alternative minimum tax
credits will be realized in future years.
 
YEAR 2000
 
     Historically, many computerized systems have used two digits rather than
four digits to define the applicable year, which could result in recognizing a
date using "00" as the year 1900 rather than the year 2000. This could result in
major failures or miscalculations.
 
     Conoco recognizes that the impact of the Year 2000 issue extends beyond
traditional computer hardware and software to automated plant systems and
instrumentation, as well as to third parties. The Year 2000 issue is being
addressed within Conoco by its individual business units, and progress is
reported periodically to management and the Board of Directors.
 
                                       18
<PAGE>   21
 
     Conoco has committed resources to conduct risk assessments and to take
corrective action, where required, within each of the following areas:
information technology, plant systems and external parties. Information
technology includes telecommunications as well as traditional computer software
and hardware in the mainframe, midrange and desktop environments. Plant systems
include all automation and embedded chips used in production, plant,
transportation and marketing facilities. External parties include any third
party with whom Conoco interacts. Most of the resources committed to this work
are internal.
 
     Managing Year 2000 risk is being handled in three tiers -- through Year
2000 Compliance Plans, Mitigation Plans and Emergency Recovery Plans. The Year
2000 Compliance Plans include inventorying and assessing risk, and outlining
action to be taken for each of these items. Year 2000 Compliance Plans have been
developed and are being implemented for all business units. Mitigation Plans
outline a list of actions that will be taken at specified times to further
minimize risk. These plans are currently being developed for areas in which the
Year 2000 Compliance Plans may not adequately address all of the relevant risk
issues. For example, Conoco cannot be guaranteed that external partners will be
ready for the Year 2000. Therefore, operations that rely heavily on external
partners will develop Mitigation Plans. Mitigation Plans will be developed, as
needed, for all business units by the end of the third quarter of 1999.
 
     Emergency Recovery Plans already exist in many of Conoco's operations to
address other issues such as oil tanker spills and plant explosions. Typically,
the Emergency Recovery Plans address the results of single events. These plans
are designed to facilitate the resumption of normal operations following a
disruption. In contrast to a "normal" disruption, the scope of Year 2000 issues
may cause multiple concurrent events. Accordingly, the Emergency Recovery Plans
will be reviewed and supplemented to address Year 2000 risks for all business
units by the end of the third quarter of 1999. The progress reported below
covers only the replacement or upgrade of existing non-compliant systems.
Replacement projects planned and managed outside of the Year 2000 Program have
been excluded. Approximately 79 percent of the work required to fix Year 2000
issues identified by the Year 2000 Program has been completed.
 
     In the information technology area, inventory and assessment audits have
been completed. Corrective action in the mainframe and midrange environments
will be completed by the end of the second quarter of 1999, in the
telecommunications and desktop areas by the end of the third quarter of 1999,
and business application software by the end of the fourth quarter of 1999.
 
     In the plant systems area, all but one of Conoco's business units have
completed their inventory and assessment audits; the remaining unit is expected
to complete this work by the end of the second quarter of 1999. Conoco is
relying on vendor testing of hardware, software and embedded chips, with
certification and validation through limited internal testing and/or industry
test results. Downtime for normally scheduled plant maintenance will be used to
conduct testing, with completion of corrective action expected by the end of the
third quarter of 1999.
 
     With respect to external parties, the inventory of critical external
parties is complete. Risks are being assessed and will be addressed in
contingency plans. Monitoring of risk in this area will continue throughout
1999.
 
     The total cost of Year 2000 activities is not expected to be material to
Conoco's operations, liquidity or capital resources. Costs are being managed
within each business unit. The total estimated cost for Conoco's Year 2000 work
is $46 million. 1997 costs were $5 million, 1998 costs were $25 million and
first quarter 1999 costs were $4 million. This includes costs for the
replacement or upgrade of existing non-compliant systems. Replacement projects
planned and managed outside of the Year 2000 program have been excluded.
 
     There can be no guarantee that third parties of business importance to
Conoco will successfully reprogram or replace, and test, all of their own
computer hardware, software and process control systems to ensure such systems
are Year 2000 compliant. Failure to address a Year 2000 issue could result in
business disruption that could materially affect Conoco's operations, liquidity
or capital resources. There is still uncertainty around the scope of the Year
2000 issue. At this time Conoco cannot quantify the potential impact of these
failures. Conoco's Year 2000 program is in place. Conoco is developing
contingency plans to address issues within Conoco's control. The program
minimizes, but does not eliminate, the issues of external parties.
 
                                       19
<PAGE>   22
 
     This disclosure is provided pursuant to Securities Exchange Act Release No.
39-40277. As such, it is protected as a forward-looking statement under Section
21E of the Securities Exchange Act of 1934. See Item 5(a) "Disclosure Regarding
Forward-Looking Information." This disclosure is also subject to protection
under the Year 2000 Information and Readiness Disclosure Act of 1998, Public Law
105-271, as a "Year 2000 Statement" and "Year 2000 Readiness Disclosure" as
defined therein.
 
EUROPEAN MONETARY UNION
 
     Within Europe, the European Economic and Monetary Union (the "EMU")
introduced a new currency, the Euro, on January 1, 1999. The new currency is in
response to the EMU's policy of economic convergence to harmonize trade policy,
eliminate business costs associated with currency exchange and to promote the
free flow of capital, goods and services.
 
     Conoco has undertaken a review of the Euro implementation and has
concentrated on areas such as operations, finance, treasury, legal, information
management, procurement and others, both in participating and nonparticipating
European Union countries where Conoco operates. Existing legacy accounting and
business systems and other business assets have been reviewed for Euro
compliance. Progress regarding Euro implementation is reported periodically to
management. Amounts spent to date and expected to be spent in the future are not
material.
 
     Because of the staggered introduction of the Euro regarding non-cash and
cash transactions, Conoco has developed its plans to address first its
accounting and business systems and second, its business assets. Conoco
undertook steps to be Euro compliant within its accounting and business systems
by the end of 1998 relative to the conversion rules when performing translations
between EMU currencies. The accounting systems were modified so that EMU
currencies are converted to other EMU currencies via the Euro rather than
directly. Conoco was in a position to conduct electronic transfers in Euros
commencing January 1, 1999. Conoco has an implementation plan to convert its
accounting and reporting systems from legacy currency to the Euro by January 1,
2002 for those operations that are in EMU countries. The plan also incorporates
steps to ensure the corresponding business assets are fully compliant by that
date, in preparation for being able to conduct business involving Euro notes and
coins.
 
     Consistent with regulations and steps the industry is taking to get the
public familiar with the Euro, conversion at the retail outlets has already
begun. The conversion program varies between countries, and ranges from
displaying conversion tables between EMU legacy currencies and the Euro at
gasoline stations, placing stickers on the gasoline pumps with the equivalent
Euro price per liter, installing "Euro corners" in the shop part of the station
with calculators and examples so that customers can practice converting from
their EMU legacy currency to the Euro, and showing the Euro equivalent total at
the bottom of receipts issued from cash registers. The business assets
conversion program will continue throughout the transition period, and in its
final stages will include new or modified pole price signs, electronic Euro
price displays at the pump, new or modified automatic cash machines, and
receipts which give a detailed itemized breakdown in Euros.
 
     Conoco does not currently expect to experience any significant operational
disruptions or to incur any significant costs, including any currency risk,
which could materially affect Conoco's liquidity or capital resources. Conoco is
preparing plans to address issues within the transitional period when both
legacy and Euro currencies may be tendered.
 
     Because of the competitive business environment within the petroleum
industry, Conoco does not anticipate any long-term competitive implications or
the need to materially change its mode of conducting business as a result of
increased price transparency.
 
RESTRUCTURING
 
     Conoco has begun implementation of plans announced in December 1998 to
reduce staffing in most business operations in order to yield cost efficiencies
available from recent structural improvements. Through March 31, 1999,
approximately 162 persons of the expected 975 have left Conoco with plans for
the remainder
 
                                       20
<PAGE>   23
 
to leave by the end of 1999. These reductions are expected to reduce costs about
$100 million annually once fully implemented. For additional information, see
Note 7 to the consolidated financial statements.
 
ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK
 
MARKET RISKS
 
     Conoco operates in the worldwide crude oil, refined product, natural gas,
natural gas liquids and electric power markets and is exposed to fluctuations in
hydrocarbon prices, electric power prices, foreign currency rates, and interest
rates that can affect the revenues and cost of operating, investing and
financing. Conoco's management has used and intends to use financial and
commodity-based derivative contracts to reduce the risk in overall earnings and
cash flow when the benefits provided are anticipated to more than offset the
risk management costs involved.
 
     Conoco has established a Financial Risk Management Policy Framework that
provides guidelines for entering into contractual arrangements (derivatives) to
manage Conoco's commodity price, foreign currency rate, and interest rate risks.
The Conoco Risk Management Committee has ongoing responsibility for the content
of this policy and has principal oversight responsibility to ensure Conoco is in
compliance with the policy and that procedures and controls are in place for the
use of commodity, foreign currency and interest rate instruments. These
procedures clearly establish derivative control and valuation processes, routine
monitoring and reporting requirements and counterparty credit approval
procedures. Additionally, Conoco's internal audit group conducts routine reviews
of these risk management activities to assess the adequacy of internal controls.
The audit results are reviewed by the Conoco Risk Management Committee and by
management.
 
     The counterparties to these contractual arrangements are limited to major
financial institutions and other established companies in the petroleum
industry. Although Conoco is exposed to credit loss in the event of
nonperformance by these counterparties, this exposure is managed through credit
approvals, limits and monitoring procedures, and limits to the period over which
unpaid balances are allowed to accumulate. Conoco has not experienced
nonperformance by counterparties to these contracts, and no material loss would
be expected from any such nonperformance.
 
  Commodity Price Risk
 
     Conoco enters into energy-related futures, forwards, swaps and options in
various markets to balance its physical systems, to meet customer needs and to
manage its price exposure on anticipated crude oil, natural gas, refined product
and electric power transactions. These instruments provide a natural extension
of the underlying cash market and are used to physically acquire a portion of
supply requirements as well as to manage pricing of near term physical
requirements. The commodity futures market has underlying principles of
increased liquidity and longer trading periods than the cash market and is one
method of managing price risk in the energy business.
 
     Conoco policy is to generally be exposed to market pricing for commodity
purchases and sales. From time to time, management may use derivatives to
establish longer-term positions to hedge the price risk for Conoco's equity
crude oil and natural gas production as well as refinery margins.
 
     Under Conoco's policy, hedging includes only those transactions that offset
physical positions and reduce overall company exposure to price risk. Trading is
defined as any transaction that does not meet the definition of hedging. Much of
the portfolio is reported in the trading category and, thereby, receives
mark-to-market accounting. As a consequence, current revenues and costs reflect
the full effect of price movement on most of Conoco's trading activity. Those
activities that qualify as hedges use deferral accounting.
 
                                       21
<PAGE>   24
 
     The fair value gain (loss) of outstanding derivative commodity instruments
and the change in fair value that would be expected from a ten percent adverse
price change are shown in the table below:
 
<TABLE>
<CAPTION>
                                                                       CHANGE IN FAIR VALUE
                                                                         FROM 10% ADVERSE
                                                          FAIR VALUE       PRICE CHANGE
                                                          ----------   --------------------
                                                                    (IN MILLIONS)
<S>                                                       <C>          <C>
AT MARCH 31, 1999
Crude Oil and Refined Products
  Hedging...............................................     $ (2)             $ (1)
  Trading...............................................       24                (3)
                                                             ----              ----
  Combined..............................................     $ 22              $ (4)
Natural Gas
  Hedging...............................................     $ (5)             $(16)
  Trading...............................................       --                 1
                                                             ----              ----
  Combined..............................................     $ (5)             $(15)
AT DECEMBER 31, 1998
Crude Oil and Refined Products
  Hedging...............................................     $ (1)             $ (5)
  Trading...............................................        3                 3
                                                             ----              ----
  Combined..............................................     $  2              $ (2)
Natural Gas
  Hedging...............................................     $(25)             $(20)
  Trading...............................................       (2)               (1)
                                                             ----              ----
  Combined..............................................     $(27)             $(21)
</TABLE>
 
     The fair values of futures contracts are based on quoted market prices
obtained from the New York Mercantile Exchange or the International Petroleum
Exchange of London. The fair values of swaps and other over-the-counter
instruments are estimated based on quoted market prices of comparable contracts
and approximate the gain or loss that would have been realized if the contracts
had been closed out at the end of the reporting period.
 
     All hedge positions offset physical positions exposed to the cash market;
none of these offsetting physical positions is included in the above table.
 
     Price-risk sensitivities were calculated by assuming an across-the-board
ten percent adverse change in prices regardless of term or historical
relationships between the contractual price of the instrument and the underlying
commodity price. In the event of an actual ten percent change in prompt month
crude or natural gas prices, the fair value of Conoco's derivative portfolio
would typically change less than that shown in the table due to lower volatility
in out-month prices.
 
  Foreign Currency Risk
 
     Conoco has foreign currency exchange rate risk resulting from operations in
approximately 40 countries around the world. Conoco does not comprehensively
hedge its exposure to currency rate changes, although it may choose to
selectively hedge exposure to foreign currency exchange rate risk. Examples
include firm commitments for capital projects, certain local currency tax
payments, and cash returns from net investments in foreign affiliates to be
remitted within the coming year. There were no open forward exchange contracts
at the end of the reporting period.
 
  Interest Rate Risk
 
     Prior to the Offerings, Conoco had no significant interest rate risk to
manage. In March 1999, Conoco hedged interest rate exposure on a portion of
public debt that was issued in April 1999 (see Note 3). The hedge was
accomplished by purchasing put options on U.S. Treasury securities with a
maturity date matching
 
                                       22
<PAGE>   25
 
the expected pricing date of the debt offering and having a total notional
amount of $2.5 billion spread over five-year, ten-year and 30-year maturities
proportional to the expected tranches of company debt to be issued. Fair value
of the put options at March 31 was $7 million. In April 1999, subsequent to
purchasing the put options, U.S. Treasury interest rates decreased and the put
options expired out of the money. Before the public debt issuance, Conoco
entered into interest rate lock agreements proportional to the expected tranches
of debt to be issued. Overall, the two hedging transactions resulted in an
immaterial net gain that will be amortized against interest expense over the
life of the various debt maturities.
 
                                       23
<PAGE>   26
 
                                    PART II
 
                               OTHER INFORMATION
 
ITEM 1. LEGAL PROCEEDINGS
 
     On March 6, 1996, the Department of Justice filed a complaint in the United
States District Court for the District of Montana against Yellowstone Pipeline
Company ("YPL") and the Conoco Pipe Line Company as a 40 percent owner and
operator of YPL. The Complaint alleges discharges of oil from a YPL pipeline in
January 1993 and seeks civil penalties of up to $25,000 per day for each
violation or up to $1,000 for each barrel of oil discharged. The parties have
reached an agreement to settle the case that requires the parties to pay a
penalty of $165,000 and construct a fish passageway in the Jocko River to
enhance the Bull Trout population. Final settlement documents were lodged with
the Court on March 30, 1999. The Notice of Lodging, which commenced the thirty
day comment period, was published in the Federal Register on April 13, 1999.
 
     On January 5, 1999, Conoco paid $105,000 in penalties and agreed to perform
certain remediation at a cost of $200,000 to settle allegations made on June 18,
1998, by the New Mexico Environmental Department that Conoco had failed to
obtain a Clean Air Act permit and violated certain conditions in existing
permits at the Maljamar Gas Plant and the MCA field.
 
     On August 31, 1998, the Louisiana Department of Environmental Quality
("LDEQ") issued a notice of violation against Conoco for failure to maintain
control equipment to control emissions from the sulfur pits at the Lake Charles
Refinery. On November 11, 1998, the LDEQ notified Conoco that it is seeking a
fine of $300,000. Conoco is contesting these allegations and the proposed
penalty and is seeking a hearing in this manner.
 
     On February 18, 1999, the Oklahoma Department of Environmental Quality
issued a Notice of Violation to Conoco's Ponca City refinery alleging certain
violations of the Oklahoma Air Pollution Control Rules. This Notice of Violation
may result in the Department seeking monetary sanctions in excess of $100,000.
Conoco intends to vigorously defend the matter.
 
     Conoco is subject to various lawsuits and claims involving a variety of
matters including, along with other oil companies, actions challenging oil and
gas royalty and severance tax payments based on posted prices, and claims for
damages resulting from leaking underground storage tanks. As a result of its
separation from DuPont, Conoco has also assumed responsibility for current and
future claims related to certain discontinued chemicals and agricultural
chemicals businesses operated by Conoco in the past. In general, the effect on
future financial results is not subject to reasonable estimation because
considerable uncertainty exists. We believe the ultimate liabilities resulting
from such lawsuits and claims may be material to results of operations in the
period in which they are recognized but will not materially affect the
consolidated financial position of Conoco.
 
ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS
 
     Conoco's annual meeting of stockholders was held on May 12, 1999 for the
purpose of (1) electing three directors, (2) approving the 1998 Stock and
Performance Incentive Plan, (3) approving the 1998 Key Employee Stock
Performance Plan and (4) ratifying the appointment of PricewaterhouseCoopers LLP
as Conoco's independent public accountants for 1999.
 
                                       24
<PAGE>   27
 
  1. Election of Directors
 
     Stockholders elected Ruth R. Harkin, Frank A. McPherson and Gary M.
Pfeiffer, each for a three-year term expiring at the 2002 Annual Meeting. The
vote tabulation for each individual director was as follows:
 
<TABLE>
<CAPTION>
                                                         VOTES CAST     VOTES CAST AGAINST
DIRECTOR                                                     FOR           OR WITHHELD
--------                                                -------------   ------------------
<S>                                                     <C>             <C>
Ruth R. Harkin........................................  2,349,266,804       1,651,292
Frank A. McPherson....................................  2,349,246,183       1,671,913
Gary M. Pfeiffer......................................  2,347,922,130       2,995,966
</TABLE>
 
     Directors continuing in office were Archie W. Dunham, William K. Reilly,
William R. Rhodes, Franklin A. Thomas and Edgar S. Woolard, Jr.
 
  2. Proposal approving the 1998 Stock and Performance Incentive Plan of Conoco
     Inc.
 
<TABLE>
<S>                                                            <C>
For.........................................................   2,314,078,440
Against.....................................................      36,170,753
Abstain.....................................................         668,903
Broker Non-Votes............................................               0
</TABLE>
 
  3. Proposal approving the 1998 Key Employee Stock Performance Plan of Conoco
     Inc.
 
<TABLE>
<S>                                                            <C>
For.........................................................   2,324,703,352
Against.....................................................      25,757,626
Abstain.....................................................         457,118
Broker Non-Votes............................................               0
</TABLE>
 
  4.Proposal ratifying the appointment of PricewaterhouseCoopers LLP as Conoco's
    independent public accountants for 1999.
 
<TABLE>
<S>                                                            <C>
For.........................................................   2,350,436,014
Against.....................................................         219,053
Abstain.....................................................         263,029
</TABLE>
 
ITEM 5. OTHER INFORMATION
 
(A) DISCLOSURE REGARDING FORWARD-LOOKING INFORMATION
 
     This quarterly report on Form 10-Q includes forward-looking statements
within the meaning of Section 27A of the Securities Act of 1933 and Section 21E
of the Securities Exchange Act of 1934. You can identify our forward-looking
statements by the words "expects," "intends," "plans," "projects," "believes,"
"estimates" and similar expressions.
 
     We have based the forward-looking statements relating to our operations on
our current expectations, estimates and projections about us and the petroleum
industry in general. We caution you that these statements are not guarantees of
future performance and involve risks, uncertainties and assumptions that we
cannot predict. In addition, we have based many of these forward-looking
statements on assumptions about future events that may prove to be inaccurate.
Accordingly, our actual outcomes and results may differ materially from what we
have expressed or forecast in the forward-looking statements. Any differences
could result from a variety of factors including the following:
 
     - fluctuations in crude oil and natural gas prices and refining and
       marketing margins
 
     - failure or delays in achieving expected production from oil and gas
       development projects
 
     - uncertainties inherent in predicting oil and gas reserves and oil and gas
       reservoir performance
 
                                       25
<PAGE>   28
 
     - lack of exploration success
 
     - disruption or interruption of our production facilities due to accidents
       or political events
 
     - international monetary conditions and exchange controls
 
     - liability for remedial actions under environmental regulations
 
     - disruption to our operations due to untimely or incomplete resolution of
       Year 2000 issues by us or other entities
 
     - liability resulting from litigation
 
     - world economic and political conditions
 
     - changes in tax and other laws applicable to our business
 
(B) SPLIT-OFF OF CONOCO FROM DUPONT
 
     On March 22, 1999, Conoco filed a registration statement with the
Securities and Exchange Commission outlining a "split-off" plan to establish
Conoco as a fully independent company. This filing is the next step in DuPont's
planned divestiture of Conoco. The split-off will be achieved through an
exchange offer in which DuPont stockholders will be given an opportunity to
exchange DuPont common stock for shares of Conoco Class B Common Stock currently
held by DuPont. In late March 1999, the Internal Revenue Service ruled that
DuPont's proposed split-off of Conoco Inc. would be a tax-free transaction.
DuPont announced on April 28, 1999 that its board of directors had approved the
split-off plan. Following a review by the SEC, and depending on market
conditions, the split-off is expected to be completed in the third quarter of
1999.
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K
 
(A) EXHIBITS
 
     The exhibit index filed with this Form 10-Q is on page 28.
 
(B) REPORTS ON FORM 8-K
 
     On March 23, 1999, Conoco filed a Current Report on Form 8-K for the
following:
 
     Item 5. Other Events and Item 7. Financial Statements and Exhibits with
respect to an unaudited pro forma statement of income for year ended December
31, 1998. This pro forma statement of income was prepared by Conoco to
illustrate the estimated effects of the initial public offering and the
separation and related transactions from DuPont as if they had occurred as of
the beginning of the period (January 1, 1998) rather than on October 21, 1998.
 
                                       26
<PAGE>   29
 
                                   SIGNATURE
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned, thereunto duly authorized.
 
                                            CONOCO INC.
                                            (Registrant)
 
                                            By:     /s/ W. DAVID WELCH
                                              ----------------------------------
                                               (As Duly Authorized Officer and
                                                Principal Accounting Officer)
 
Date: May 13, 1999
 
                                       27
<PAGE>   30
 
                                 EXHIBIT INDEX
 
<TABLE>
<CAPTION>
        EXHIBIT
         NUMBER                                  DESCRIPTION
        -------                                  -----------
<C>                      <S>
          3.1            -- Second Amended and Restated Certificate of Incorporation
                            of Conoco Inc.*
          3.2            -- By-laws of Conoco Inc., as amended May 12, 1999**
          4.1            -- Form of Indenture between the Company and the Trustee
                            relating to the debt securities***
         10.1            -- Deferred Compensation Plan for Non-employee Directors, as
                            amended May 12, 1999**
         10.2            -- 1998 Stock and Performance Incentive Plan, as amended May
                            12, 1999**
         10.3            -- 1998 Key Stock Performance Plan, as amended May 12,
                            1999**
         12              -- Computation of Ratio of Earnings to Fixed Charges**
         27              -- Financial Data Schedule**
</TABLE>
 
---------------
 
  * Incorporated by reference to exhibit of the same number filed as part of
    Conoco's Form 10-Q for the quarterly period ended September 30, 1998.
 
 ** Filed herein.
 
*** Incorporated by reference to exhibit of the same number filed as part of
    Conoco's Registration Statement on Form S-3, File No. 333-72291.
 
                                       28