<PAGE>   1
================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                    FORM 10-Q
(Mark One)

[X]   QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(D) OF THE SECURITIES
      EXCHANGE ACT OF 1934

For the quarterly period ended September 30, 1999

                                       OR

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

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

                          Commission File Number 1-2475

                                SHELL OIL COMPANY
             (Exact Name of Registrant as Specified in its Charter)

<TABLE>
<CAPTION>

              Delaware                                           13-1299890
<S>                                                 <C>
      (State of Incorporation)                     (I.R.S. Employer Identification No.)

    One Shell Plaza, Houston, Texas                                77002
(Address of Principal Executive Offices)                         (Zip Code)
</TABLE>

        Registrant's Telephone Number, Including Area Code (713) 241-6161

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 [ ]

The number of shares of Common Stock, $10.00 par value, outstanding as of
September 30, 1999 - 1,000 shares.

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

                         OMISSION OF CERTAIN INFORMATION

In accordance with General Instruction H of Form 10-Q, the registrant is
omitting Part II, Items 2, 3, and 4 because:

(1) Royal Dutch Petroleum Company, a Netherlands company, and The "Shell"
Transport and Trading Company, p.l.c., an English company, each of which is a
reporting company under the Securities Exchange Act of 1934 that has filed all
material required to be filed by it pursuant to Section 13, 14, or 15(d)
thereof, own directly or indirectly 60 percent and 40 percent, respectively, of
the shares of the companies of the Royal Dutch/Shell Group of Companies,
including all the equity securities of the registrant; and (2) during the
preceding thirty-six calendar months and any subsequent period of days, there
has not been any material default in the payment of principal, interest, sinking
or purchase fund installment, or any other material default not cured within
thirty days with respect to any indebtedness of the registrant or its
subsidiaries, and there has not been any material default in the payment by the
registrant or its subsidiaries of rentals under material long-term leases.

================================================================================


<PAGE>   2

                          PART I. FINANCIAL INFORMATION

                       SHELL OIL COMPANY AND SUBSIDIARIES
                        CONSOLIDATED STATEMENT OF INCOME
                               Millions of Dollars

<TABLE>
<CAPTION>

                                                                  THIRD QUARTER                   NINE MONTHS
                                                                 --------------           ---------------------------
                                                                1999           1998           1999            1998
                                                              -------       --------        -------         -------
<S>                                                           <C>           <C>             <C>             <C>
REVENUES
    Sales and other operating revenue..................       $ 5,298         $3,667        $13,112         $13,927
    Less:  Consumer excise and sales taxes.............            25              2             76             798
                                                              -------         ------        -------         -------
                                                                5,273          3,665         13,036          13,129
    Equity in income of affiliates.....................           395            146            567             417
    Interest and other income..........................            23            115             58             215
                                                              -------         ------        -------         -------
          TOTAL........................................         5,691          3,926         13,661          13,761
                                                              -------         ------        -------         -------

COSTS AND EXPENSES
    Purchased raw materials and products...............         3,628          2,254          8,341           8,258
    Operating expenses.................................           710            668          2,161           2,055
    Selling, general and administrative expenses.......           100            163            284             616
    Exploration, including exploratory dry holes.......            37             62            120             242
    Research expenses..................................            32             37             99             116
    Depreciation, depletion and amortization...........           301            357            779           1,176
    Gain on asset sales................................          (421)          (204)          (507)           (285)
    Interest and discount amortization.................            70            108            227             294
                                                              -------         ------        -------         -------
          TOTAL........................................         4,457          3,445         11,504          12,472
                                                              -------         ------        -------         -------

INCOME BEFORE INCOME TAXES AND
MINORITY INTEREST......................................       $ 1,234         $  481        $ 2,157         $ 1,289

    Federal and other income taxes.....................           309            209            439             483
    Minority interest in income
       of subsidiaries.................................            25             14             51              60
                                                              -------         ------        -------         -------

NET INCOME.............................................       $   900         $  258        $ 1,667         $   746
                                                              =======         ======        =======         =======
</TABLE>

Note: Certain 1998 amounts have been reclassified to conform with current year
      presentation.



                                       2
<PAGE>   3


                       SHELL OIL COMPANY AND SUBSIDIARIES
                           CONSOLIDATED BALANCE SHEET
                               Millions of Dollars

<TABLE>
<CAPTION>

                                                                                 SEPTEMBER 30,      DECEMBER 31,
                                                                                     1999                1998
                                                                              ----------------     ---------------
<S>                                                                           <C>                  <C>
ASSETS
CURRENT ASSETS
   Cash and cash equivalents...............................................      $     879           $     322
   Receivables and prepayments, less allowance for
      doubtful accounts....................................................          3,112               2,235
   Owing by related parties................................................            845                 618
   Inventories of products.................................................            776                 723
   Inventories of materials and supplies...................................            132                 150
                                                                                 ---------           ---------
             TOTAL CURRENT ASSETS..........................................          5,744               4,048
INVESTMENTS................................................................          9,284               9,345
LONG-TERM RECEIVABLES AND DEFERRED CHARGES.................................          1,825               1,706
PROPERTY, PLANT AND EQUIPMENT AT COST, LESS
   ACCUMULATED DEPRECIATION, DEPLETION AND
   AMORTIZATION OF $10,919 AT SEPTEMBER 30, 1999
   AND $12,735 AT DECEMBER 31, 1998........................................         10,242              11,444
                                                                                 ---------           ---------
             TOTAL.........................................................      $  27,095           $  26,543
                                                                                 =========           =========


LIABILITIES AND SHAREHOLDER'S EQUITY
CURRENT LIABILITIES
   Accounts payable - trade................................................      $   1,249           $   1,490
   Other payables and accruals.............................................          1,631               1,406
   Income, operating and consumer taxes....................................            732                  88
   Owing to related parties................................................            720                 553
   Short-term debt.........................................................          5,174               5,301
                                                                                 ---------           ---------
           TOTAL CURRENT LIABILITIES.......................................          9,506               8,838
LONG-TERM DEBT.............................................................            294                 490
DEFERRED INCOME TAXES......................................................          1,455               2,000
LONG-TERM LIABILITIES......................................................          2,570               2,287
MINORITY INTEREST AND PREFERRED STOCK OF SUBSIDIARIES......................          1,537               1,542
SHAREHOLDER'S EQUITY
   Common stock - 1,000 shares of $10 per share
       par value...........................................................             --                  --
   Capital in excess of par value..........................................          2,206               2,206
   Earnings reinvested.....................................................          9,527               9,180
                                                                                 ---------           ---------
           TOTAL SHAREHOLDER'S EQUITY......................................         11,733              11,386
                                                                                 ---------           ---------
           TOTAL...........................................................      $  27,095           $  26,543
                                                                                 =========           =========
</TABLE>



                                       3
<PAGE>   4



                       SHELL OIL COMPANY AND SUBSIDIARIES
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                               Millions of Dollars

<TABLE>
<CAPTION>

                                                                               NINE MONTHS
                                                                           -----------------
                                                                          1999             1998
                                                                         -------          -----
<S>                                                                     <C>           <C>
CASH FLOWS FROM OPERATING ACTIVITIES
   Net Income ....................................................      $ 1,667       $   746
   Adjustments to reconcile net income to net cash
       provided by operating activities:
         Depreciation, depletion, amortization ...................          779         1,176
         Gain on asset sales .....................................         (507)         (285)
         Dividends in excess of (less than) equity income ........         (221)           17
         (Increases) decreases in working capital:
                Receivables and prepayments ......................       (1,002)         (549)
                Inventories ......................................          (35)         (139)
                Current payables and accruals ....................          693           446
           Deferred income taxes .................................         (545)          (93)
           Minority interest in income of subsidiaries ...........           51            60
           Other noncurrent items ................................          155           190
                                                                        -------       -------
              Net Cash Provided by Operating Activities ..........        1,035         1,569

CASH FLOWS PROVIDED BY (USED FOR) INVESTING ACTIVITIES
   Capital Expenditures ..........................................       (1,207)       (3,105)
   Proceeds from property sales and salvage ......................        2,491           160
   Other investments .............................................          (65)          507
                                                                        -------       -------
              Net Cash Provided by (Used for) Investing
                   Activities ....................................        1,219        (2,438)

CASH FLOWS PROVIDED BY (USED FOR) FINANCING ACTIVITIES
   Proceeds from issuance of long-term debt ......................           --           324
   Principal payments on long-term debt ..........................         (460)         (332)
   Proceeds from sales of securities of subsidiaries .............          (52)          321
   Dividends to shareholder ......................................       (1,275)       (1,238)
   Dividends to minority interests ...............................          (48)          (60)
   Increase in short-term obligations ............................          138         1,897
                                                                        -------       -------
              Net Cash Provided by (Used for) Financing
                   Activities ....................................       (1,697)          912

NET CASH FLOWS
   Increase in cash and cash equivalents .........................      $   557       $    43
                                                                        =======       =======

CASH AND CASH EQUIVALENTS
   Balance at beginning of period ................................      $   322       $   342
   Increase in cash and cash equivalents .........................          557            43
                                                                        -------       -------
              Balance at end of period ...........................      $   879       $   385
                                                                        =======       =======
</TABLE>


                                       4
<PAGE>   5


                       SHELL OIL COMPANY AND SUBSIDIARIES

                      NOTES TO INTERIM FINANCIAL STATEMENTS

A.  INTERIM FINANCIAL STATEMENT MATTERS

      The unaudited financial statements and summarized notes of Shell Oil
Company ("the Company") and its consolidated subsidiaries ("Shell Oil") included
in this report do not include complete financial information and should be read
in conjunction with the Consolidated Financial Statements and the Notes to
Consolidated Financial Statements filed with the Securities and Exchange
Commission in the Registrant's Annual Report on Form 10-K for the year ended
December 31, 1998. The financial information presented in the financial
statements included in this report reflects all adjustments which are, in the
opinion of management, necessary for a fair statement of results for the interim
periods presented. Any such adjustments are of a normal recurring nature, except
as may otherwise be described in Management's Discussion and Analysis of
Financial Condition and Results of Operations.

      The results for the third quarter of 1999 should not be construed as
necessarily indicative of future financial results.


B. EQUILON ENTERPRISES LLC

      Summarized unaudited financial information for Equilon Enterprises LLC
("Equilon"), formed January 1, 1998 and jointly owned 56 percent by Shell Oil
and 44 percent by Texaco Inc. ("Texaco") is presented below on a 100 percent
Equilon basis:

<TABLE>
<CAPTION>

                                                               Three Months Ended             Nine Months Ended
                                                                  September 30                   September 30
                                                          ----------------------------    --------------------------
                                                              1999            1998            1999             1998
                                                              ----            ----            ----             -----
                                                                              (millions of dollars)
<S>                                                         <C>             <C>             <C>             <C>
   Gross Revenues......................................     $8,501          $6,100          $19,955         $18,195
   Income Before Tax ..................................        330             232              378             542
</TABLE>

      Shell Oil accounts for its interest in Equilon using the equity method of
accounting. Under this method, Shell Oil's share of Equilon's results of
operations is recorded on a one-line basis to "Equity in Income of Affiliates"
in the Consolidated Statement of Income. Additionally, since Equilon is a
limited liability company, Shell Oil records the provision for income taxes and
related liability applicable to its share of Equilon's income in its
consolidated financial statements.


C. MOTIVA ENTERPRISES LLC

      Summarized unaudited financial information for Motiva Enterprises LLC
("Motiva"), formed July 1, 1998 and jointly owned 35 percent by Shell Oil and
32.5 percent each by Texaco and by Saudi Refining, Inc., a corporate affiliate
of Saudi Aramco, is presented below on a 100 percent Motiva basis:

<TABLE>
<CAPTION>

                                                               Three Months Ended               Nine Months Ended
                                                                   September 30                 September 30, 1999
                                                          ----------------------------     ----------------------------
                                                              1999            1998
                                                              ----            ----
                                                                              (millions of dollars)
<S>                                                       <C>              <C>                       <C>
   Gross Revenues......................................   $  3,416         $ 2,877                   $ 8,432
   Income Before Tax ..................................         45              59                        65
</TABLE>

      Shell Oil accounts for its interest in Motiva using the equity method of
accounting. Under this method, Shell Oil's share of Motiva's results of
operations is recorded on a one-line basis to "Equity in Income of Affiliates"
in the Consolidated Statement of Income. Additionally, since Motiva is a limited


                                       5
<PAGE>   6

liability company, Shell Oil records the provision for income taxes and related
liability applicable to its share of Motiva's income in its consolidated
financial statements.


D. INTERIM SEGMENT INFORMATION

      The following segment information has been prepared in accordance with
Statement of Financial Accounting Standards ("SFAS") No. 131, "Disclosure about
Segments of an Enterprise and Related Information," which was adopted by Shell
Oil in 1998. The adoption of SFAS No. 131 did not result in a change in Shell
Oil's reportable segments; however, the net income for the three month and nine
month periods ended September 30, 1998 for each segment has been restated from
that previously reported. The restatement is primarily to reflect the allocation
to the segments of interest income and interest expense previously reported as
"Nonallocated Items."

      Income taxes are allocated to the operating segments on the basis of the
respective segments' contributions to taxable income reduced by applicable tax
credits. However, the allocation among the segments of a tax benefit realized in
the third quarter of 1999 was based upon the agreed value to the segments of the
transaction as determined by management.

<TABLE>
<CAPTION>
                                                          Three months ended September 30, 1999
                                     -------------------------------------------------------------------------------
                                     Oil and   Downstream      Oil       Chemical      All       Nonalloc.
                                       Gas         Gas       Products    Products     Other       Items        Total
                                     --------    --------    --------    --------    --------    --------    --------
                                                                  (millions of dollars)

<S>                                  <C>         <C>        <C>          <C>         <C>         <C>         <C>
Sales and other operating
  revenues, including intersegment   $  1,166    $  2,621    $    919    $  1,341    $    112    $     24    $  6,183
Intersegment sales and revenues          (505)        (70)       (122)       (108)        (92)        (13)       (910)
                                     --------    --------    --------    --------    --------    --------    --------
Total external revenues              $    661    $  2,551    $    797    $  1,233    $     20    $     11    $  5,273
                                     ========    ========    ========    ========    ========    ========    ========
Segment net income (loss)            $    656    $     20    $    111    $    134    $     --    $    (21)   $    900
Segment assets                         10,187       4,441       6,106       5,421         330         610      27,095

----------------------------------
Segment assets at
   December 31, 1998                 $ 10,106    $  4,307    $  5,970    $  4,608    $    342    $  1,210    $ 26,543
</TABLE>

<TABLE>
<CAPTION>
                                                      Three months ended September 30, 1998 (restated)
                                     --------------------------------------------------------------------------------
                                     Oil and    Downstream     Oil       Chemical      All       Nonalloc.
                                       Gas         Gas       Products    Products     Other        Items       Total
                                     --------    --------    --------    --------    --------    --------    --------
                                                                  (millions of dollars)

<S>                                  <C>         <C>         <C>         <C>         <C>        <C>           <C>
Sales and other operating
  revenues, including intersegment   $    790    $  1,670    $    445    $  1,322    $    142    $     31    $  4,400
Intersegment sales and revenues          (301)        (13)        (72)       (211)       (129)         (9)       (735)
                                     --------    --------    --------    --------    --------    --------    --------
Total external revenues              $    489    $  1,657    $    373    $  1,111    $     13    $     22    $  3,665
                                     ========    ========    ========    ========    ========    ========    ========
Segment net income (loss)            $    126    $    (24)   $     99    $     62    $      1    $     (6)   $    258
Segment assets                         12,362       4,886       7,561       5,470         198       1,771      32,248

----------------------------------
Segment assets at
   December 31, 1997                 $ 13,123    $     --    $  9,277    $  5,342    $    211    $  1,648    $ 29,601
</TABLE>



                                       6
<PAGE>   7
<TABLE>
<CAPTION>
                                                          Nine months ended September 30, 1999
                                     --------------------------------------------------------------------------------
                                     Oil and    Downstream     Oil       Chemical      All       Nonalloc.
                                       Gas         Gas       Products    Products     Other       Items        Total
                                     --------    --------    --------    --------    --------    --------    --------
                                                                (millions of dollars)
<S>                                  <C>         <C>         <C>         <C>         <C>        <C>           <C>
Sales and other operating
  revenues, including intersegment   $  2,848    $  6,456    $  2,051    $  3,853    $    419    $     76    $ 15,703
Intersegment sales and revenues        (1,289)       (185)       (302)       (550)       (297)        (44)     (2,667)
                                     --------    --------    --------    --------    --------    --------    --------
Total external revenues              $  1,559    $  6,271    $  1,749    $  3,303    $    122    $     32    $ 13,036
                                     ========    ========    ========    ========    ========    ========    ========

Segment net income (loss)            $  1,190    $     37    $    201    $    299    $     (2)   $    (58)   $  1,667
</TABLE>



<TABLE>
<CAPTION>

                                                    Nine months ended September 30, 1998 (restated)
                                     --------------------------------------------------------------------------------
                                       Oil and  Downstream     Oil       Chemical      All      Nonalloc.
                                        Gas        Gas       Products    Products     Other       Items        Total
                                     --------    --------    --------    --------    --------    --------    --------
                                                                (millions of dollars)
<S>                                  <C>         <C>         <C>         <C>         <C>         <C>         <C>
Sales and other operating
  revenues, including intersegment   $  2,727    $  5,056    $  3,597    $  4,123    $    417    $     85    $ 16,005
Intersegment sales and revenues        (1,087)        (66)       (362)       (961)       (367)        (33)     (2,876)
                                     --------    --------    --------    --------    --------    --------    --------
Total external revenues              $  1,640    $  4,990    $  3,235    $  3,162    $     50    $     52    $ 13,129
                                     ========    ========    ========    ========    ========    ========    ========

Segment net income (loss)            $    405    $    (25)   $    200    $    232    $     20    $    (86)   $    746
</TABLE>




E. EMPLOYEE SEVERANCE PROGRAMS

      As reported in the Company's Annual Report on Form 10-K for the year ended
December 31, 1998, during 1998 Shell Oil recorded provisions for employee
severance programs of approximately $115 million affecting approximately 1,200
employees. During the second and third quarters of 1999, new severance programs
affecting approximately 500 employees were announced, and additional provisions
totaling $52 million were recorded. The costs related to these severance
programs are reflected on the Consolidated Statement of Income primarily as an
increase in Operating Expenses.

      The following table reflects the provisions recorded during 1998, the
additional provisions recorded in 1999, the payments made through September 30,
1999 and the remaining obligations as of September 30, 1999. Payment of the
remaining obligations will be made in future periods in accordance with the
provisions of the severance programs.

<TABLE>
<CAPTION>
                               Provisions Recorded
                                     During:
                                -----------------           Payments thru          Obligations Remaining
                                1998         1999        September 30, 1999        at September 30, 1999
                                ----         ----        ------------------        ---------------------
                                                       (millions of dollars)
<S>                            <C>           <C>        <C>                         <C>
Employee Severance             $ 115         $ 52               $ 83                        $ 84
</TABLE>


      At December 31, 1998, approximately one-half of the employees affected by
the 1998 programs had terminated; the remaining terminations were substantially
completed during the first nine months of 1999. At September 30, 1999
approximately 370 of the employees affected by the 1999 programs had terminated
with the remaining terminations expected to be substantially completed by
December 31, 1999.

                                       7
<PAGE>   8

F. CONTINGENCIES AND OTHER MATTERS

      Shell Oil is subject to a number of possible loss contingencies. These
include actions based upon environmental laws involving present and past
operating and waste disposal locations and related private claims, contract and
product liability actions and federal, state and private actions challenging the
correctness of oil and gas royalty calculations. In addition, federal, state and
local income, property and excise tax returns are being examined and certain
interpretations by Shell Oil of complex tax statutes, regulations and practices
are being challenged.

      Since 1984, the Company has been named with others as a defendant in
numerous product liability cases, including class actions, involving the failure
of residential plumbing systems constructed with polybutylene plastic pipe. The
Company has also been sued regarding failures in polybutylene pipe connecting
users with utility water lines and polybutylene pipe used in municipal water
distribution systems. The Company fabricated the resin for this pipe. Two other
substantial manufacturers made the resins for the polyacetal insert fittings
used in many of the residential plumbing systems (the fittings co-defendants)
and are also defendants in those cases. The Company and the fittings
co-defendants have agreed on a mechanism to fund the payment of most of the
residential plumbing claims in the United States as the result of two class
action settlements (the "class action settlement"). The class action settlement
provides for the creation of an entity to receive and handle claims and for a
$950 million fund to pay such claims, which claims may be filed until 2009,
depending on various factors. The entity, Consumer Plumbing Recovery Center, was
created in 1995. If the settlement funds are exhausted, additional funds may be
provided by the defendants, or claimants who have not received their full
benefits under the class action settlements may seek their remedy in a new court
proceeding at that time. Additionally, claims continue to be filed involving
alleged problems with polybutylene pipe used in municipal water distribution
systems. The Company will continue to defend these matters vigorously but it
cannot currently predict when or how polybutylene related matters will finally
be resolved.

      In an October 1997 decision by the United States District Court in
Delaware, certain income tax credits recorded by Shell Oil in previous years
arising out of production of oil from reserves which it believes classify as
"tar sands" for tax credits were denied because the Court determined that Shell
Oil used the wrong definition of tar sands production to calculate the same. In
June 1999, the Third Circuit upheld the lower court's decision. Shell Oil
believes that many of its tar sands tax credits are validly claimed under the
alternative definition asserted by the government in the District Court case,
and is pursuing such claims in the Court of Federal Claims.

      The Company's assessment of these matters is continuing. Future provisions
may be required as administrative and judicial proceedings progress and the
scope and nature of remediation programs and related costs estimates are
clarified. However, while periodic results may be significantly affected by
costs in excess of provisions related to one or more of these proceedings, based
upon developments to date, the management of the Company anticipates that it
will be able to meet related obligations without a material adverse effect on
its financial position.

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




                                       8
<PAGE>   9



                     MANAGEMENT'S DISCUSSION AND ANALYSIS OF
                  FINANCIAL CONDITION AND RESULTS OF OPERATIONS


RESULTS OF OPERATIONS

      AS DISCUSSED IN NOTE D OF THE NOTES TO INTERIM FINANCIAL STATEMENTS, THE
NET INCOME FOR THE THREE MONTH AND NINE MONTH PERIODS ENDING SEPTEMBER 30, 1998
FOR EACH OF SHELL OIL'S REPORTABLE OPERATING SEGMENTS HAS BEEN RESTATED FROM
THAT PREVIOUSLY REPORTED. THE 1998 RESTATEMENT WAS MADE TO BE CONSISTENT WITH
THE 1999 PRESENTATION REFLECTING THE ADOPTION OF STATEMENT OF FINANCIAL
ACCOUNTING STANDARDS NO. 131, "DISCLOSURES ABOUT SEGMENTS OF AN ENTERPRISE AND
RELATED INFORMATION."


      Shell Oil reported third quarter 1999 net income of $900 million, an
increase of $642 million compared to the third quarter of 1998. Excluding
special items in both quarters, adjusted net income in the 1999 quarter totaled
$658 million, an increase of $470 million.

      The major elements in these significantly higher earnings were sharply
higher prices for crude oil and natural gas. Average domestic crude oil prices
were up 67 percent over the same period in 1998, while average natural gas
prices jumped 38 percent.

      For the first nine months of 1999, net income was $1,667 million, an
increase of $921 million over the same period last year. Excluding special
items, adjusted net income for 1999 totaled $1,212 million, up $541 million over
1998. Lower operating costs, lower depreciation expense resulting in part from
1999 asset sales and the effect of suspending depreciation on assets held for
sale, and higher average crude oil prices were the primary contributors to these
improved earnings.

      Special items in the 1999 periods benefited net income $242 million for
the quarter and $455 million for the first nine months. Special items in the
third quarter of 1999 were comprised primarily of gains from asset sales.
Special items increased 1998 net income by $70 million for the quarter and $75
million in the first nine months


OIL AND GAS EXPLORATION AND PRODUCTION

<TABLE>
<CAPTION>

Income Highlights                                Third Quarter               Nine Months
-----------------                            --------------------        --------------------
(millions of dollars)                         1999          1998          1999          1998
                                             ------        ------        ------        ------

<S>                                          <C>           <C>           <C>           <C>
Segment Net Income...................        $  656        $  126        $1,190        $  405
Special Items .......................           173            56           326            98
                                             ------        ------        ------        ------
Adjusted Net Income..................           483            70           864           307
</TABLE>


      Oil and gas exploration and production earnings in the third quarter of
1999 totaled $656 million, an increase of $530 million over 1998. For the first
nine months of 1999, earnings were $1,190 million, up $785 million. Excluding
special items in the comparable periods, adjusted net income increased $413
million in the 1999 quarter versus 1998 and $557 million in the nine-month
comparison. Third quarter 1999 special items consisted primarily of gains on
asset sales.

      The significant increase in earnings in the third quarter of 1999 over the
same period last year was due primarily to sharply higher average crude oil and
natural prices. The increase in earnings in the


                                       9
<PAGE>   10


nine months comparison was primarily attributable to reduced operating costs and
exploratory expenses, including dry holes, while also benefiting from higher
average crude oil prices. Also contributing to the nine months improvement was
lower depreciation expense, resulting in part from 1999 asset sales and the
effect of suspending depreciation on assets held for sale.

      During the third quarter of 1999, Shell Oil sold a portion of its
ownership in various deepwater Gulf of Mexico properties, primarily the
Macaroni, Europa and Angus fields. In each case, Shell Oil remains the operator
of these properties.

      For the third quarter of 1999, domestic crude oil prices averaged $17.85
per barrel, increasing $7.13 per barrel, or 67 percent over the 1998 quarter.
For the first nine-month periods, domestic crude oil prices averaged $13.74 per
barrel, up $2.39 per barrel, or 21 percent. Average natural gas prices were up
$.71 per thousand cubic feet, or 38 percent, averaging $2.59 per thousand cubic
feet. For the nine months of 1999, natural gas prices averaged $2.12, about the
same as in the 1998 comparative period.

      Average domestic crude oil production during the 1999 periods was 428,000
barrels per day for the quarter and 429,000 barrels per day for the first nine
months, decreasing 3,000 and 18,000 barrels per day, respectively, compared to
1998. These reductions are attributable to property sales in the shelf region of
the Gulf of Mexico and onshore, as well as normal production declines. Partially
offsetting the declines was new and increased production in the deepwater Gulf
of Mexico and favorable weather conditions in 1999 which negatively impacted
production in the 1998 period. Natural gas production averaged 1,922 million
cubic feet daily during the third quarter of 1999, up 130 million cubic feet
daily, or 7 percent. New and increased deepwater production and operating
conditions more than offset the effects of property sales and natural declines
elsewhere. For the nine month period of 1999, natural gas production averaged
1,995 million cubic feet daily, an increase of 74 million, or 4 percent.

      Domestic crude oil and natural gas production numbers include Shell Oil's
net production plus a prorata share, based on ownership interest, of domestic
equity companies' production. Equity companies are those companies in which
Shell Oil has significant influence but not control.

DOWNSTREAM GAS

<TABLE>
<CAPTION>

Income Highlights                                                Third Quarter                     Nine Months
-----------------                                            ---------------------           ----------------------
(millions of dollars)                                         1999           1998             1999            1998
                                                             ------        -------           ------          ------

<S>                                                          <C>           <C>               <C>             <C>
   Segment Net Income (Loss)...........................      $  20             (24)          $  37              (25)
   Special Items ......................................         61              --             114               --
                                                             -----         -------           -----           ------
   Adjusted Net Income (Loss)..........................        (41)            (24)            (77)             (25)
</TABLE>

      Downstream gas earnings for the third quarter of 1999 were $20 million, up
$44 million over the same period last year. For the first nine months of 1999,
earnings totaled $37 million, up $62 million over the 1998 period. Excluding
special items related to gains from asset sales, downstream gas incurred a loss
of $41 million in the quarter and $77 million for the first nine months,
declining $17 million and $52 million respectively, from the 1998 periods.

      During the third quarter of 1999, benefits from improved ongoing NGL
processing margins and volumes and higher onshore pipeline storage margins, were
more than offset by higher operating and technology costs related to the
marketing of electricity and depressed natural gas margins, particularly in
Canada. In addition, nine month 1999 earnings were lower than the same period in
1998 due to higher allocated interest costs. Partially offsetting the lower nine
month earnings was reduced depreciation


                                       10
<PAGE>   11


expense resulting from 1999 asset sales.

      Also during the third quarter of 1999, Shell Oil combined its Louisiana
and Mississippi natural gas liquids (NGL) business with Enterprise Products
Partners L.P. In exchange, Tejas Energy, LLC, an affiliate of Shell Oil,
received 14.5 million convertible special partnership units in Enterprise, 6.0
million contingent convertible special partnership units (such contingency to be
fulfilled on or before December 31, 2001) and $166 million in cash.


OIL PRODUCTS

<TABLE>
<CAPTION>

Income Highlights                                                Third Quarter                    Nine Months
-----------------                                            ---------------------          -----------------------
(millions of dollars)                                         1999           1998            1999             1998
                                                             ------         ------          ------           ------

<S>                                                          <C>            <C>             <C>              <C>
   Segment Net Income..................................      $  111         $   99          $  201           $  200
   Special Items ......................................          --             14              15              (16)
                                                             ------         ------          ------           ------
   Adjusted Net Income.................................         111             85             186              216
</TABLE>

      Shell Oil's oil products segment consists primarily of its share of
results from Equilon, which began operations in January, 1998 (Shell Oil
interest - 56 percent), Motiva, which began operations in July, 1998 (Shell Oil
interest - 35 percent), and the Deer Park Refining Limited Partnership (Shell
Oil interest - 50 percent). Shell Oil accounts for its investment in each of
these companies using the equity method of accounting.

      Oil products earnings totaled $111 million in the third quarter of 1999,
an increase of $12 million over the 1998 period. For the nine months of 1999,
earnings were $201 million, an increase of $1 million over the comparable 1998
period. Excluding special items, adjusted net income increased $26 million in
the quarter comparison, but decreased $30 million in the nine months comparison.

      The improvement in earnings in the third quarter of 1999 over 1998 was due
to strong refining margins on the West Coast, benefits of synergy gains in the
Alliances (Equilon and Motiva) and lower interest costs, which more than offset
weaker marketing margins. Earnings in the nine months of 1999 were lower
compared to 1998 due to depressed refining margins, particularly in the Eastern
and Gulf Coast regions


CHEMICAL PRODUCTS

<TABLE>
<CAPTION>

Income Highlights                                                Third Quarter                    Nine Months
-----------------                                            ---------------------          -----------------------
(millions of dollars)                                         1999           1998            1999             1998
                                                             ------         ------          ------           ------

<S>                                                         <C>             <C>             <C>              <C>
   Segment Net Income..................................      $  134         $   62          $  299           $  232
   Special Items ......................................           8             --              --               (9)
                                                             ------         ------          ------           ------
   Adjusted Net Income.................................         126             62             299              241
</TABLE>

      Chemical products earnings, including special items, were $134 million in
the third quarter of 1999, an increase of $72 million over 1998. For the first
nine months of 1999, chemical products earnings totaled $299 million, an
increase of $67 million. Excluding special items in the comparable 1999 and 1998
periods, adjusted net income increased $64 million for the 1999 quarter and $58
million for the 1999 nine months.


                                       11
<PAGE>   12
      In the third quarter of 1999, margins for primary chemicals improved
resulting from increased selling prices. Additionally, depreciation expense was
lower reflecting in part the effect of the suspension of depreciation on assets
held for sale. These benefits, however, were more than offset by lower margins
in downstream businesses resulting from higher feedstock costs. For the nine
months of 1999 compared to 1998, earnings were lower due to depressed margins
across most business lines, but partially offset by lower depreciation expense.


ALL OTHER

      All other operating segments' earnings in the third quarter of 1999 were
nil, compared to earnings of $1 million in last year's quarter. For the first
nine months of 1999, the other operating segment incurred a loss of $2 million,
a decrease of $22 million from 1998. The decline in the nine-month comparison is
mainly due to lower margins derived from service operations.


NONALLOCATED ITEMS

      Nonallocated costs reduced earnings $21 million in the third quarter and
$58 million in the first nine months of 1999. Costs in the third quarter of 1999
were $15 million higher than in the 1998 period, which benefited from an
undistributed insurance recovery. Costs for the first nine months of 1999 were
$28 million lower than in 1998, which included a high level of expenditures
associated with the brand initiative program.



FINANCIAL CONDITION

CAPITAL RESOURCES AND LIQUIDITY

      Cash flow provided by operating activities totaled $1,035 million for the
first nine months of 1999, compared with $1,569 million in the comparable period
last year, a decrease of $534 million. Cash generated from operating activities,
coupled with proceeds from property sales totaling $2,491 million, were used for
capital expenditures of $1,207 million, dividend payments of $1,275 million, and
reduction of debt of $322 million.



OTHER MATTERS

REPORT ON YEAR 2000 ISSUES

      Shell Oil has been engaged in the identification, analysis and remediation
of the Year 2000 ("Y2K") computer date problem since 1997. This problem is
associated with the incorrect interpretation by the computer of dates which are
numerically related to the change of the millennium. Large and small computing
devices and associated software used in running large business applications as
well as some kinds of industrial automation systems are potentially subject to
this problem.

      Under the Shell Oil governance model, each business organization has
independent responsibility for identification, analysis and remediation of Y2K
problems within such business, and in 1997, Year 2000 Teams were formed in each
business organization to deal with the Y2K problem. The Teams communicate
through a central focal point committee which tracks and updates Year 2000
progress reports from each business at the overall Shell Oil level. This Shell
Oil Year 2000 Team also


                                       12
<PAGE>   13


provides a vehicle for exchange of ideas and experiences to achieve improved
efficiencies and results. The Chief Information Officer of each business
represents the organization on the Shell Oil Year 2000 Team. Additionally,
confirmation is sought from those equity companies where Shell Oil has a
significant voting interest of an active and appropriate Y2K program.

      Shell Oil Year 2000 Teams have identified and analyzed the use of computer
technology in the respective businesses to determine where there were business
operation issues associated with the Y2K problem. Priority in such reviews was
placed first on health, safety and environmental issues, then on areas which
could materially affect third parties or revenues. These reviews necessarily
included both internal uses of technology as well as key trading interfaces,
which might be adversely affected by third party customers', suppliers' or
service providers' use of computing technology with Y2K problems.

      The Shell Oil businesses divided their analysis of the Y2K problem into
three areas: 1) business information, computing and telecommunication systems
("IT Systems"); 2) industrial automation systems ("Imbedded Technology
Systems"); and 3) potential problems involving the Y2K problems of third party
suppliers, customers and service providers (each a "Third Party" and together
"Third Parties").

      The analysis and inventory of potential Y2K problems has been completed in
all areas involving critical IT Systems and Imbedded Technology Systems, with
remediation requirements identified and remediation plans developed. At
September 30, 1999, remediation of Y2K problems in all such areas in which
issues have been identified had been substantially completed with only very
small amounts of remediation work remaining to be completed during the fourth
quarter of 1999. The remaining remediation work is predominantly associated with
the implementation of already completed corrective work. Remediation has been
primarily handled by internal company staff, although some outside companies
have been involved in the remediation associated with particular systems. The
analysis of interfaces with key Third Parties is substantially complete and
communication with some of these parties will continue through the fourth
quarter of 1999 to insure appropriate coordination and, where necessary or
appropriate, adjustment of contingency plans in the event a Third Party cannot
meet its commitments to Shell Oil. Analyses and remediation of non-critical IT
Systems, Imbedded Technology Systems and Third Party interfaces will continue
through the remainder of the year.

      As to the Imbedded Technology Systems used in industrial automation within
Shell Oil, the various Shell Oil businesses have used several approaches in the
identification and analysis of the potential Y2K problem in such systems,
including field installation inspection, and inspection of design blueprints,
with field-testing to confirm the adequacy of design information. At September
30, 1999, remediation of substantially all material Y2K problems with this
technology had been completed with the remaining remediation expected to be
completed as part of other scheduled facility maintenance occurring during the
fourth quarter of 1999.

      Due to a business-driven demand for improved computing systems throughout
Shell Oil, the primary business computing systems in each Shell Oil business
organization are being replaced in this decade. These new systems are
represented to be fully Y2K compliant by their manufacturers, and Shell Oil
believes that it will have no Y2K issues in its important business computing
systems. While acquisition of these new IT Systems for business computing
avoided the necessity of dealing with Y2K issues in the predecessor systems, the
cost of these systems was incurred primarily for other business reasons. The
majority of the costs of each such system are being capitalized and charged
against income over the estimated useful life of the systems. Funds for the
acquisition of these systems are included in the capital budget of the
respective businesses.

                                       13
<PAGE>   14

      Costs associated with the identification, analysis and remediation of Y2K
problems, including the repair or replacement of imbedded technology systems,
are currently projected by the businesses at approximately $150 million. These
costs are being charged to expense as incurred and do not include Y2K costs of
equity companies. At September 30, 1999, approximately 95 percent of such
expenditure had been committed or incurred. Funding for these efforts has been a
part of the normal budgeting of current operations within each business.

      Beyond the internal programs in the Shell Oil businesses, significant
efforts are continuing in order to understand the position of key Third Parties
with respect to possible business interruptions due to Y2K problems in their
systems. Current indications are that all of Shell Oil's major Third Party
customers, suppliers and service providers are well aware of this problem and
have programs underway to address it. Physical testing of key interfaces and
ongoing discussions are continuing with certain Third Parties to best position
Shell Oil to continue its business operations without interruption. Specific
attention is being given to Third Parties that have critical relationships with
Shell Oil to insure that there is not a disruption in the flow of those products
or services that are essential to the ability of Shell Oil to carry on its
business operations. However, since Shell Oil will remain dependent on Third
Party confirmations in certain areas, appropriate contingency plans have been
developed in each of Shell Oil's businesses.

      The key objective of Shell Oil's extensive program to address the Y2K
computer technology problem is the significant reduction or complete elimination
of the risk to business operations. Internal audits completed during the first
nine months of 1999 of Shell Oil's major business units have further validated
the coverage of the Y2K remediation programs in meeting this objective. These
audits will continue during the remainder of 1999. As a contingency plan, steps
are being developed to manage this issue around key dates where unanticipated
Y2K problems may arise. Current plans include the positioning of skilled
computer staff in the various areas of business operations to insure quick
response to any unexpected Y2K problems arising due to failure to previously
detect the problem or due to inadequate remediation. Shell Oil is continuing to
review its business operation contingency plans in order to understand what
additions may be appropriate to those plans to deal with residual risk
associated with Y2K problems. These plans include decisions on operating
schedules and staff deployment during time periods in which Y2K-related problems
are most likely to occur.

      Shell Oil realizes that its failure or the failure of critical Third
Parties to identify and correct a material Y2K problem could result in an
interruption in or failure of certain normal business activities or operations.
While such failures could materially and adversely affect Shell Oil's operations
and relationships with Third Parties, the objective of Shell Oil's Year 2000
Team is the significant reduction or complete elimination of these risks. Shell
Oil expects to achieve this goal. As stated above, steps are being taken to
manage this issue around key dates where the problem may arise.

      The discussion of Shell Oil's Y2K efforts and expectations regarding the
same includes forward-looking statements within the meaning of Section 27A of
the Securities Act of 1933. Shell Oil's ability to achieve Year 2000 readiness
and the level of costs associated therewith could be adversely impacted by,
among other things: the availability and cost of programming and testing
resources; vendors' ability to install or modify hardware, software or other
computer technology in Shell Oil systems; and unanticipated problems identified
as the Year 2000 Teams conclude their analysis and verification of IT and
Imbedded Technology Systems. Additionally, no precedent exists as to the manner
in which to fully detect and eliminate Y2K risks. Thus, it is possible that
despite all efforts to identify, analyze and remediate Y2K related problems, not
all potential problems may be detected or all remediation efforts operate as
intended; it is impossible to accurately predict the impact on Shell Oil in any
such case. Finally, the failure of Third Parties to achieve acceptable Y2K
compliance and the absence of available contingent suppliers and resources could
also materially adversely affect Shell Oil.


                                       14
<PAGE>   15

STATEMENTS OF FINANCIAL ACCOUNTING STANDARDS NOT YET ADOPTED

      In June 1998 the Financial Accounting Standards Board issued Statement of
Financial Accounting Standards No. 133, "Accounting for Derivative Instruments
and Hedging Activities" ("SFAS 133"). As issued, this new standard is effective
for fiscal years beginning after June 15, 1999. In June 1999, the Financial
Accounting Standard Board issued SFAS 137 which deferred the effective date of
SFAS 133 by one year to be effective for fiscal years beginning after June 15,
2000 (January 1, 2001 for the Company). SFAS 133 requires that all derivative
instruments be recorded on the balance sheet at their fair value. Changes in the
fair value of derivatives are recorded each period in current earnings or other
comprehensive income, depending on whether a derivative is designated as part of
a hedge transaction and, if it is, the type of hedge transaction. The Company
has not yet completed its evaluation of the impact of the adoption of this new
standard.


      In addition to the economic conditions and other matters discussed above
affecting Shell Oil, the operations, earnings and financial condition of Shell
Oil may be affected by political developments; litigation; and legislation,
regulation and other actions taken by federal, state, local and foreign
governmental entities, including those matters discussed in Note F. of the Notes
to Interim Financial Statements.

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

                           PART II. OTHER INFORMATION


ITEM 1.  LEGAL PROCEEDINGS.

      In July 1999, the Company received a Notice of Violation from the EPA
Region I Office alleging violations under the Connecticut State Implementation
Plan at the Bridgeport, Connecticut terminal (formerly owned by Shell Oil but
now a Motiva Enterprises LLC facility). Motiva, the Company and the EPA are
engaging in discussions regarding the allegations of the notice. The EPA has
informed Motiva that it intends to refer this matter to the U.S. Department of
Justice for the filing of a civil action because the penalty amount sought
exceeds the guidance policy for the assessment of administrative penalties.


ITEM 6.   EXHIBITS AND REPORTS ON FORM 8-K

         (a)    Exhibits.
                27.  Financial Data Schedule.

         (b)    Reports on Form 8-K.
                None

                                       15
<PAGE>   16


                                   SIGNATURES

      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.


                                          SHELL OIL COMPANY



                                      By  N. J. CARUSO
                                          -------------------------------------
                                          N. J. Caruso, Chief Financial Officer
                                          and Controller (Principal Accounting
                                          and Duly Authorized Officer)


Date:  November 12, 1999



                                       16
<PAGE>   17



                                INDEX TO EXHIBITS

<TABLE>
<CAPTION>

Exhibit
Number        Description
------        -----------

<S>           <C>
  27          Financial Data Schedule
</TABLE>