<PAGE>   1



                       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 September 30, 1999

                                       OR


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


   For the Transition Period from                     to
                                  -------------------    ---------------------

                         Commission File Number 0-13546

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

                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
             ------------------------------------------------------
             (Exact Name of Registrant as Specified in Its Charter)

           Delaware                                           41-1464066
-------------------------------                          ----------------------
(State or Other Jurisdiction of                            (I.R.S. Employer
 Incorporation or Organization)                          Identification Number)

     Suite 100, One Post Oak Central                          77056-4400
----------------------------------------                      ----------
  2000 Post Oak Boulevard, Houston, TX                        (Zip Code)
(Address of Principal Executive Offices)

       Registrant's Telephone Number, Including Area Code: (713) 296-6000

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
                                     ---    ---



<PAGE>   2


                         PART I - FINANCIAL INFORMATION


ITEM 1 - FINANCIAL STATEMENTS


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                               STATEMENT OF INCOME
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                   FOR THE QUARTER           FOR THE NINE MONTHS
                                                 ENDED SEPTEMBER 30,         ENDED SEPTEMBER 30,
                                              -------------------------   -------------------------
                                                 1999          1998          1999          1998
                                              -----------   -----------   -----------   -----------

<S>                                           <C>           <C>           <C>           <C>
REVENUES:
   Oil and gas production revenues            $ 2,067,810   $ 1,713,277   $ 5,789,695   $ 6,062,749
   Interest income                                 38,702        21,820        74,508        47,068
                                              -----------   -----------   -----------   -----------
                                                2,106,512     1,735,097     5,864,203     6,109,817
                                              -----------   -----------   -----------   -----------

EXPENSES:
   Depreciation, depletion and amortization       788,292       622,671     2,287,411     2,070,659
   Lease operating expense                        176,035       380,910       529,023       771,372
   Administrative                                 135,000       129,137       405,000       405,116
                                              -----------   -----------   -----------   -----------
                                                1,099,327     1,132,718     3,221,434     3,247,147
                                              -----------   -----------   -----------   -----------
NET INCOME                                    $ 1,007,185   $   602,379   $ 2,642,769   $ 2,862,670
                                              ===========   ===========   ===========   ===========

NET INCOME ALLOCATED TO:
   Managing Partner                           $   338,507   $   195,817   $   866,543   $   826,414
   Investing Partners                             668,678       406,562     1,776,226     2,036,256
                                              -----------   -----------   -----------   -----------
                                              $ 1,007,185   $   602,379   $ 2,642,769   $ 2,862,670
                                              ===========   ===========   ===========   ===========
NET INCOME PER INVESTING PARTNER UNIT         $       588   $       352   $     1,559   $     1,737
                                              ===========   ===========   ===========   ===========
WEIGHTED AVERAGE INVESTING PARTNER
   UNITS OUTSTANDING                              1,136.7       1,154.4       1,139.5       1,172.5
                                              ===========   ===========   ===========   ===========
</TABLE>

                 The accompanying notes to financial statements
                    are an integral part of this statement.

                                       1

<PAGE>   3


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                             STATEMENT OF CASH FLOWS
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                    FOR THE NINE MONTHS ENDED SEPTEMBER 30,
                                                                    ---------------------------------------
                                                                             1999            1998
                                                                         ------------    ------------

<S>                                                                      <C>             <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                            $  2,642,769    $  2,862,670
   Adjustments to reconcile net income to net cash
      provided by operating activities:
         Depreciation, depletion and amortization                           2,287,411       2,070,659
         Changes in operating assets and liabilities:
             Decrease in accrued revenues receivable                          509,151         344,054
             Increase (decrease) in accrued operating expenses payable        (35,809)         77,852
             Increase in payable to Apache Corporation                         43,855         135,274
                                                                         ------------    ------------
         Net cash provided by operating activities                          5,447,377       5,490,509
                                                                         ------------    ------------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Additions to oil and gas properties                                     (1,112,072)     (2,144,221)
   Non-cash portion of oil and gas property additions                         286,390        (951,355)
   Proceeds from sales of oil and gas properties                              140,620         363,534
   Increase in drilling advances                                                   --          72,020
                                                                         ------------    ------------
         Net cash used in investing activities                               (685,062)     (2,660,022)
                                                                         ------------    ------------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Repurchase of Partnership Units                                            (45,512)       (348,000)
   Distributions to Investing Partners                                       (855,728)             --
   Distributions to Managing Partner, net                                  (1,122,295)       (804,419)
                                                                         ------------    ------------
         Net cash used in financing activities                             (2,023,535)     (1,152,419)
                                                                         ------------    ------------

NET INCREASE IN CASH AND CASH EQUIVALENTS                                   2,738,780       1,678,068

CASH AND CASH EQUIVALENTS, BEGINNING OF YEAR                                1,324,949         691,797
                                                                         ------------    ------------
CASH AND CASH EQUIVALENTS, END OF PERIOD                                 $  4,063,729    $  2,369,865
                                                                         ============    ============
</TABLE>

                 The accompanying notes to financial statements
                    are an integral part of this statement.

                                       2

<PAGE>   4


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                                  BALANCE SHEET
                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                  SEPTEMBER 30,     DECEMBER 31,
                                                                      1999              1998
                                                                 --------------    --------------

                               ASSETS

<S>                                                              <C>               <C>
CURRENT ASSETS:
   Cash and cash equivalents                                     $    4,063,729    $    1,324,949
   Accrued revenues receivable                                          788,848         1,297,999
                                                                 --------------    --------------
                                                                      4,852,577         2,622,948
                                                                 --------------    --------------

OIL AND GAS PROPERTIES, on the basis of full cost accounting:
   Proved properties                                                169,303,152       168,331,700
   Less - Accumulated depreciation, depletion and amortization     (163,401,505)     (161,114,094)
                                                                 --------------    --------------
                                                                      5,901,647         7,217,606
                                                                 --------------    --------------
                                                                 $   10,754,224    $    9,840,554
                                                                 ==============    ==============

               LIABILITIES AND PARTNERS' CAPITAL

CURRENT LIABILITIES:
   Distribution payable                                          $    3,123,493    $           --
   Accrued exploration and development                                  878,310           591,920
   Accrued operating expenses payable and other                          62,558            98,367
   Payable to Apache Corporation                                        113,828            69,973
                                                                 --------------    --------------
                                                                      4,178,189           760,260
                                                                 --------------    --------------

PARTNERS' CAPITAL:
   Managing Partner                                                     341,308           597,060
   Investing Partners (1,135.8 and 1,141.0 units
      outstanding, respectively)                                      6,234,727         8,483,234
                                                                 --------------    --------------
                                                                      6,576,035         9,080,294
                                                                 --------------    --------------
                                                                 $   10,754,224    $    9,840,554
                                                                 ==============    ==============
</TABLE>

                 The accompanying notes to financial statements
                    are an integral part of this statement.

                                       3

<PAGE>   5


                     APACHE OFFSHORE INVESTMENT PARTNERSHIP
                          NOTES TO FINANCIAL STATEMENTS
                                   (UNAUDITED)


     The financial statements included herein have been prepared by the Apache
Offshore Investment Partnership (the Partnership), without audit, pursuant to
the rules and regulations of the Securities and Exchange Commission, and reflect
all adjustments which are, in the opinion of management, necessary for a fair
statement of the results for the interim periods, on a basis consistent with the
annual audited financial statements. All such adjustments are of a normal,
recurring nature. Certain information, accounting policies, and footnote
disclosures normally included in financial statements prepared in accordance
with generally accepted accounting principles have been omitted pursuant to such
rules and regulations, although the Partnership believes that the disclosures
are adequate to make the information presented not misleading. These financial
statements should be read in conjunction with the financial statements and the
summary of significant accounting policies and notes thereto included in the
Partnership's latest annual report on Form 10-K.


1.   RECEIVABLE FROM/PAYABLE TO APACHE

     Receivable from/payable to Apache Corporation, the Partnership's managing
partner (Apache or the Managing Partner), represents the net result of the
Investing Partners' revenue and expenditure transactions in the current month.
Generally, cash in this amount will be transferred from/to Apache in the month
after the Partnership's transactions are processed and the net results of
operations are determined.


2.   RIGHT OF PRESENTMENT

     As provided in the Partnership Agreement, as amended (the Amended
Partnership Agreement), a first right of presentment offer for 1999 of $8,410
per Unit, plus interest to the date of the payment, was made to Investing
Partners based on a valuation date of December 31, 1998. As a result, the
Partnership agreed in July 1999 to acquire 5.14835 Units for a total of $45,512
in cash. A second right of presentment offer of $6,769 per Unit, plus interest
to the date of payment, was made to the Investing Partners on November 1, 1999,
based on a valuation date of June 30, 1999.

     The Partnership is not in a position to predict how many Units will be
presented for repurchase during the fourth quarter of 1999 and cannot, at this
time, determine if the Partnership will have sufficient funds available to
purchase Units. The Partnership has no obligation to purchase any Units
presented to the extent it determines that it has insufficient funds for such
purchases. The Amended Partnership Agreement contains limitations on the number
of Units that the Partnership can repurchase, including a limit of 10 percent of
the outstanding Units on an annual basis.

                                       4

<PAGE>   6


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


RESULTS OF OPERATIONS

NET INCOME AND REVENUE

     The Partnership reported net income of $1 million in the third quarter of
1999, versus $.6 million in the prior year period. Net income per Investing
Partner Unit increased 67 percent, from $352 per Unit to $588 per Unit. Higher
oil and natural gas prices during the current period contributed to the
increase.

     For the first nine months of 1999, net income of $2.6 million, or $1,559
per Investing Partner Unit, decreased eight percent and 10 percent,
respectively, from $2.9 million, or $1,737 per Investing Partner Unit, in the
same period last year. The declines were attributable to lower natural gas
prices and production, combined with higher depreciation, depletion and
amortization (DD&A) expense.

     Revenues increased 21 percent, from $1.7 million in the third quarter of
1998 to $2.1 million in the third quarter of 1999. Natural gas and crude oil
sales represented 77 percent and 21 percent, respectively, of the Partnership's
total revenues during the third quarter of 1999. For the first nine months of
1999, revenues decreased four percent to $5.9 million as lower natural gas
prices and production more than offset an increase in oil prices. Natural gas
and crude oil sales contributed 77 percent and 22 percent, respectively, to the
Partnership's total revenues during the first nine months of 1999.

     The Partnership's oil and gas production volume and price information is
summarized in the following table (gas volumes presented in thousand cubic feet
(Mcf) per day):

<TABLE>
<CAPTION>
                                             FOR THE QUARTER ENDED                        FOR THE NINE MONTHS ENDED
                                                  SEPTEMBER 30,                                  SEPTEMBER 30,
                                   --------------------------------------------   --------------------------------------------
                                                                      INCREASE                                       INCREASE
                                      1999           1998            (DECREASE)     1999            1998            (DECREASE)
                                   ----------     ----------         ----------   ----------     ----------         ----------

<S>                                <C>            <C>                    <C>      <C>            <C>                    <C>
Gas volume - Mcf per day                6,903          7,857            (12%)          8,106          8,622             (6%)
Average gas price - per Mcf        $     2.55     $     1.91             34%      $     2.04     $     2.11             (3%)
Oil volume - barrels per day              248            287            (14%)            303            305             (1%)
Average oil price - per barrel     $    19.74     $    12.60             57%      $    15.48     $    13.10             18%
</TABLE>

THIRD QUARTER 1999 COMPARED TO THIRD QUARTER 1998

     Natural gas production revenues for the third quarter of 1999 totaled $1.6
million, 17 percent higher than the third quarter of 1998. Natural gas prices
increased 34 percent for the third quarter of 1999 compared to the year-earlier
period, which favorably impacted revenue by $.5 million. Natural gas volumes for
the quarter declined 12 percent from a year ago due to production declines at
Matagorda 681, and downtime for repairs at Ship Shoal 259 and East Cameron 60.

     The Partnership's crude oil production revenues for the third quarter of
1999 totaled $.5 million, a 36 percent increase from the third quarter of 1998.
The $.1 million increase in oil sales was attributable to the 57 percent
increase in average realized oil price, offset by a 14 percent decrease in oil
production.

YEAR-TO-DATE 1999 COMPARED TO YEAR-TO-DATE 1998

     Gas sales for the first nine months of 1999 of $4.5 million decreased $.5
million, or nine percent, when compared to the same period in 1998. Average
realized gas prices decreased $.07 per Mcf, or three percent, when compared with
the first nine months of 1998, negatively impacting sales by $.2 million. Gas
production for the first nine months of 1999 decreased by six percent when
compared to the same period in 1998, negatively impacting revenues by $.3
million. Production decreases in 1999 were primarily due to natural declines in
production.

                                       5

<PAGE>   7


     For the nine months ended September 30, 1999, oil sales increased 17
percent to $1.3 million when compared to the same period last year. The
Partnership's oil sales revenues were favorably impacted by an 18 percent
increase in realized prices.

OPERATING EXPENSES

     The Partnership's DD&A rate, expressed as a percentage of oil and gas
production revenues, was approximately 38 percent during the third quarter of
1999 compared to 36 percent during the same period in 1998. For the first nine
months, the Partnership's DD&A rate rose from 34 percent in 1998 to 40 percent
in 1999. The increase in the DD&A rate for the nine-month period was primarily a
result of lower natural gas prices in 1999.

     Lease operating expense (LOE) in the third quarter of 1999 declined
substantially from the third quarter of 1998 due to lower workover activity. For
the first nine months of 1999, LOE of $.5 million was down 31 percent from a
year ago due to lower repair and workover expense in 1999.

CASH FLOW, LIQUIDITY AND CAPITAL RESOURCES

CAPITAL RESOURCES AND LIQUIDITY

     The Partnership's primary capital resource is net cash provided by
operating activities, which was $5.4 million for the first nine months of 1999.
Net cash provided by operating activities in 1999 was down one percent from a
year ago, as the eight percent decrease in net income in 1999 was largely offset
by the impact of reduced revenue receivables. Future cash flows will be
influenced similarly by fluctuations in product prices, production levels and
operating costs.

CAPITAL COMMITMENTS

     The Partnership's primary needs for cash are for operating expenses,
drilling and recompletion expenditures, distributions to Investing Partners, and
the purchase of Units offered by Investing Partners under the right of
presentment.

     During the first nine months of 1999, the Partnership's oil and gas
property additions totaled $1.1 million. These additions related primarily to
recompletions at South Timbalier Block 295 and drilling activity at North Padre
Block 969. Based on information supplied by the operators of the properties, the
Partnership anticipates capital expenditures of approximately $.5 million for
the remainder of 1999. The anticipated capital expenditures primarily relate to
South Timbalier Block 295. Such estimates may change based on realized prices,
drilling results or changes by the operator to the development plan.

     The Partnership made distributions to Investing Partners of $750 per Unit
on March 18, 1999, and $2,750 per Unit on October 4, 1999. The amount of future
distributions will be dependent on actual and expected production levels,
realized and expected oil and gas prices, expected drilling and recompletion
expenditures, and prudent cash reserves for future dismantlement and abandonment
costs that will be incurred after the Partnership's reserves are depleted.

     As provided in the Amended Partnership Agreement, a first right of
presentment offer for 1999 of $8,410 per Unit, plus interest to the date of
payment, was made to Investing Partners, based on a valuation date of December
31, 1998. As a result, the Partnership agreed in July 1999 to acquire 5.14835
Units for a total of $45,512 in cash. A second right of presentment offer for
1999 of $6,769 per Unit, plus interest to the date of payment, was made to
Investing Partners on November 1, 1999, based on a valuation date of June 30,
1999. The Partnership is not in a position to predict how many Units will be
presented for repurchase during the fourth quarter and cannot, at this time,
determine if the Partnership will have sufficient funds available to repurchase
Units. The Partnership has no obligation to purchase any Units presented to the
extent it determines that it has insufficient funds for such purchases. The
Amended Partnership Agreement contains limitations on the number of Units that
the Partnership can repurchase, including a limit of 10 percent of the
outstanding Units on an annual basis.

     On May 18, 1999, the Managing Partner acquired from Shell Offshore Inc. and
affiliated Shell entities (Shell) its interest in certain Gulf of Mexico
properties, together with certain production-related assets and proprietary 3D
seismic data. The purchase price, subject to post closing adjustments, was
$687.6 million in cash and one million shares of

                                       6

<PAGE>   8


Apache common stock. As a result of Apache's purchase of the properties from
Shell, Apache and the Partnership expect an acceleration of recompletion
projects at South Timbalier Block 295.

IMPACT OF THE YEAR 2000 ISSUE

     The inability of some computer programs and embedded computer chips to
distinguish between the year 1900 and the year 2000 (the Year 2000 issue) poses
a serious threat of business disruption to any organization that utilizes
computer technology and computer chip technology in their business systems or
equipment. Apache, as Managing Partner, manages the Partnership's operations.
Apache uses a portion of its staff for this purpose and is reimbursed for actual
costs paid on behalf of the Partnership, as well as for general, administrative
and overhead costs properly allocable to the Partnership. Apache has formed a
Year 2000 Task Force with representation from major business units to inventory
and assess the risk of hardware, software, telecommunications systems, office
equipment, embedded chip controls and systems, process control systems, facility
control systems and dependencies on external trading partners. The project
phases, expected completion dates and percentage complete as of September 1999
are as follows:

<TABLE>
<CAPTION>
              PHASE                       COMPLETION DATE     PERCENT COMPLETE
-----------------------------------       ---------------     ----------------

<S>                                        <C>                      <C>
Organization                                   July 1998            100%

Assessment                                 November 1998            100%
    Desktop Computers
    Network Hardware
    Software
    Embedded Systems
    External Trading Partners
    Building/Infrastructure Systems
    Telecommunications Systems

Implementation/Replacement                 November 1999             90%
    Computer Hardware
    Core Business Software
    Desktop Software
    Embedded Systems
    Building Systems

Contact External Trading Partners             March 1999            100%

Contingency Planning                       November 1999             90%
</TABLE>

     To date, the Managing Partner is not aware of any significant Year 2000
issues that would cause problems in the area of safety, environmental or
business interruption. Apache has assessed the risks associated with hardware,
software, infrastructure, embedded chips and external trading partners that are
not Year 2000 compliant. While Apache is confident that Year 2000 remediation
efforts will succeed in minimizing exposure to business disruption, plans are
being developed that will allow continuation of business in all but the worst
case scenarios. All remediation and replacement efforts and contingency planning
are expected to be complete by November 1999. All critical external trading
partners have been contacted to determine Year 2000 readiness. Such responses
indicate they will be compliant by year-end.

     In 1997, the Managing Partner initiated a project to replace existing
business software as it relates to Apache's production, land, marketing,
accounting and financial systems to more effectively and efficiently meet its
business needs. Replacement computer systems selected by the Managing Partner
from SAP America, Inc., PricewaterhouseCoopers LLP, Innovative Business
Solutions and Landmark Graphics will properly recognize dates beyond December
31, 1999. The implementation of the business software project was completed and
operational effective with January 1999 production.

                                       7

<PAGE>   9


     The Managing Partner expects that its cost to achieve Year 2000 compliance
will not exceed $4 million, excluding the cost of implementing business
replacement systems. These costs will be borne by the Managing Partner and will
not have any impact on the financial results of the Partnership.

     The Managing Partner presently believes that with conversions to new
software and completion of efforts planned by the Year 2000 Task Force, the risk
associated with Year 2000 will be significantly reduced. However, the Managing
Partner is unable to assure that the consequences of Year 2000 failures of
systems maintained by Apache or by third parties will not materially adversely
impact the Partnership's results of operations, liquidity or financial
condition.

FORWARD-LOOKING STATEMENTS AND RISK

     Certain statements in this report, including statements of the future
plans, objectives, and expected performance of the Partnership, are
forward-looking statements that are dependent on certain events, risks and
uncertainties that may be outside the Partnership's control and which could
cause actual results to differ materially from those anticipated. Some of these
include, but are not limited to, economic and competitive conditions, inflation
rates, legislative and regulatory changes, financial market conditions,
political and economic uncertainties of foreign governments, future business
decisions, and other uncertainties, all of which are difficult to predict.

     There are numerous uncertainties inherent in estimating quantities of
proved oil and gas reserves and in projecting future rates of production and
timing of development expenditures. The total amount or timing of actual future
production may vary significantly from reserves and production estimates. The
drilling of exploratory wells can involve significant risks, including those
related to timing, success rates and cost overruns. Lease and rig availability,
complex geology and other factors can affect these risks. Future oil and gas
prices also could affect results of operations and cash flows.

                                       8

<PAGE>   10


                           PART II - OTHER INFORMATION


ITEM 1. LEGAL PROCEEDINGS

        None.

ITEM 2. CHANGES IN SECURITIES

        None.

ITEM 3. DEFAULTS UPON SENIOR SECURITIES

        None.

ITEM 4. SUBMISSION OF MATTERS TO A VOTE OF SECURITY HOLDERS

        None.

ITEM 5. OTHER INFORMATION

        None.

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K

        a.   Exhibits.

             27.1    Financial Data Schedule.

        b.   Reports on Form 8-K - None.

                                       9

<PAGE>   11


                                   SIGNATURES


Pursuant to the requirements of Section 13 or 15(d) 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.


                                      APACHE OFFSHORE INVESTMENT PARTNERSHIP
                                      By: Apache Corporation, General Partner



Dated: November 11, 1999              /s/ Roger B. Plank
                                      ------------------------------------------
                                      Roger B. Plank
                                      Vice President and Chief Financial Officer


Dated: November 11, 1999              /s/ Thomas L. Mitchell
                                      ------------------------------------------
                                      Thomas L. Mitchell
                                      Vice President and Controller
                                      (Chief Accounting Officer)



<PAGE>   12


                                  EXHIBIT INDEX




EXHIBIT NO.         DESCRIPTION
-----------         -----------

   27.1       -     Financial Data Schedule