<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, 1998

                                 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 0-10474

                      IEA MARINE CONTAINER INCOME FUND III,

                       (A CALIFORNIA LIMITED PARTNERSHIP)
             (Exact name of registrant as specified in its charter)

          California                              94-2717330
(State or other jurisdiction of                (I.R.S. Employer
incorporation or organization)                Identification No.)

         444 Market Street, 15th Floor, San Francisco, California 94111
            (Address of principal executive offices)     (Zip Code)
                                        
                                 (415) 677-8990
              (Registrant's telephone number, including area code)

Indicate by check mark whether the registrant (1) has filed all reports required
to be filed by Section 13 or 15(d) of the Securities Exchange Act of 1934 during
the preceding 12 months (or for such shorter period that the registrant was
required to file such reports), and (2) has been subject to such filing
requirements for the past 90 days. Yes [X] No [ ]

<PAGE>   2
                      IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                  REPORT ON FORM 10-Q FOR THE QUARTERLY PERIOD
                            ENDED SEPTEMBER 30, 1998

                                TABLE OF CONTENTS

<TABLE>
<CAPTION>
                                                                                           PAGE
                                                                                           ----
<S>                                                                                        <C>
PART I -- FINANCIAL INFORMATION

 Item 1. Financial Statements

         Balance Sheets - September 30, 1998 (unaudited) and December 31, 1997               4

         Statements of Operations for the three and nine months ended 
         September 30, 1998 and 1997 (unaudited)                                             5

         Statements of Cash Flows for the nine months ended September 30, 
         1998 and 1997 (unaudited)                                                           6

         Notes to Financial Statements (unaudited)                                           7

 Item 2. Management's Discussion and Analysis of Financial Condition and 
         Results of Operations                                                              10

 Item 3. Quantitative and Qualitative Disclosures About Market Risk                         11

PART II-- OTHER INFORMATION

 Item 1. Legal Proceedings                                                                  12

 Item 3. Defaults Upon Senior Securities                                                    13

 Item 5. Other Information                                                                  13

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


                                       2
<PAGE>   3

                                PART I - FINANCIAL INFORMATION

Item 1. Financial Statements

        Presented herein are the Registrant's balance sheets as of September 30,
        1998 and December 31, 1997, statements of operations for the three and
        nine months ended September 30, 1998 and 1997, and statements of cash
        flows for the nine months ended September 30, 1998 and 1997.


                                       3
<PAGE>   4
                      IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                                 BALANCE SHEETS

                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                                        September 30,     December 31,
                                                                            1998              1997
                                                                        -------------     ------------
<S>                                                                     <C>               <C>
                                          Assets

Current assets:

   Cash and cash equivalents, includes $795,668 at
     September 30, 1998 and $399,284 at December 31, 1997
       in interest-bearing accounts                                      $  795,768        $  399,411

   Net lease receivables due from Leasing Company
      (notes 1 and 2)                                                        22,056            80,812
                                                                         ----------        ----------
         Total current assets                                               817,824           480,223
                                                                         ----------        ----------

Container rental equipment, at cost                                              --         1,912,276
   Less accumulated depreciation                                                 --         1,318,038
                                                                         ----------        ----------
      Net container rental equipment                                             --           594,238
                                                                         ----------        ----------
                                                                         $  817,824        $1,074,461
                                                                         ==========        ==========
                 Liabilities and Partners' Capital

Current liabilities:

   Accounts payable and accrued expenses                                 $  125,016        $       --
                                                                         ----------        ----------
      Total current liabilities                                             125,016                --
                                                                         ----------        ----------
Partners' capital:

   General partners                                                           1,250             1,045
   Limited partners                                                         691,558         1,073,416
                                                                         ----------        ----------
         Total partners' capital                                            692,808         1,074,461
                                                                         ----------        ----------
                                                                         $  817,824        $1,074,461
                                                                         ==========        ==========
</TABLE>

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


                                       4
<PAGE>   5
                      IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                            STATEMENTS OF OPERATIONS

                                   (UNAUDITED)

<TABLE>
<CAPTION>
                                                      Three Months Ended                    Nine Months Ended
                                                --------------------------------     ------------------------------
                                                September 30,      September 30,     September 30,    September 30,
                                                    1998               1997              1998              1997
                                                -------------      -------------     -------------    -------------
<S>                                            <C>                 <C>               <C>              <C>
Net lease revenue (expense) (notes 1 and 3)      $  (14,233)        $   78,441        $   86,872        $  229,030

Other operating expenses:

   Other general and administrative expenses          9,779              9,607            41,064            31,029
                                                 ----------         ----------        ----------        ----------
       Earnings (loss) from operations              (24,012)            68,834            45,808           198,001

Other income:

   Interest income                                    3,544              4,825            11,656            17,460
   Net gain on disposal of equipment                102,215             27,757           129,067           100,075
                                                 ----------         ----------        ----------        ----------
                                                    105,759             32,582           140,723           117,535
                                                 ----------         ----------        ----------        ----------
       Net earnings                              $   81,747         $  101,416        $  186,531        $  315,536
                                                 ==========         ==========        ==========        ==========
Allocation of net earnings:

   General partners                              $    2,332         $    4,835        $    5,886        $   13,599
   Limited partners                                  79,415             96,581           180,645           301,937
                                                 ----------         ----------        ----------        ----------
                                                 $   81,747         $  101,416        $  186,531        $  315,536
                                                 ==========         ==========        ==========        ==========
Limited partners' per unit share of net earnings $     2.65         $     3.21        $     6.02        $    10.06
                                                 ==========         ==========        ==========        ==========
</TABLE>

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


                                       5
<PAGE>   6
                     IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                            STATEMENTS OF CASH FLOWS

                                  (UNAUDITED)

<TABLE>
<CAPTION>
                                                                   Nine Months Ended
                                                           ---------------------------------
                                                           September 30,       September 30,
                                                               1998                1997
                                                           -------------       -------------
<S>                                                        <C>                 <C>
Net cash provided by operating activities                   $    73,192         $   347,095

Cash flows provided by investing activities:

   Proceeds from disposal of equipment                          891,349             431,327

Cash flows used in financing activities:

   Distribution to partners                                    (568,184)         (1,028,314)
                                                            -----------         -----------
Net increase (decrease) in cash and cash equivalents            396,357            (249,892)

Cash and cash equivalents at January 1                          399,411             656,333
                                                            -----------         -----------
Cash and cash equivalents at September 30                   $   795,768         $   406,441
                                                            ===========         ===========
</TABLE>

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


                                       6
<PAGE>   7
                      IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                     NOTES TO UNAUDITED FINANCIAL STATEMENTS

(1)  Summary of Significant Accounting Policies

     (a) Nature of Operations

         IEA Marine Container Income Fund III, (A California Limited
         Partnership) (the "Partnership"), was organized under the laws of the
         State of California on January 3, 1980 for the purpose of owning and
         leasing marine dry cargo containers. The managing general partner is
         Cronos Capital Corp. ("CCC"); the associate general partner is Lehman
         Brothers, Inc. CCC, with its affiliate, Cronos Containers Limited (the
         "Leasing Company"), manages the business of the partnership.

         The Partnership commenced operations on April 3, 1981, when the minimum
         subscription proceeds of $500,000 were obtained. The Partnership
         offered 30,000 units of limited partnership interest at $500 per unit,
         or $15,000,000. The offering terminated on June 26, 1981, at which time
         30,000 limited partnership units had been purchased.

         Commencing in 1991, the Partnership's 11th year of operations, the
         Partnership began focusing its attention on the disposition of its
         fleet in accordance with one of its original investment objectives,
         realizing the residual value of its containers after the expiration of
         their economic useful lives, estimated to be between 10 to 15 years
         after placement in leased service. The Partnership, in its 18th year of
         operations, has focused its attention on disposing of its remaining
         fleet. As of September 30, 1998, the remaining equipment in the
         Partnership's fleet was sold.

     (b) Leasing Company and Leasing Agent Agreement

         Pursuant to the Limited Partnership Agreement of the Partnership, all
         authority to administer the business of the Partnership is vested in
         CCC. CCC has entered into a Leasing Agent Agreement whereby the Leasing
         Company has the responsibility to manage the leasing operations of all
         equipment owned by the Partnership. Pursuant to the Agreement, the
         Leasing Company is responsible for leasing, managing and re-leasing the
         Partnership's containers to ocean carriers and has full discretion over
         which ocean carriers and suppliers of goods and services it may deal
         with. The Leasing Agent Agreement permits the Leasing Company to use
         the containers owned by the Partnership, together with other containers
         owned or managed by the Leasing Company and its affiliates, as part of
         a single fleet operated without regard to ownership. Since the Leasing
         Agent Agreement meets the definition of an operating lease in Statement
         of Financial Accounting Standards (SFAS) No. 13, it is accounted for as
         a lease under which the Partnership is lessor and the Leasing Company
         is lessee.

         The Leasing Agent Agreement generally provides that the Leasing Company
         will make payments to the Partnership based upon rentals collected from
         ocean carriers after deducting direct operating expenses and management
         fees to CCC. The Leasing Company leases containers to ocean carriers,
         generally under operating leases which are either master leases or term
         leases (mostly two to five years). Master leases do not specify the
         exact number of containers to be leased or the term that each container
         will remain on hire but allow the ocean carrier to pick up and drop off
         containers at various locations; rentals are based upon the number of
         containers used and the applicable per-diem rate. Accordingly, rentals
         under master leases are all variable and contingent upon the number of
         containers used. Most containers are leased to ocean carriers under
         master leases; leasing agreements with fixed payment terms are not
         material to the financial statements. Since there are no material
         minimum lease rentals, no disclosure of minimum lease rentals is
         provided in these financial statements.


                                       7
<PAGE>   8
                      IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                     NOTES TO UNAUDITED FINANCIAL STATEMENTS

     (c) Basis of Accounting

         The Partnership utilizes the accrual method of accounting. Net lease
         revenue is recorded by the Partnership in each period based upon its
         leasing agent agreement with the Leasing Company. Net lease revenue is
         generally dependent upon operating lease rentals from operating lease
         agreements between the Leasing Company and its various lessees, less
         direct operating expenses and management fees due in respect of the
         containers specified in each operating lease agreement.

     (d) Financial Statement Presentation

         These financial statements have been prepared without audit. Certain
         information and footnote disclosures normally included in financial
         statements prepared in accordance with generally accepted accounting
         procedures have been omitted. It is suggested that these financial
         statements be read in conjunction with the financial statements and
         accompanying notes in the Partnership's latest annual report on Form
         10-K.

         The preparation of financial statements in conformity with generally
         accepted accounting principles (GAAP) requires the Partnership to make
         estimates and assumptions that affect the reported amounts of assets
         and liabilities and disclosure of contingent assets and liabilities at
         the date of the financial statements and the reported amounts of
         revenues and expenses during the reported period. Actual results could
         differ from those estimates.

         The interim financial statements presented herewith reflect all
         adjustments of a normal recurring nature which are, in the opinion of
         management, necessary to a fair statement of the financial condition
         and results of operations for the interim periods presented.

(2)  Net Lease Receivables Due from Leasing Company

     Net lease receivables due from the Leasing Company are determined by
     deducting direct operating payables and accrued expenses, base management
     fees and incentive fees payable to CCC and its affiliates from the rental
     billings payable by the Leasing Company to the Partnership under operating
     leases to ocean carriers for the containers owned by the Partnership. Net
     lease receivables at September 30, 1998 and December 31, 1997 were as
     follows:

<TABLE>
<CAPTION>
                                                             September 30,   December 31,
                                                                 1998            1997
                                                             -------------   ------------
         <S>                                                 <C>             <C>
         Lease receivables, net of doubtful accounts of
            $11,568 at September 30, 1998 and $21,489
            at December 31, 1997                               $ 22,056        $158,688

         Less:

         Direct operating payables and accrued expenses              --          38,347
         Damage protection reserve                                   --          39,529
                                                               --------        --------
                                                               $ 22,056        $ 80,812
                                                               ========        ========
</TABLE>


                                       8
<PAGE>   9
                      IEA MARINE CONTAINER INCOME FUND III,
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                     NOTES TO UNAUDITED FINANCIAL STATEMENTS

(3)  Net Lease Revenue

     Net lease revenue is determined by deducting direct operating expenses and
     base management fees to CCC from the rental revenue billed by the Leasing
     Company under operating leases to ocean carriers for the containers owned
     by the Partnership. Net lease revenue (expense) for the three and
     nine-month periods ended September 30, 1998 and 1997 was as follows:

<TABLE>
<CAPTION>
                                                       Three Months Ended               Nine Months Ended
                                                  -----------------------------    ----------------------------
                                                  September 30,   September 30,    September 30,  September 30,
                                                      1998             1997            1998            1997
                                                  -------------   -------------    -------------  -------------
<S>                                               <C>             <C>              <C>            <C>
         Rental revenue                             $     --         $111,104        $158,359        $383,640
         Less:
         Rental equipment operating expenses              --            9,780          23,825          76,363
         Base management fees                         14,233           22,883          47,662          78,247
                                                    --------         --------        --------        --------
                                                    $(14,233)        $ 78,441        $ 86,872        $229,030
                                                    ========         ========        ========        ========
</TABLE>


                                       9
<PAGE>   10

Item 2. Management's Discussion and Analysis of Financial Condition and Results
        of Operations

It is suggested that the following discussion be read in conjunction with the
Registrant's most recent annual report on Form 10-K.

1)   Material changes in financial condition between September 30, 1998 and
     December 31, 1997.

     As discussed in prior quarterly reports, the managing general partner has
     focused its efforts on liquidating the remaining equipment in the fleet and
     winding up the Registrant's operations. The Registrant disposed of the
     balance of its container equipment during the first nine months of 1998,
     totaling 783 containers, equaling approximately 10% of the Registrant's
     original fleet of containers. During the second calendar quarter of 1998,
     CCC, as the managing general partner of the Registrant, sought bids from
     independent buyers of used containers for the remaining fleet of containers
     owned by the Registrant. The Registrant accepted the highest bid and sold
     its remaining 616 containers to an unrelated third party during the third
     calendar quarter of 1998 for $575,315 in cash. The sales price represented
     approximately 127% of the net book value, at June 30, 1998, of the
     containers sold. At the time of sale, at the buyer's request, CCC agreed to
     manage the containers sold under an equipment lease agreement with a term
     expiring August 31, 2001, subject to annual one-year renewal terms, unless
     the buyer or CCC elects not to renew the terms of the agreement. The terms
     of the management agreement were independently negotiated between the buyer
     and CCC.

     With the sale of the Registrant's remaining containers during the third
     calendar quarter of 1998, the Registrant's container operations have
     ceased. The Registrant is currently in the final phase of the liquidation
     and wind-up stage of operations, focusing on the collection of its lease
     receivables, a component of net lease receivables. The Registrant
     anticipates that the remaining net lease receivables will be collected and
     the liabilities discharged during the fourth quarter of 1998, or as soon as
     practicable. By year end, the Registrant will then undertake a final
     distribution to its partners and proceed to cancel the Certificate of
     Limited Partnership, thus terminating the Partnership. The Partnership will
     then be dissolved. The remaining cash balance at September 30, 1998
     includes amounts reserved for expenses relating to the Registrant's final
     liquidation and subsequent dissolution.

2)   Material changes in the results of operations between the three and
     nine-month periods ended September 30, 1998 and the three and nine-month
     periods ended September 30, 1997.

     At the beginning of 1998, the Registrant had 782 containers remaining in
     the fleet. These containers were disposed of during 1998. Accordingly, the
     Registrant's container operations ceased during the third quarter of 1998.
     Approximately 125% and 69%, respectively, of the Registrant's net earnings
     for the three and nine-month periods ended September 30, 1998, were from
     gain on disposal of equipment, as compared to 27% and 32%, respectively,
     for the same three and nine-month periods in the prior year. In the future,
     rental equipment operating expenses, a component of net lease revenue, will
     consist of costs associated with the recovery of the doubtful accounts of
     certain lessees, including legal expenses and the provision for doubtful
     accounts. General and administrative expenses included investor processing,
     tax, legal, and audit expenses.

     Year 2000

     The Registrant relies upon the financial and operational systems provided
     by the Leasing company and its affiliates, as well as the systems provided
     by other independent third parties to service the three primary areas of
     its business: investor processing/maintenance; container leasing/asset
     tracking; and accounting finance. The Registrant has received confirmation
     from its third-party investor processing/maintenance vendor that their
     system is Year 2000 compliant. The Registrant does not expect a material
     increase in its vendor servicing fee to reimburse Year 2000 costs.
     Container leasing/asset tracking and accounting/finance services are
     provided to the Registrant by CCC and its affiliate, Cronos Containers
     Limited (the "Leasing Company"), pursuant to the respective Limited
     Partnership Agreement and Leasing Agent Agreement. CCC and the Leasing
     Company have initiated a program to prepare their 


                                       10
<PAGE>   11

     systems and applications for the Year 2000. Preliminary studies indicate
     that testing, conversion and upgrading of system applications is expected
     to cost CCC and the Leasing Company less than $500,000. Pursuant to the
     Limited Partnership Agreement, CCC or the Leasing Company, may not seek
     reimbursement of data processing costs associated with the Year 2000
     program. The financial impact of making these required system changes is
     not expected to be material to the Registrant's financial position, results
     of operations or cash flows.

     Cautionary Statement

     This Quarterly Report on Form 10-Q contains statements relating to future
     results of the Registrant, including certain projections and business
     trends, that are "forward-looking statements" as defined in the Private
     Securities Litigation Reform Act of 1995. Actual results may differ
     materially from those projected as a result of certain risks and
     uncertainties, including but not limited to changes in: economic
     conditions; trade policies; demand for and market acceptance of leased
     marine cargo containers; competitive utilization and per-diem rental rate
     pressures; as well as other risks and uncertainties, including but not
     limited to those described in the above discussion of the marine container
     leasing business under Item 2., Management's Discussion and Analysis of
     Financial Condition and Results of Operations; and those detailed from time
     to time in the filings of Registrant with the Securities and Exchange
     Commission.

Item 3. Quantitative and Qualitative Disclosures About Market Risk

Not applicable.


                                       11
<PAGE>   12
                           PART II - OTHER INFORMATION

Item 1. Legal Proceedings

        As reported in the Registrant's Current Report on Form 8-K and Amendment
        No. 1 to Current Report on Form 8-K, filed with the Commission on
        February 7, 1997 and February 26, 1997, respectively, Arthur Andersen,
        London, England, resigned as auditors of the Cronos Group, a Luxembourg
        corporation headquartered in Orchard Lea, England (the "Parent
        Company"), on February 3, 1997.

        The Registrant retained a new auditor, Moore Stephens, P.C. on April 10,
        1997, as reported in its Current Report on Form 8-K, filed April 14,
        1997.

        In connection with its resignation, Arthur Andersen also prepared a
        report pursuant to Section 10A(b)(2) of the Securities Exchange Act of
        1934 as amended, for filing by the Parent Company with the Securities
        and Exchange Commission ("SEC") citing its inability to obtain what it
        considered to be adequate responses to its inquiries primarily regarding
        the payment of $1.5 million purportedly in respect of professional fees
        relating to a proposed strategic alliance. This sum was returned to the
        Parent Company in January 1997.

        Following the report of Arthur Andersen, the SEC, on February 10, 1997,
        commenced a private investigation of the Parent Company for the purpose
        of investigating the matters discussed in such report and related
        matters. The SEC's investigation can result in several types of civil or
        administrative sanctions against the Parent Company and individuals
        associated with the Parent Company, including the assessment of monetary
        penalties. Actions taken by the SEC do not preclude additional actions
        by any other federal, civil or criminal authorities or by other
        regulatory organizations or by third parties.

        The SEC's investigation is continuing, and some of the Parent Company's
        present and former officers and directors and others associated with the
        Parent Company have given testimony. However, no conclusion of any
        alleged wrongdoing by the Parent Company or any individual has been
        communicated to the Parent Company by the SEC.

        The Registrant does not believe that the focus of the SEC's
        investigation is upon the Registrant or CCC. CCC is unable to predict
        the outcome of the SEC's ongoing private investigation of the Parent
        Company.

        As reported in the Registrant's Current Report on Form 8-K, filed with
        the SEC on May 21, 1998, the Parent Company reported that its Chairman
        and CEO, Stefan M. Palatin, was suspended from his duties pending the
        investigation of fraud charges against him by Austrian government
        authorities. On June 8, 1998, the Parent Company's Board of Directors
        removed Mr. Palatin as Managing Director and Chief Executive Officer.
        Mr. Palatin resigned from the Board of Directors of the Parent Company
        on July 6, 1998. Mr. Rudolf J. Weissenberger has been appointed to
        replace Mr. Palatin as an executive director and Chief Executive
        Officer. Also, on June 8, 1998, the Board approved a proposal to add two
        independent directors to the Board. The Board engaged legal counsel to
        provide legal advice and commence legal action, if appropriate, against
        former officers or directors of the Parent Company (including Mr.
        Palatin) if it is determined that they engaged in any misfeasance or
        improper self-dealing.

        Mr. Palatin had been a director of CCC; he resigned from his position as
        director on April 23, 1998.

        CCC further understands that Austrian authorities have initiated
        investigations of persons in addition to Mr. Palatin, including Mr.
        Weissenberger and Dr. Axel Friedberg. The investigations which remain
        pending have not resulted in any action being taken against Mr.
        Weissenberger, and he has informed the Parent Company that he


                                       12
<PAGE>   13

        does not believe that there is any basis for any action to be taken
        against him. Dr. Friedberg has been a non- executive director of the
        Parent Company since 1997. In August 1998, charges were presented
        against Dr. Friedberg. Dr. Friedberg has denied any wrongdoing and, on
        September 14, 1998, filed objections to the charges against him.

Item 3. Defaults Upon Senior Securities

        See Item 5. Other Information.

Item 5. Other Information

        In 1993, the Parent Company negotiated a credit facility (hereinafter,
        the "Credit Facility") with several banks for the use of the Parent
        Company and its affiliates, including CCC. At December 31, 1996,
        approximately $73,500,000 in principal indebtedness was outstanding
        under the Credit Facility. As a party to the Credit Facility, CCC is
        jointly and severally liable for the repayment of all principal and
        interest owed under the Credit Facility. The obligations of CCC, and the
        five other subsidiaries of the Parent Company that are borrowers under
        the Credit Facility, are guaranteed by the Parent Company.

        Following negotiations in 1997 with the banks providing the Credit
        Facility, an Amended and Restated Credit Agreement was executed in June
        1997, subject to various actions being taken by the Parent Company and
        its subsidiaries, primarily relating to the provision of additional
        collateral. This Agreement was further amended in July 1997 and the
        provisions of the Agreement and its Amendment converted the facility to
        a term loan, payable in installments, with a final maturity date of May
        31, 1998. The terms of the Agreement and its Amendment also provided for
        additional security over shares in the subsidiary of the Parent Company
        that owns the head office of the Parent Company's container leasing
        operations. They also provided for the loans to the former Chairman of
        $5,900,000 and $3,700,000 to be restructured as obligations of the
        former Chairman to another subsidiary of the Parent Company (not CCC),
        together with the pledge to this subsidiary company of 2,030,303 Common
        Shares beneficially owned by him in the Parent Company as security for
        these loans. They further provided for the assignment of these loans to
        the lending banks, together with the pledge of 1,000,000 shares and the
        assignment of the rights of the Parent Company in respect of the other
        1,030,303 shares. Additionally, CCC granted the lending banks a security
        interest in the fees to which it is entitled for the services it renders
        to the container leasing partnerships of which it acts as general
        partner, including its fee income payable by the Registrant. The Parent
        Company did not repay the Credit Facility at the amended maturity date
        of May 31, 1998.

        On June 30, 1998, the Parent Company entered into a third amendment (the
        "Third Amendment") to the Credit Facility. The Third Amendment became
        effective as of that date, subject to the satisfaction thereafter of
        various conditions, including: the Parent Company must deliver its
        audited financial statements for 1997 by a specified date and; on or
        prior to July 30, 1998, the Parent Company must furnish proof that any
        defaults under any other indebtedness have been waived and must also
        furnish various legal opinions, officers' certificates and other loan
        documentation. All of these conditions were fulfilled by August 14,
        1998. Under the Third Amendment, the remaining principal amount of
        $36,800,000 will be amortized in varying monthly amounts commencing on
        July 31, 1998 with $26,950,000 due on September 30, 1998 and a final
        maturity date of January 8, 1999. The Parent Company did not repay the
        amount due on September 30, 1998. The directors of the Parent Company
        currently are holding discussions with the lenders to refinance or
        extend its debt that became due on September 30, 1998.

        The directors of the Parent Company also are pursuing alternative
        sources of financing to meet the amended repayment obligations under the
        Third Amendment. Failure to meet revised lending terms would constitute
        an event of default with the lenders. The declaration of an event of
        default would result in further defaults with other lenders under loan
        agreement cross-default provisions. Should a default of the term loans
        be enforced, the Parent Company and CCC may be unable to continue as
        going concerns.


                                       13
<PAGE>   14

        CCC is currently in discussions with the management of the Parent
        Company to provide assurance that the management of the container
        leasing partnerships managed by CCC, including the Registrant, is not
        disrupted pending a refinancing or reorganization of the indebtedness of
        the Parent Company and its affiliates.

        The Registrant is not a borrower under the Credit Facility, and neither
        the containers nor the other assets of the Registrant have been pledged
        as collateral under the Credit Facility.

        CCC is unable to determine the impact, if any, these concerns may have
        on the future operating results and financial condition of the
        Registrant or CCC and the Leasing Company's ability to manage the
        Registrant's fleet in subsequent periods.


                                       14
<PAGE>   15

Item 6.  Exhibits and Reports on Form 8-K

(a)  Exhibits

<TABLE>
<CAPTION>
            Exhibit
              No.                       Description                             Method of Filing
            -------    ---------------------------------------------------      ----------------
            <S>        <C>                                                      <C>
             3(a)      Limited Partnership  Agreement of the Registrant,
                       amended and restated as of February 11, 1981             *

             3(b)      Certificate of Limited Partnership of the Registrant     **

             27        Financial Data Schedule                                  Filed with this
                                                                                document
</TABLE>

(b)     Reports on Form 8-K

        No reports on Form 8-K were filed by the Registrant during the quarter
        ended September 30, 1998.

-----------

*     Incorporated by reference to Exhibit "A" to the Prospectus of the
      Registrant dated February 12, 1981, included as part of Registration
      Statement on Form S-1 (No. 2-70401)

**    Incorporated by reference to Exhibit 3.4 to the Registration Statement on
      Form S-1 (No. 2-70401)


                                       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.

                                       IEA MARINE CONTAINER INCOME FUND III
                                       (A California Limited Partnership)

                                       By   Cronos Capital Corp.
                                            The Managing General Partner

                                       By   /s/ Dennis J. Tietz
                                            ------------------------------------
                                            Dennis J. Tietz
                                            President and Director of 
                                            Cronos Capital Corp. ("CCC")
                                            Principal Executive Officer of CCC

Date: November 13, 1998


                                       16
<PAGE>   17

                                        EXHIBIT INDEX

<TABLE>
<CAPTION>
Exhibit
  No.                       Description                             Method of Filing
-------    ---------------------------------------------------      ----------------
<S>        <C>                                                      <C>
 3(a)      Limited Partnership  Agreement of the Registrant,
           amended and restated as of February 11, 1981             *

 3(b)      Certificate of Limited Partnership of the Registrant     **

 27        Financial Data Schedule                                  Filed with this
                                                                    document
</TABLE>

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

*     Incorporated by reference to Exhibit "A" to the Prospectus of the
      Registrant dated February 12, 1981, included as part of Registration
      Statement on Form S-1 (No. 2-70401)

**    Incorporated by reference to Exhibit 3.4 to the Registration Statement on
      Form S-1 (No. 2-70401)