<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 MARCH 31, 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 MARCH 31, 1998

                                TABLE OF CONTENTS



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

  Item 1. Financial Statements

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

          Statements of Operations for the three months ended 
            March 31, 1998 and 1997 (unaudited)                                 5

          Statements of Cash Flows for the three months ended March 31, 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


PART II - OTHER INFORMATION

  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 March 31,
          1998 and December 31, 1997, statements of operations for the three
          months ended March 31, 1998 and 1997, and statements of cash flows for
          the three months ended March 31, 1998 and 1997.




                                       3
<PAGE>   4

                      IEA MARINE CONTAINER INCOME FUND III
                       (A CALIFORNIA LIMITED PARTNERSHIP)

                                 BALANCE SHEETS

                                   (UNAUDITED)


<TABLE>
<CAPTION>
                                                                             March 31,     December 31,
                                                                               1998            1997
                                                                            ----------      ----------
<S>                                                                         <C>             <C>       
                    Assets
Current assets:
    Cash and cash equivalents, includes $312,876 at March 31, 1998 and
       $399,284 at December 31, 1997 in interest-bearing accounts           $  323,499      $  399,411
    Net lease receivables due from Leasing Company
       (notes 1 and 2)                                                          65,249          80,812
                                                                            ----------      ----------

           Total current assets                                                388,748         480,223
                                                                            ----------      ----------

Container rental equipment, at cost                                          1,668,292       1,912,276
    Less accumulated depreciation                                            1,147,249       1,318,038
                                                                            ----------      ----------
       Net container rental equipment                                          521,043         594,238
                                                                            ----------      ----------

                                                                            $  909,791      $1,074,461
                                                                            ==========      ==========

               Partners' Capital

Partners' capital:
    General partners                                                        $      124      $    1,045
    Limited partners                                                           909,667       1,073,416
                                                                            ----------      ----------

           Total partners' capital                                             909,791       1,074,461
                                                                            ----------      ----------

                                                                            $  909,791      $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
                                                      -----------------------
                                                      March 31,     March 31,
                                                        1998          1997
                                                      --------      --------
<S>                                                   <C>           <C>     
Net lease revenue (notes 1 and 3)                     $ 48,589      $107,741

Other operating expenses:
   Other general and administrative expenses            12,925        10,092
                                                      --------      --------

     Earnings from operations                           35,664        97,649

Other income:
   Interest income                                       4,397         7,100
   Net gain on disposal of equipment                    13,073        39,917
                                                      --------      --------
                                                        17,470        47,017
                                                      --------      --------

     Net earnings                                     $ 53,134      $144,666
                                                      ========      ========

Allocation of net earnings:
   General partners                                   $  1,257      $  3,199
   Limited partners                                     51,877       141,467
                                                      --------      --------

                                                      $ 53,134      $144,666
                                                      ========      ========

Limited partners' per unit share of net earnings      $   1.73      $   4.72
                                                      ========      ========
</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>
                                                            Three Months Ended
                                                         -------------------------
                                                         March 31,       March 31,
                                                           1998            1997
                                                         ---------       ---------
<S>                                                      <C>             <C>      
Net cash provided by (used in) operating activities      $ (16,881)      $ 124,965

Cash flows provided by investing activities:
   Proceeds from disposal of equipment                     158,773         182,572

Cash flows used in financing activities:
   Distribution to partners                               (217,804)       (455,924)
                                                         ---------       ---------


Net decrease in cash and cash equivalents                  (75,912)       (148,387)


Cash and cash equivalents at January 1                     399,411         656,333
                                                         ---------       ---------


Cash and cash equivalents at March 31                    $ 323,499       $ 507,946
                                                         =========       =========
</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.

          As of March 31, 1998, 8% of the original equipment remained in the
          Partnership's fleet and was comprised of 599 twenty-foot and 83
          forty-foot marine dry cargo containers. 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
          another 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. During this phase, the Partnership has actively
          disposed of containers within its fleet, while cash proceeds from
          equipment disposals, in addition to cash from operations, provided the
          cash flow for distributions to the limited partners. The Partnership,
          in its 18th year of operations, will continue to focus its attention
          during the remainder of 1998 on disposing of its remaining fleet.

      (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.




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

                     NOTES TO UNAUDITED FINANCIAL STATEMENTS


      (b) Leasing Company and Leasing Agent Agreement - (Continued)

          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.

      (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.




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

                     NOTES TO UNAUDITED FINANCIAL STATEMENTS


(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 March 31, 1998 and December 31, 1997 were as follows:


<TABLE>
<CAPTION>
                                                                     March 31,    December 31,
                                                                       1998          1997
                                                                     --------     ------------
<S>                                                                  <C>           <C>     
         Lease receivables, net of doubtful accounts of $31,852
           at March 31, 1998 and $21,489 at December 31, 1997        $149,166      $158,688
         Less:
         Direct operating payables and accrued expenses                48,671        38,347
         Damage protection reserve                                     35,246        39,529
                                                                     --------      --------

                                                                     $ 65,249      $ 80,812
                                                                     ========      ========
</TABLE>


(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 for the three-month periods ended
      March 31, 1998 and 1997 was as follows:


<TABLE>
<CAPTION>
                                                    Three Months Ended
                                                  -----------------------
                                                  March 31,     March 31,
                                                    1998          1997
                                                  --------      --------
<S>                                               <C>           <C>     
         Rental revenue                           $ 83,594      $146,144
         Less:
         Rental equipment operating expenses        17,783         9,175
         Base management fees                       17,222        29,228
                                                  --------      --------

                                                  $ 48,589      $107,741
                                                  ========      ========
</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 March 31, 1998 and
      December 31, 1997.

      December 31, 1997 marked the completion of the Registrant's 17th year of
      operations. At March 31, 1998, the Registrant operated only 8% of its
      original container fleet. Due to the declining cash flows from operations
      and sales proceeds from a rapidly diminishing fleet, the managing general
      partner has determined that it is in the best interest of the limited
      partners to dissolve the Partnership before such time that fixed operating
      costs exceed operating revenues. It is, therefore, the intent of the
      managing general partner to liquidate the remaining equipment in the fleet
      and wind up the Registrant's operations during the second quarter of 1998.
      The managing general partner is in active negotiations with qualified
      buyers who are interested in purchasing the remaining containers in the
      Registrant's fleet, and expects to agree on the terms of the purchase
      agreement near the end of the second quarter of 1998. When all of the
      equipment has been disposed and the Registrant's debt receivables and
      liabilities have been collected and discharged, the Partnership will then
      be dissolved. The managing general partner will then undertake a final
      distribution of the Registrant's assets to the limited partners and
      proceed to cancel the Certificate of Limited Partnership, thus terminating
      the Partnership.

      As discussed in the Registrant's report for the year ended December 31,
      1997, the Registrant entered 1998 with a view towards disposing its
      remaining container fleet. During the first three months of 1998, the
      Registrant disposed of 100 containers as part of its ongoing container
      operations, contributing to a decline in the Registrant's operating
      results and related cash balances. At March 31, 1998, 8% of the original
      equipment remained in the Registrant's fleet, as compared to 10% at
      December 31, 1997, and was comprised of the following:


<TABLE>
<CAPTION>
                                        20-Foot  40-Foot
                                        -------  -------
<S>                                       <C>       <C>
         Containers on lease:
               Term leases                 39        9
               Master leases              507       59
                                          ---      ---
                   Subtotal               546       68

         Containers off lease              53       15
                                          ---      ---

               Total container fleet      599       83
                                          ===      ===
</TABLE>


<TABLE>
<CAPTION>
                                                     20-Foot               40-Foot
                                                ----------------       -----------------
                                                Units        %         Units        %
                                                -----      -----       -----      ------
<S>                                             <C>          <C>         <C>        <C> 
         Total purchases                        7,257        100%        890        100%
              Less disposals                    6,658         92%        807         91%
                                                -----      -----       -----      -----

         Remaining fleet at March 31, 1998        599          8%         83          9%
                                                =====      =====       =====      =====
</TABLE>




                                       10
<PAGE>   11
      The Registrant's diminishing fleet size and its related operating
      performance contributed to a 19% decline in net lease receivables at March
      31, 1998, when compared to December 31, 1997. During the first quarter of
      1998, distributions from operations and sales proceeds amounted to
      $217,804, reflecting distributions to the general and limited partners for
      the fourth quarter of 1997. This represents an increase from the $208,334
      distributed during the fourth quarter of 1997, reflecting distributions
      for the third quarter of 1997. The increase in distributions is
      attributable to an increase in sales proceeds distributed to its partners.
      The Registrant's efforts to dispose of the remaining fleet should produce
      lower operating results and, consequently, reduce distributions to its
      partners in subsequent quarters. Additionally, the Registrant may refrain
      from distributing cash generated from operations and sales proceeds to its
      partners, reserving all excess cash as part of its working capital in
      order to maintain sufficient cash reserves for expenses relating to its
      final liquidation and subsequent dissolution.

      Market conditions that existed during 1997 persisted through the first
      quarter of 1998. Low container prices, favorable interest rates and the
      abundance of available capital continued to discourage ocean carriers and
      other transport companies from leasing containers at levels comparable to
      previous years. By the end of 1997, the volatility of the Hong Kong and
      other Asian financial markets began to negatively impact trade, shipping
      and container leasing. As a result, the Registrant's container utilization
      rate declined from 91% at December 31, 1997 to 89% at March 31, 1998.
      Per-diem rental rates continued to remain under pressure as a result of
      the following factors: start-up leasing companies offering new containers
      and low rental rates in an effort to break into the leasing market;
      established leasing companies reducing rates to very low levels; and a
      continuing oversupply of containers. These leasing market conditions
      impacted the Registrant's financial condition and operating performance
      during the first quarter of 1998.

2)    Material changes in the results of operations between the three-month
      period ended March 31, 1998 and the three-month period ended March 31,
      1997.

      Net lease revenue for the three-month period ended March 31, 1998 was
      $48,589, a decline of 55% from the same three-month period in the prior
      year. Approximately 25% of the Registrant's net earnings for the
      three-month period ended March 31, 1998 were from gain on disposal of
      equipment, as compared to 28% for the same three-month period in the prior
      year. As the Registrant continues to dispose of its containers in
      subsequent periods, net gain on disposal may fluctuate and should
      contribute significantly to the Registrant's net earnings.

      Gross rental revenue (a component of net lease revenue) for the
      three-month period ended March 31, 1998 was $83,594, reflecting a decline
      of 43% from the same three-month period in 1997. Gross rental revenue was
      impacted by the Registrant's diminishing fleet size and a decline in
      per-diem rental rates. Average per-diem rental rates decreased
      approximately 9%, when compared to the same three-month period in the
      prior year. Average utilization rates remained constant when compared to
      the same three-month period in the prior year. The Registrant's average
      fleet size and utilization rates for the three-month periods ended March
      31, 1998 and March 31, 1997 were as follows:


<TABLE>
<CAPTION>
                                                                     Three Months Ended
                                                                     -------------------
                                                                     March 31,  March 31,
                                                                      1998        1997
                                                                     ------      ------
<S>                                                                    <C>       <C>  
         Average fleet size (measured in twenty-foot equivalent
             units (TEU))                                              817       1,325
         Average Utilization                                            90%         90%
</TABLE>



                                       11
<PAGE>   12
      Rental equipment operating expenses were 21% of the Registrant's gross
      lease revenue during the three-month period ended March 31, 1998, as
      compared to 6% during the three-month period ended March 31, 1997.
      Contributing to these increases was a charge of approximately $11,000 to
      further provide for and replenish the reserve for doubtful accounts. The
      Registrant's decision to dispose of its off-hire containers also
      contributed to lower rental equipment operating expenses, as well as lower
      base management fees.

      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 Parent Company is the indirect corporate parent of CCC, the General
      Partner of the Registrant. In its letter of resignation to the Parent
      Company, Arthur Andersen stated that it resigned as auditors of the Parent
      Company and all other entities affiliated with the Parent Company. While
      its letter of resignation was not addressed to CCC, Arthur Andersen
      confirmed to CCC that its resignation as auditors of the entities referred
      to in its letter of resignation included its resignation as auditors of
      CCC and the Registrant.

      CCC does not believe, based upon the information currently available to
      it, that Arthur Andersen's resignation was triggered by any concern over
      the accounting policies and procedures followed by the Registrant.

      Arthur Andersen's report on the financial statements of CCC and the
      Registrant, for years preceding 1996, has not contained an adverse opinion
      or a disclaimer of opinion, nor was any such report qualified or modified
      as to uncertainty, audit scope, or accounting principles.

      During the Registrant's 1995 fiscal year and the subsequent interim period
      preceding Arthur Andersen's resignation, there were no disagreements
      between CCC or the Registrant and Arthur Andersen on any matter of
      accounting principles or practices, financial statement disclosure, or
      auditing scope or procedure.

      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 the provisions of 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 (the "SEC"). 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 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.

      In 1993, the Parent Company negotiated a credit facility (herinafter, 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. At December 31, 1997, approximately $37,600,000 was outstanding
      under the Credit Facility.



                                       12
<PAGE>   13
      The terms of the Agreement and its Amendment also provide 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 Stefan M. Palatin, the Chairman of the
      Parent Company (the "Chairman") and its Chief Executive Officer (and a
      Director of CCC), of approximately $5,990,000 and $3,700,000 (totaling
      approximately $9,690,000) to be restructured as obligations of the
      Chairman to another subsidiary of the Parent Company. These obligations
      have been collaterally assigned to the lending banks, together with the
      pledge of 1,000,000 shares of the Parent Company's Common Stock owned by
      the Chairman. These 1,000,000 shares represent 11% of the issued and
      outstanding shares of Common Stock of the Parent Company as of December
      31, 1997. The shares of the Parent Company are traded on NASDAQ (CRNSF).
      (The Chairman, including the 1,000,000 shares pledged to the banks, owns
      approximately 55% of the issued and outstanding shares of Common Stock of
      the Parent Company as of December 31, 1997). 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 lending banks have indicated that they will not renew the Credit
      Facility, and the Parent Company has yet to secure a source for repayment
      of the balance due under the Credit Facility at May 31, 1998. 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.

      The Registrant 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.

      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 it 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 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.



                                       13
<PAGE>   14
      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.



                                       14
<PAGE>   15
                           PART II - OTHER INFORMATION


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 March 31, 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: May 15, 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)