**UNITED
      STATES**


**SECURITIES
      AND EXCHANGE COMMISSION**


**Washington,
      D.C. 20549**





**FORM
      10-K**




**x**
            **ANNUAL
                REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES EXCHANGE
                ACT OF
                1934**





**For
      the fiscal year ended** **December
      31, 2005**





**Commission
      File No.** **333-123328**





**CATERPILLAR
      FINANCIAL ASSET TRUST 2005-A**


**(** **Issuer
      of Securities)**





**CATERPILLAR
      FINANCIAL FUNDING CORPORATION**


**(Exact
      name of Registrant as specified in its charter)**





**Nevada**
            **88-0342613****(State
                of incorporation)**
            **(IRS
                Employer Identification
                Number)**





**Greenview
                Plaza**
              **4040
                South Eastern Ave. Suite 344**
              **Las
                Vegas, Nevada**
            **89119****(Address
                of principal executive offices)**
            **(Zip
                Code)**





**Registrant's
      telephone number, including area code:** **(702) 735-2514**







**Securities
      registered pursuant to Section 12(b) of the Act: None**





**Securities
      registered pursuant to Section 12(g) of the Act: None**







**Indicate
      by a check mark if the Registrant is a well-known seasoned issuer, as defined
      in
      Rule 405 of the Securities Act.**


**Yes** **o** **No** **x**





**Indicate
      by a check mark if the Registrant is not required to file reports pursuant
      to
      Section 13 or 15(d) of the Act.**


**Yes** **o** **No** **x**





**Indicate
      by a 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** o





**Indicate
      by a check mark if disclosure of delinquent filers pursuant to Item 405 of
      Regulation S-K is not contained herein, and will not be contained, to the best
      of Registrant’s knowledge, in definitive proxy or information statements
      incorporated by reference in Part III of this Form 10-K or any amendment to
      this
      Form 10-K.** **x** ****





**Indicate
      by check mark whether the Registrant is a large accelerated filer, an
      accelerated filer, or a non-accelerated file (as defined in Rule 12b-2 of the
      Act).**


**Large
      accelerated Filer** o **Accelerated Filer** **o** **Non-accelerated Filer** **x**





**Indicate
      by a check mark whether the Registrant is a shell company (as defined in Rule
      12b-2 of the Act).**


**Yes** **o** **No** **x**





**State
      the aggregate market value of the voting and non-voting common equity held
      by
      non-affiliates computed by reference to the price at which the common equity
      was
      last sold, or the average bid and asked price of such common equity, as of
      the
      last business day of the registrant’s most recently completely second fiscal
      quarter.   Not applicable**




At
      March
      28, 2006, one hundred shares of the common stock of the Registrant were
      outstanding, all of which are owned by Caterpillar Financial Services
      Corporation. The issuer does not have any voting stock.





**PART
      I.**





**Item
      1. Business**


This
      Annual Report on Form 10-K is filed with respect to Caterpillar Financial Asset
      Trust 2005-A (the “Trust”), a Delaware statutory trust formed pursuant to a
      Trust Agreement, dated as of April 8, 2005 between Caterpillar Financial Funding
      Corporation (the "Seller"), and Chase Bank U.S.A., N.A., as owner trustee.
      The
      Trust issued $843,140,000 in aggregate principal amount of asset-backed notes,
      Classes A-1, A-2, A-3, A-4 and B (the “Notes”) pursuant to an Indenture dated as
      of April 1, 2005 (the “Indenture”), between the Trust and U.S. Bank National
      Association , as indenture trustee. The Trust also issued $10,677,293 in
      aggregate principal amount of certificates, which were not offered to the
      public.





**Item
      1A. Risk Factors**


Not
      Applicable





**Item
      1B. Unresolved Staff Comments**


None





**Item
      2. Properties**


On
      April
      28, 2005, the Trust issued:





·
            Asset
                Backed Certificates (the “Certificates”):


$
      10,677,293 aggregate principal amount


·
            Asset
                Backed Notes (the “Notes”):


$
      214,300,000 aggregate principal amount of Class A-1 3.2056%


$
      219,000,000 aggregate principal amount of Class A-2 3.66%


$
      244,000,000 aggregate principal amount of Class A-3 3.90%


$
      142,360,000 aggregate principal amount of Class A-4 4.10%


$  
      23,480,000 aggregate principal amount of Class B 4.27%





The
      Certificates evidence fractional undivided interests in the Trust. The Seller
      retained the entire principal amount of the Certificates. The Notes evidence
      debt obligations of the Trust.





The
      property of the Trust includes (i) installment sale contracts and finance leases
      (collectively, “receivables”) that are transferred to that Trust, (ii) all
      monies (including accrued interest) due or received under the receivables on
      or
      after the applicable cut-off date, (iii) amounts as from time to time may be
      held in one or more accounts established and maintained by the servicer pursuant
      to the related sale and servicing agreement, (iv) security interests in the
      financed equipment and in certain other cross-collateralized equipment, (v)
      the
      rights to proceeds from claims on physical damage, credit life, liability and
      disability insurance policies, if any, covering the financed equipment or
      obligors, as the case may be, (vi) the proceeds of any repossessed financed
      equipment, (vii) the rights of the Seller under the Purchase Agreement dated
      April 1, 2005 (the “Purchase Agreement”) between the Servicer and the Seller
      and, (viii) the interest of the seller in any proceeds from recourse to
      Caterpillar dealers with respect to receivables, (ix) the interest earned on
      short-term investments made by the trust, and (x) any proceeds of the
      foregoing.





As
      of
      December 31, 2005, the end of the fiscal year of the Trust for which this Form
      10-K annual report is being filed, the aggregate principal balance of the
      receivables remaining in the Trust was approximately $626,771,525.





For
      additional information regarding principal and interest payments in respect
      to
      the Certificates and the Notes and information regarding servicing compensation
      and other fees paid by the Trust during the year ending December 31, 2005,
      refer
      to Exhibits 99.1 - 99.4.





**Item
      3. Legal Proceedings**


The
      Registrant knows of no material pending legal proceedings involving the
      Trust.





**Item
      4. Submission of Matters to a Vote of Security Holders**


There
      were no matters submitted to a vote of the Security Holders in the reporting
      year.





**PART
      II.**





**Item
      5. Market For Registrant’s Common Equity, Related Stockholder Matters, and
      Issuer Purchases of**


**Equity
      Securities**


(a)
            To
                the best knowledge of the Registrant, there is no established public
                market for the Certificates.





(b)
            As
                of December 31, 2005, the Seller was the sole Certificateholder of
                record.





**Item
      6. Selected Financial Data**


**** Not
      Applicable





**Item
      7. Management’s Discussion and Analysis of Financial Condition and Results of
      Operations**


Not Applicable





**Item
      7A. Quantitative and Qualitative Disclosures About Market
      Risk**


Not Applicable





**Item
      8. Financial Statements and Supplementary Data**


Not Applicable





**Item
      9. Changes in and Disagreements with Accountants on Accounting and Financial
      Disclosure**


Not Applicable





**Item
      9A. Controls and Procedures**


Not Applicable





**Item
      9B. Other Information**


None





**PART
      III.**





**Item
      10. Directors and Executive Officers of the Registrant**





Not
      Applicable





**Item
      11. Executive Compensation**





Not
      Applicable





**Item
      12. Security Ownership of Certain Beneficial Owners and Management and Related
      Stockholders**


**Matters**





Caterpillar
      Financial Funding Corporation owns 100% of the certificates issued by the
      Trust





**Item
      13. Certain Relationships and Related Transactions**





Caterpillar
      Financial Funding Corporation, the Seller, Depositor and sole Certificateholder
      of record, is a wholly owned subsidiary of Caterpillar Financial Services
      Corporation, the Servicer and Administrator for the Trust. The aggregate
      servicing fees and administration fees paid by the Trust to Caterpillar
      Financial Services Corporation during the fiscal year are set forth in Exhibit
      99.3.





In
      addition, in 2005, Caterpillar Financial Services Corporation performed
      administrative services on behalf of Caterpillar Financial Funding Corporation
      pursuant to a services agreement. The total compensation paid under such
      agreement for 2005 was $121,200.








**Item
      14. Principal Accounting Fees and Services**





Not
      Applicable





**PART
      IV.**





**Item
      15. Exhibits and Financial Statement Schedules**





(a)  The
      following documents are filed as part of this report:


Exhibit
      No.


31
            Certification of Steven R.
                Elsesser,
                Controller of Caterpillar Financial Services Corporation, as required
              pursuant
                to Section 302 of the Sarbanes-Oxley Act of
                2002


99.1
            Trust Annual
              Statement
              of Compliance


99.2
            Trust
                Statement to
                Certificateholders


99.3
            Trust
                Statement to
                Noteholders


99.4
            Trust
                Servicer’s
                Certificate


99.5
            Report
                of Independent
                Auditors





(b)
      Current Reports on Form 8-K (each of which includes, along other things, a
      Monthly Statement to Noteholders) incorporated by reference from the
      Registrant's filings with the Securities and Exchange Commission, dated May
      25,
      June 27, July 25, August 25, September 26, October 25, November 25 and December
      27, 2005.





**Supplemental
      information to be furnished with reports filed pursuant to Section 15(d) of
      the
      Act by Registrants which have not registered Securities pursuant to Section
      12
      of the Act.**





No
      Annual
      report, proxy statement, form of proxy, or other proxy soliciting material
      has
      been sent to Certificateholders, and the Registrant does not presently
      contemplate sending any such materials subsequent to the filing of this
      report.








**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.








Caterpillar
                Financial Funding Corporation(Registrant)








Dated:
                March 29, 2006
            
            
            
            
            By:
            */s/
                Steven R. Elsesser***Steven
                R. Elsesser, Chief Financial OfficerDated:
                March 29, 2006
            
            
            
            
            By:
            */s/
                James A. Duensing***James
                A. Duensing, Treasurer