UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  SCHEDULE 13D
                    Under the Securities Exchange Act of 1934

                                (AMENDMENT NO. 4)

                        Southern Peru Copper Corporation
                                (Name of Issuer)

                     COMMON STOCK, PAR VALUE $0.01 PER SHARE
                         (Title of Class of Securities)

                                    843611104
                                 (CUSIP Number)

                              S. DAVID COLTON, ESQ.
                            PHELPS DODGE CORPORATION
                            ONE NORTH CENTRAL AVENUE
                                PHOENIX, AZ 85004
                                 (602) 234-8143

   (Name, Address and Telephone Number of Person Authorized to Receive Notices
                               and Communications)


                                    Copy to:
                             MICHAEL W. BLAIR, ESQ.
                            DEBEVOISE & PLIMPTON LLP
                                919 THIRD AVENUE
                               NEW YORK, NY 10022
                                 (212) 909-6000

                                  JUNE 9, 2005

         (Date of Event which Requires Filing Statement on Schedule 13D)



If the filing person has previously filed a statement on Schedule 13G to report
the acquisition that is the subject of this Schedule 13D, and is filing this
schedule because of Sections 240.13d-1(e), 240.13d-1(f) or 240.13d-1(g),
check the following box [ ].

NOTE: Schedules filed in paper format shall include a signed original and five
copies of the schedule, including all exhibits. See Rule 13d-7 for other parties
to whom copies are to be sent.

*  The remainder of this cover page shall be filled out for a reporting person's
   initial filing on this form with respect to the subject class of securities,
   and for any subsequent amendment containing information which would alter
   disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).

                        (Continued on following pages)


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                                  SCHEDULE 13D
                                (AMENDMENT NO. 4)

                                                            CUSIP NO.  843611104
--------------------------------------------------------------------------------
(1)    NAME OF REPORTING PERSON

       Phelps Dodge Overseas Capital Corporation

       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
--------------------------------------------------------------------------------
(2)    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
       (A) (X)

       (B) ( )
--------------------------------------------------------------------------------
(3)    SEC USE ONLY
--------------------------------------------------------------------------------
(4)    SOURCE OF FUNDS

       N/A
--------------------------------------------------------------------------------
(5)    CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED               ( )
       PURSUANT TO ITEMS 2(D) OR 2(E)
--------------------------------------------------------------------------------
(6)    CITIZENSHIP OR PLACE OF ORGANIZATION

       Delaware
--------------------------------------------------------------------------------
              (7)         SOLE VOTING POWER
  NUMBER OF  
                          None
   SHARES     ------------------------------------------------------------------
              (8)         SHARED VOTING POWER             
BENEFICIALLY                                  
                          None                            
  OWNED BY    ------------------------------------------------------------------
              (9)         SOLE DISPOSITIVE POWER          
    EACH                                       
                          None                            
  REPORTING   ------------------------------------------------------------------
              (10)        SHARED DISPOSITIVE POWER        
 PERSON WITH                                              
                          None                            
--------------------------------------------------------------------------------
(11)   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       None
--------------------------------------------------------------------------------
(12)   CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
       SHARES                                                           ( )
--------------------------------------------------------------------------------
(13)   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

       0% of total Common Shares
--------------------------------------------------------------------------------
(14)   TYPE OF REPORTING PERSON

       CO
--------------------------------------------------------------------------------


                                        3



                                                            CUSIP NO.  843611104
--------------------------------------------------------------------------------
(1)    NAME OF REPORTING PERSON

       Climax Molybdenum B.V.

       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
--------------------------------------------------------------------------------
(2)    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
       (A) (X)

       (B) ( )
--------------------------------------------------------------------------------
(3)    SEC USE ONLY
--------------------------------------------------------------------------------
(4)    SOURCE OF FUNDS

       N/A
--------------------------------------------------------------------------------
(5)    CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED               ( )
       PURSUANT TO ITEMS 2(D) OR 2(E)
--------------------------------------------------------------------------------
(6)    CITIZENSHIP OR PLACE OF ORGANIZATION

       Netherlands
--------------------------------------------------------------------------------
              (7)         SOLE VOTING POWER
  NUMBER OF  
                          None
   SHARES     ------------------------------------------------------------------
              (8)         SHARED VOTING POWER             
BENEFICIALLY                                  
                          None                            
  OWNED BY    ------------------------------------------------------------------
              (9)         SOLE DISPOSITIVE POWER          
    EACH                                       
                          None                            
  REPORTING   ------------------------------------------------------------------
              (10)        SHARED DISPOSITIVE POWER        
 PERSON WITH                                              
                          None                            
--------------------------------------------------------------------------------
(11)   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       None
--------------------------------------------------------------------------------
(12)   CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
       SHARES                                                           ( )
--------------------------------------------------------------------------------
(13)   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

       0% of total Common Shares
--------------------------------------------------------------------------------
(14)   TYPE OF REPORTING PERSON

       CO
--------------------------------------------------------------------------------


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                                                            CUSIP NO.  843611104
--------------------------------------------------------------------------------
(1)    NAME OF REPORTING PERSON

       Phelps Dodge Corporation

       I.R.S. IDENTIFICATION NO. OF ABOVE PERSON
--------------------------------------------------------------------------------
(2)    CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP
       (A) (X)

       (B) ( )
--------------------------------------------------------------------------------
(3)    SEC USE ONLY
--------------------------------------------------------------------------------
(4)    SOURCE OF FUNDS

       N/A
--------------------------------------------------------------------------------
(5)    CHECK IF DISCLOSURE OF LEGAL PROCEEDINGS IS REQUIRED               ( )
       PURSUANT TO ITEMS 2(D) OR 2(E)
--------------------------------------------------------------------------------
(6)    CITIZENSHIP OR PLACE OF ORGANIZATION

       New York
--------------------------------------------------------------------------------
              (7)         SOLE VOTING POWER
  NUMBER OF  
                          None
   SHARES     ------------------------------------------------------------------
              (8)         SHARED VOTING POWER             
BENEFICIALLY                                  
                          None                            
  OWNED BY    ------------------------------------------------------------------
              (9)         SOLE DISPOSITIVE POWER          
    EACH                                       
                          None                            
  REPORTING   ------------------------------------------------------------------
              (10)        SHARED DISPOSITIVE POWER        
 PERSON WITH                                              
                          None                            
--------------------------------------------------------------------------------
(11)   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

       None
--------------------------------------------------------------------------------
(12)   CHECK IF THE AGGREGATE AMOUNT IN ROW (11) EXCLUDES CERTAIN
       SHARES                                                           ( )
--------------------------------------------------------------------------------
(13)   PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (11)

       0% of total Common Shares
--------------------------------------------------------------------------------
(14)   TYPE OF REPORTING PERSON

       CO
--------------------------------------------------------------------------------


                                       5


      This Amendment No. 4 ("Amendment No. 4") amends and supplements the
statement on Schedule 13D initially filed on January 12, 1996, as amended by
filings on December 29, 2004, April 8, 2005 and June 3, 2005 (the "Original
Filing"). Information reported in the Original Filing remains in effect except
to the extent that it is amended, restated or superseded by information
contained in this Amendment No. 4. Capitalized terms used and not defined in
this Amendment No. 4 have the meanings set forth in the Original Filing.

ITEM 4.  PURPOSE OF TRANSACTION

        Item 4 of the Original Filing is hereby amended and supplemented by
adding the following:

      On June 9, 2005, Phelps Dodge Overseas and Climax entered into an
Underwriting Agreement (the "Underwriting Agreement") with Citigroup Global
Markets Inc., UBS Securities LLC, the Company, Cerro and SPC Investors.

      Pursuant to the Underwriting Agreement, Phelps Dodge Overseas and Climax
agreed to sell to the underwriters named therein (the "Underwriters") 8,338,415
and 2,055,814 shares of Common Stock, respectively, at a purchase price of
$40.635 per share. Phelps Dodge Overseas and Climax also agreed to sell an
additional 625,381 and 154,186 shares of Common Stock, respectively, at the same
purchase price upon the exercise by the Underwriters of an over-allotment option
(the "Over-Allotment Option").

      The shares to be sold by Phelps Dodge Overseas and Climax pursuant to the
Underwriting Agreement, including the shares subject to the Over-Allotment
Option, represented all of the Common Stock held by Phelps Dodge Overseas and
Climax.

      The foregoing description of the Underwriting Agreement is qualified in
its entirety by reference to the Underwriting Agreement which is filed as
Exhibit 1 hereto and incorporated herein by reference.

      On June 10, 2005, the Underwriters exercised their Over-Allotment Option
in full. On June 15, 2005, Phelps Dodge Overseas and Climax sold a total of
8,963,796 and 2,210,000 shares of Common Stock, respectively, to the
Underwriters pursuant to the Underwriting Agreement. This total included all of
the shares of Common Stock subject to the Over-Allotment Option.

      The transaction, which constituted a sale of all of the shares of Common
Stock held by Phelps Dodge Overseas and Climax, resulted in aggregate proceeds
(before expenses and taxes) of approximately $454 million.

ITEM 5.  INTEREST IN SECURITIES OF THE ISSUER

Item 5 of the Original Filing is hereby amended and restated in its entirety as
follows:

        (a) Following the June 15, 2005 transaction described above, neither
Phelps Dodge Overseas nor Climax is the beneficial owner of any shares of Common
Stock in the Company. 

                                        6


As a result, PDC can no longer be deemed to be the beneficial owner of any
shares of Common Stock in the Company.

        To the best knowledge of Phelps Dodge Overseas, Climax and PDC, none of
the persons listed on Schedules A, B or C attached hereto is the beneficial
owner of any shares of Common Stock, other than J. Steven Whisler, who owns 800
shares of Common Stock.

        (b) None of Phelps Dodge Overseas, Climax nor PDC has sole or shared
power to vote or to direct the vote, nor sole or shared power to dispose or
direct the disposition, of any shares of Common Stock.

        J. Steven Whisler has the sole power to vote or to direct the vote, 
and the sole power to dispose or direct the disposition, of the Common Stock
that he owns.

        (c) On January 2, 1996, the Exchange Offer and the Founding Stockholder
Exchange were completed, resulting in the acquisition by Phelps Dodge Overseas
of 11,173,796 shares of Class A Common Stock of the Company.

        On December 17, 2004, Phelps Dodge Overseas transferred 2,210,000 shares
of Class A Common Stock of the Company to PDC as a dividend. Through a series of
capital contributions and an inter-company purchase, the 2,210,000 shares of
Class A Common Stock of the Company were subsequently transferred to Climax on
December 22, 2004.

        On May 19, 2005, at the New York City office of the Company's counsel,
each of Phelps Dodge Overseas and Climax converted all of their Class A Common
Stock into an equal number of fully paid and non-assessable shares of the
Company's Common Stock.

        On June 14, 2005, Ramiro G. Peru sold 600 shares of Common Stock at a 
purchase price of $43.72 per share through a broker in an unsolicited 
market-order transaction. Mr. Peru no longer owns any shares of Common Stock.

        On June 15, 2005, Phelps Dodge Overseas and Climax sold a total of
8,963,796 and 2,210,000 shares of Common Stock, respectively, to the
Underwriters pursuant to the Underwriting Agreement at a purchase price of
$40.635 per share (see above). The transaction was consummated at the New York
City office of the counsel for the Underwriters.

        (e) On June 15, 2005, after consummation of the transaction described
above, none of PDC, Phelps Dodge Overseas nor Climax may be deemed to be the
beneficial owner of more than 5% of the Company's Common Stock.

ITEM 6. CONTRACTS, ARRANGEMENTS, UNDERSTANDINGS OR RELATIONSHIPS WITH RESPECT TO
SECURITIES OF THE ISSUER.

      Item 6 of the Original Filing is hereby amended and supplemented by adding
the following:

      On June 9, 2005, Phelps Dodge Overseas and Climax entered into an
Underwriting Agreement with Citigroup Global Markets Inc., UBS Securities LLC,
the Company, Cerro and SPC Investors. On June 10, the Underwriters delivered a
written notice exercising in full their 


                                        7


Over-Allotment Option. The description of the Underwriting Agreement under Item
4 is incorporated herein by reference in its entirety.

ITEM 7. MATERIALS TO BE FILED AS EXHIBITS.

Exhibit No.     Title

 1              Underwriting Agreement, dated June 9, 2005, between Southern
                Peru Copper Corporation, Cerro Trading Company, Inc., SPC
                Investors, L.L.C., Phelps Dodge Overseas Capital Corporation,
                Climax Molybdenum B.V., Citigroup Global Markets Inc. and UBS
                Securities LLC.

 2              Joint Filing Agreement, dated June 23, 2005, between Phelps
                Dodge Overseas Capital Corporation, Climax Molybdenum B.V.
                and Phelps Dodge Corporation


                                       8


                                    SIGNATURE

      After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Dated:  June 23, 2005


                                    PHELPS DODGE OVERSEAS CAPITAL CORPORATION



                                    By: /s/ S. David Colton
                                        --------------------------------------
                                        Name:   S. David Colton
                                        Title:  Senior Vice President
                                                and General Counsel

                                    CLIMAX MOLYBDENUM B.V.




                                    By: /s/ David H. Thornton
                                        --------------------------------------
                                        Name:   David H. Thornton
                                        Title:  Director



                                    PHELPS DODGE CORPORATION




                                    By: /s/ S. David Colton
                                        --------------------------------------
                                        Name:   S. David Colton
                                        Title:  Senior Vice President
                                                and General Counsel


                                        9