SC TO-T/A

================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                                  -----------

                                 SCHEDULE TO/A
                                 (RULE 14d-100)
                 TENDER OFFER STATEMENT UNDER SECTION 14(d)(1)
          OR SECTION 13(e)(1) OF THE SECURITIES EXCHANGE ACT OF 1934.
                               (AMENDMENT NO. 1)

                                SOUTHDOWN, INC.
                       (Name of Subject Company (issuer))

                             CENA ACQUISITION CORP.
                              CEMEX, S.A. de C.V.
                      (Names of Filing Persons (offerors))

                                  -----------

                    COMMON STOCK, PAR VALUE $1.25 PER SHARE;
                       RIGHTS TO PURCHASE PREFERRED STOCK
                         (Title of Class of Securities)

                                  -----------

                                   841297104
                     (CUSIP Number of Class of Securities)

                               RAMIRO VILLARREAL
                              CEMEX, S.A. de C.V.
                           AVE. CONSTITUCION 444 PTE.
                      MONTERREY, NUEVO LEON, MEXICO 64000
                         TELEPHONE: (011-528) 328-3000
  (NAME, ADDRESS AND TELEPHONE NUMBER OF PERSON AUTHORIZED TO RECEIVE NOTICES
                AND COMMUNICATIONS ON BEHALF OF FILING PERSONS)

                                   COPIES TO:


 Randall H. Doud, Esq.                         Frank Ed Bayouth II, Esq.
 Skadden, Arps, Slate, Meagher &               Skadden, Arps, Slate, Meagher &
 Flom LLP                                      Flom LLP
 Four Times Square                             1600 Smith Street, Suite 4400
 New York, N.Y. 10036                          Houston, Texas  77002
 Telephone: 212-735-3000                       Telephone:  713-655-5100


[_]  CHECK THE BOX IF THE FILING RELATES SOLELY TO PRELIMINARY
     COMMUNICATIONS MADE BEFORE THE COMMENCEMENT OF A TENDER OFFER.

CHECK THE APPROPRIATE BOXES BELOW TO DESIGNATE ANY TRANSACTIONS TO WHICH
THE STATEMENT RELATES:

[X]  THIRD-PARTY TENDER OFFER SUBJECT TO RULE 14d-1.
[_]  ISSUER TENDER OFFER SUBJECT TO RULE 13e-4.
[_]  GOING-PRIVATE TRANSACTION SUBJECT TO RULE 13e-3.
[_]  AMENDMENT TO SCHEDULE 13D UNDER RULE 13d-2.

     Check the following box if the filing is a final amendment reporting the
results of the tender offer: [_]

================================================================================


      This Amendment No.1 to the Tender Offer Statement on Schedule TO (the
"Schedule TO"), filed initially with the Securities and Exchange Commission on
October 5, 2000, relates to the third-party tender offer by CENA Acquisition
Corp. ("Purchaser"), a Delaware corporation and an indirect subsidiary of CEMEX,
S.A. de C.V., a company organized under the laws of the United Mexican States
("CEMEX"), to purchase all outstanding shares of common stock, par value $1.25
per share, of Southdown, Inc., a Louisiana corporation, including related
preferred stock purchase rights issued in respect of the Company Common Stock
(such common stock and related rights, collectively, the "Shares"), at a price
of $73.00 per share, net to the seller in cash and without interest thereon,
upon the terms and subject to the conditions set forth in the Offer to Purchase,
dated October 5, 2000 (the "Offer to Purchase"), and the related Letter of
Transmittal (which, together with any amendments or supplements thereto,
constitute the "Offer"), which were filed as Exhibits (a)(1)(A) and (a)(1)(B),
respectively, to the Schedule TO. Unless otherwise defined herein, all
capitalized terms used herein shall have the respective meanings given such
terms in the Offer to Purchase.

ITEMS 1 AND 4.

      Items 1 and 4 are hereby amended and supplemented to add the following:

      On October 20, 2000, CEMEX announced that the Expiration Date was extended
to 12:00 Midnight, New York City time, on Friday, November 3, 2000.  Reference
is hereby made to the Press Release issued by CEMEX, dated October 20, 2000, a
copy of which is filed as Exhibit (a)(5)(E) hereto and is incorporated herein by
reference.

ITEM 11.

      For technical reasons, on October 19, 2000, CEMEX refiled its Notification
and Report Form with respect to the Offer and the Merger with the Antitrust
Division of the Department of Justice (the "Antitrust Division") and the Federal
Trade Commission (the "FTC").  As a result of the refiling, the waiting period
applicable to the purchase of Shares pursuant to the Offer will now expire at
11:59 p.m., New York City time, on Friday, November 3, 2000 unless the Antitrust
Division or the FTC extends the waiting period by requesting from CEMEX
additional information or documentary material relevant to the Offer.

ITEM 12.  EXHIBITS.

99(a)(5)(E) Press Release dated October 20, 2000.


                                   SIGNATURE

      After due 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.

                                    CENA Acquisition Corp.


                                    By:    /s/ Jeffrey H. Smith
                                        -----------------------
                                          Name:  Jeffrey H. Smith
                                          Title: Director and Treasurer


                                    CEMEX, S.A. de C.V.


                                    By:     /s/ Francisco Garza
                                        -----------------------
                                          Name:   Francisco Garza
                                          Title:  President of CEMEX North
                                                  America and Trading


Dated: October 20, 2000

                                       3


                                 EXHIBIT INDEX

EXHIBIT NO.         EXHIBIT NAME
- -----------         ------------

(a)(5)(E)        Press Release dated October 20, 2000.

                                       4

EX-99.(A)(5)(E)

                                                               EXHIBIT (a)(5)(E)

[CEMEX Logo]

FOR IMMEDIATE RELEASE

Contact Information:
Abraham Rodriquez
Phone: 011-528-328-3631
Facsimile: 011-528-328-7221

Daniel Perez Whitaker
(528) 152-2747
daniel_pw@cemex.com

Jose Antonio Gonzalez
(212) 317-6008
josegonzalez@cemex.com



                             UPDATE ON CEMEX OFFER

MONTERREY, Mexico--(BUSINESS WIRE)--Oct. 20, 2000--CEMEX, S.A. de C.V.
(NYSE: CX - news) announced today that for technical reasons, on October 19,
2000, it refiled with the Antitrust Division of the Department of Justice and
the Federal Trade Commission its Notification and Report Form with respect to
CEMEX's offer to purchase all outstanding stock of Southdown, Inc. (NYSE:SWD -
news).

As a result of the refiling, the waiting period applicable to CEMEX's purchase
of Southdown common stock pursuant to the offer will now expire at 11:59 p.m.,
New York City time, on Friday, November 3, 2000 unless the Antitrust Division or
the Federal Trade Commission extends the waiting period by requesting from CEMEX
additional information or documentary material relevant to the offer. Because
the expiration date of the waiting period will not expire until November 3,
2000, CEMEX has extended its offer to expire at 12:00 Midnight, New York City
time, on Friday, November 3, 2000.

As of the close of business on October 19, 2000, approximately 719,742 shares of
common stock had been validly tendered and not withdrawn pursuant to CEMEX's
offer.

CEMEX is one of the three largest cement companies in the world with
approximately 65 million metric tons of production capacity. It is also the
world's largest trader of cement and the world's leading producer of white
cement. CEMEX is engaged in the production, distribution, marketing and sale of
cement, ready-mix concrete, aggregates and clinking through operating
subsidiaries in four different continents. For more information, visit
www.cemex.com.