Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F. Form 20-F....x.....Form 40-F ........

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1): ____

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7): ____

Indicate by check mark whether by furnishing the information contained in this Form, the registrant is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes ..... No.....x.....

If “Yes” is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-________

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Teléfonos de México, S.A de C.V.
A Mexican Company

MATERIAL FACT

Teléfonos de México, S.A de C.V. (“TELMEX”), as the controlling shareholder of Embratel Participações S.A. (“EMBRAPAR”), in reference to the request for registration of a tender offer, to be intermediated by UNIBANCO – União de Bancos Brasileiros S.A., for the purchase of all of the outstanding common and preferred shares of EMBRAPAR (“Tender Offer”), which was announced through the Material Fact dated May 8, 2006 and submitted to the Brazilian Securities and Exchange Commission (“CVM”) through TELMEX’s wholly owned subsidiary Telmex Solutions Telecomunicações Ltda. (“Telmex Solutions”), for the purpose of canceling the registration of EMBRAPAR as a public company, considering the provisions of section 1.2.3.1 of the form of Notice of Tender Offer and in compliance with CVM Instruction no. 358/02, announces to the public its decision to continue the Tender Offer and its request that CVM continue analyzing the application for registration of the Tender Offer, in spite of the fact that the condition set forth in section 1.2.3 (iii) of the form of Notice of Tender Offer was met.

TELMEX communicates that it shall maintain the Tender Offer until June 7, 2006, regardless of the market conditions from the date of this announcement until June 6, 2006. In the event that, at the close of trading on the São Paulo Stock Exchange (“BOVESPA”) on June 6, 2006, the condition set forth in section 1.2.3 (iii) of the form of Notice of Tender Offer is met, TELMEX will announce to the public, before the start of trading on BOVESPA on June 7, 2006, its decision to maintain or withdraw the Tender Offer.

Neither TELMEX nor Telmex Solutions has commenced the Tender Offer to which this communication relates, and the Tender Offer is still subject to CVM’s approval. Holders of EMBRAPAR’s shares and/or American Depositary Shares should read the Tender Offer Statement and the other documents relating to the Tender Offer that are filed with the Securities and Exchange Commission (“SEC”) in the United States when they become available, because they will contain important information. A Portuguese translation of these documents will be filed with CVM. This material will also be available free of charge on the SEC’s website at www.sec.gov.

Rio de Janeiro, May 24, 2006

Teléfonos de México, S.A. de C.V.

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SIGNATURE

                     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.

		TELÉFONOS DE MÉXICO, S.A. DE C.V.
Date:  May 25, 2006		By:	/s/      Adolfo Cerezo Perez
			Name: Adolfo Cerezo Pérez
			Title: Chief Financial Officer

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