FORM 6-K

SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549

Report of Foreign Private Issuer

Pursuant to Rule 13a-16 or 15d-16 of

the Securities Exchange Act of 1934

For the month of June 2010

Commission File Number: 001-32741

Telmex Internacional, S.A.B. de C.V.

(Exact Name of the Registrant as Specified in the Charter)

Telmex International

(Translation of Registrant's Name into English)

Av. Insurgentes Sur 3500

Colonia Peña Pobre

México City 14060, México, D.F.

(Address of principal executive offices)

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....Ö.....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-

ANNOUNCEMENT TO THE PUBLIC 
In Mexico City, Federal District, on June 16, 2010. Telmex Internacional, S.A.B. de C.V. (“TELINT”) (Mexican Stock Exchange or BMV Ticket Symbol: “TELINT”; NYSE: “TII”, LATIBEX: “XTII”) hereby informs that it has been notified of the definitive results of the exchange offer issued by América Móvil, S.A.B. de C.V. (“América Móvil”) to the holders of Series A Shares, Series L Shares and TII A Shares and TII L Shares in the form of American depositary shares of Telmex Internacional, S.A.B. de C.V., as provided for in the announcement issued today by América Móvil, which states the following:

“… América Móvil, S.A.B. de C.V. Announces Final Results of

Exchange Offers for Telmex Internacional, S.A.B. de C.V. and Carso Global Telecom, S.A.B. de C.V.

(Mexico City, June 16, 2010)—América Móvil, S.A.B. de C.V. (“América Móvil”)(NYSE: AMX) today announced the final results of its exchange offer to holders of Series A Shares (“TII A Shares”), Series L Shares (“TII L Shares”) and TII A Shares and TII L Shares in the form of American depositary shares (respectively, “TII A ADSs” and “TII L ADSs”) of Telmex Internacional, S.A.B. de C.V. (“Telmex Internacional”).  América Móvil also announced the final results of its exchange offer to holders of Series A-1 Shares (“CGT Shares”) and CGT Shares in the form of American depositary shares (“CGT ADSs”) of Carso Global Telecom, S.A.B. de C.V. (“CGT”). The exchange offers expired on June 10, 2010.

Based on a final count by Inversora Bursátil, S.A. de C.V., Casa de Bolsa, Grupo Financiero Inbursa and the exchange agent, The Bank of New York Mellon, the following securities were tendered (including shares represented by American depositary shares (“ADSs”)): 64,303,485 TII A Shares, 5,850,107,024 TII L Shares and 3,462,401,592 CGT Shares.

All shares and ADSs that were validly tendered and not withdrawn have been accepted for payment in accordance with the terms of the exchange offers and applicable law. Upon consummation of the exchange offers, América Móvil owns 93.56% of Telmex Internacional’s outstanding shares and 99.44% of CGT’s outstanding shares.

Of the TII A Shares and TII L Shares (including shares represented by ADSs) tendered, cash elections were made with respect to 2,297,057,405 shares.  Based upon these results, América Móvil paid Ps. 26,783,689,342.30 (equivalent to approximately U.S.$2,120,640,486, based on the exchange rate of June 15, 2010) to tendering shareholders of Telmex Internacional who elected to receive cash, and América Móvil issued 1,349,272,707 América Móvil Series L Shares (“AMX L Shares”) (including AMX L Shares repre sented by ADSs) to tendering shareholders of Telmex Internacional who elected to receive stock.  América Móvil issued 7,088,921,019 AMX L Shares (including AMX L Shares represented by ADSs) to tendering shareholders of CGT.  Tender holders of TII A ADSs and TII L ADSs are expected to receive AMX L Shares in the form of ADSs or cash on June 18, 2010.

As a result of the exchange offers, América Móvil has 40,546,724,182 shares of capital stock outstanding as of June 16, 2010.

About América Móvil

América Móvil is the leading provider of wireless services in Latin America.  As of March 31, 2010, it had 206.4 million wireless subscribers and 3.8 million landlines in the Americas.

Important Additional Information

This announcement is not an offering document and does not constitute an offer to sell or the solicitation or an offer to buy securities or a solicitation of any vote or approval.  This announcement is not for publication, release or distribution in or into or from any jurisdiction where it would otherwise be prohibited.

Forward-Looking Statements

Certain statements contained in this press release may constitute “forward-looking statements”.  All statements in this press release, other than those relating to historical information or current condition, are forward-looking statements.  Such forward-looking statements are based on current expectations and involve inherent risks and uncertainties, including factors that could delay, divert or change any of them, and could cause outcomes and results to differ materially from current expectations.  No forward-looking statement can be guaranteed.  Among other risks, there can be no guarantee that the exchange offers will be completed, or if it is completed, that it will close within the anticipated time period.  América Móvil undertakes no obligation to publicly update any forward-looking statement, whether as a result of new information, future events, or otherwise….”.

Limitation of Liability: This press release contains certain forecasts or projections, which reflect the current views and/or expectations of the company and its management with respect to its performance, business and future events. The forecasts may include, without limitation, any statement that may predict, indicate or imply future results, performance or achievements, and may contain terms such as “believe”, “anticipate”, “expect”, “in our opinion”, “will probably result in” or any other words or phrases of similar meaning. Such statements are subject to certain risks, uncertainties and assumptions. Please be advised that a number of important factors could cause actual results to differ materially from the plans, objectives, expectations, estimates and intentions expressed in this release. In no event, neither the company nor any of its subsidiaries, affiliates, directors, officers, agents or employees will be liable to third parties (including investors) for any investment decision made or action taken in reliance on the information contained in this press release or for any consequential, special or similar damages.

Date: June 16, 2010.

TELMEX INTERNACIONAL, S.A.B. DE C.V.

By: __________________          

Name: Oscar Von Hauske Solís
Title: Chief Executive Officer

Ref: Announcement to the Public

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