SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

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 2008

Commission File Number 1-13758

PORTUGAL TELECOM, SGPS, S.A.

(Exact name of registrant as specified in its charter)

Av. Fontes Pereira de Melo, 40
1069 - 300 Lisboa, Portugal

(Address of principal executive office)

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 o

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

Yes o No x

Portugal Telecom

Release 5 June 2008, Lisbon

Acquisition of own shares through financial derivative instruments

Portugal Telecom informs that as part of the share buyback programme under execution, it has the right to acquire an additional 10,073,059 shares through equity swap agreements.

The total number of own shares that PT currently holds through equity swap agreements is 30,713,059 shares, of which 20,640,000 shares were contracted under the previous share buyback programme. As a result, the number of outstanding shares, adjusting for equity swaps on own shares recognised in the balance sheet, is 911,882,118.

As part of the share buyback programme under execution, a total of 196,334,382 own shares has been acquired. The total amount returned to shareholders to date, through the share buyback programme under execution since March 2007, totals Euro 1,842 million.

Portugal Telecom, SGPS, SA

Avenida Fontes Pereira de Melo, 40

1069-300 Lisbon

Portugal

www.telecom.pt

Public company

Share capital _ Euro 28,277,855.31

Registered in the Commercial
Registry Office of Lisbon

and Corporation no. _ 503 215 058

Portugal Telecom is listed on the Euronext and New York Stock Exchange. Information may be accessed on the Reuters under the symbols PTC.LS and PT and on Bloomberg under the symbol PTC PL.

Nuno Vieira

Investor Relations Director

nuno.t.vieira@telecom.pt

Tel.: +351 21 500 1701

Fax: +351 21 500 0800

http://ir.telecom.pt

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.

Date: June 6, 2008

	PORTUGAL TELECOM, SGPS, S.A.

	By:	/s/ Nuno Vieira
		Nuno Vieira Investor Relations Director

FORWARD-LOOKING STATEMENTS

This document may contain forward-looking statements. These statements are statements that are not historical facts, and are based on management’s current view and estimates of future economic circumstances, industry conditions, company performance and financial results. The words “anticipates”, “believes”, “estimates”, “expects”, “plans” and similar expressions, as they relate to the company, are intended to identify forward-looking statements. Statements regarding the declaration or payment of dividends, the implementation of principal operating and financing strategies and capital expenditure plans, the direction of future operations and the factors or trends affecting financial condition, liquidity or results of operations are examples of forward-looking statements. Such statements reflect the current views of management and are subject to a number of risks and uncertainties. There is no guarantee that the expected events, trends or results will actually occur. The statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, and operating factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations.