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 April 2015

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.

 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.

Announcement  |  Lisbon  |  1 April 2015

Material fact disclosed by Oi

Portugal Telecom, SGPS S.A. hereby informs on the Material fact disclosed by Oi, S.A. related to the Approval by Telemar Participações Shareholders of the Planned Measures for the Transaction Goals Published on February 20, 2014, according to the company’s announcements attached hereto.

www.ptsgps.pt

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Oi S.A.

CORPORATE TAXPAYERS’ REGISTRY (CNPJ/MF) No. 76.535.764/0001-43

BOARD OF TRADE (NIRE) No. 33 3 0029520-8

PUBLICLY-HELD COMPANY

MATERIAL FACT

Approval by Telemar Participações Shareholders of the Planned Measures for the

Transaction Goals Published on February 20, 2014

Completion of the Exchange of Oi Shares for Securities of Rio Forte

Oi S.A. (“Oi” - Bovespa: OIBR3, OIBR4; NYSE: OIBR and OIBR.C), pursuant to art. 157, paragraph 4, of Law No. 6,404/76 and Instruction No. 358/02 of the Brazilian Securities and Exchange Commission (Comissão de Valores Mobiliários — CVM), and in furtherance with the Material Fact published on March 26, 2015, informs its shareholders and the market in general, that on this date, Telemar Participações S.A. (“TmarPart”) disclosed the following Material Fact.

“Telemar Participações S.A. (“TmarPart”), pursuant to art. 157, paragraph 4, of Law No. 6,404/76 and Instruction No. 358/02 of the Brazilian Securities and Exchange Commission (Comissão de Valores Mobiliários — CVM), and in furtherance of the Material Fact published on March 26, 2015, informs that, in the shareholders’ meeting scheduled for March 31, 2015, in accordance with the terms of TmarPart’s Shareholders’ Agreement, the management of TmarPart and Oi, respectively, received the approval to begin taking the applicable steps to adopt a set of measures to meet the main goals of the planned business combination of Oi, TmarPart, and Portugal Telecom, SGPS, S.A. (“PT SGPS”), as published on February 20, 2014, (the “Transaction”), according to the terms below.

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The shareholders of TmarPart unanimously approved the adoption of an alternative share structure, after analyzing options and taking into consideration the current obstacles to a registration of TmarPart shares with the U.S. Securities and Exchange Commission (“SEC”) that would be necessary to allow the incorporação de ações (“Merger of Shares”) of Oi and TmarPart, as described in the Material Fact of March 26, 2015. The adopted alternative share structure allows the main goals of the Transaction to be met, with Oi able to adopt the corporate governance best practices prescribed by the regulations of the Novo Mercado segment of the BM&F Bovespa S.A. — Bolsa de Valores, Mercadorias e Futuros (“BM&F Bovespa”) and disperse its voting rights, keeping in mind the final objective of opportunely completing the Transaction with the result of listing the shares currently held by Oi shareholders, and, at a later point, those of the shares held by PT SGPS, on the Novo Mercado.

1. Measures Approved by the Shareholders of TmarPart to Meet the Goals of the Transaction

The alternative share structure includes a voluntary exchange of Oi’s preferred shares for common shares (in other words, at the option of the preferred shareholder), at an exchange rate of 0.9211 common shares for each preferred share issued by Oi, as already published for the Merger of Shares between Oi and TmarPart, and used for the pricing of the public offering of shares by Oi on April 28, 2014.

The voluntary exchange proposal requires that at least two-thirds of Oi’s preferred shareholders (ex-treasury) agree to exchange their shares for common shares (the “Condition for the Exchange”), within a period of 30 days, commencing after the General Shareholders’ Meeting of Oi at which the opening of the period for the exchange is deliberated (the “Voluntary Exchange of Preferred Shares”).

As preliminary steps for the beginning of the period for the Voluntary Exchange of Preferred Shares, the following steps, which are closely related to one another, need to be approved and implemented simultaneously, concurrently and inseparable one from the other (the “Preliminary Steps”):

(i)                                     Merger of the entities that directly or indirectly own shares of Oi (“Simplification of Corporate Ownership”);

(ii)                                  Approval of the new by laws of Oi, reflecting the improved standards of Oi’s corporate governance;

(iii)                               Election of Oi’s new Board of Directors, with a term expiring at the General Shareholders’ Meeting that approves Oi’s financial statements for the year ending on December 31, 2017.

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2. Main Steps of the Simplification of Corporate Ownership

The following corporate restructuring transactions will be completed with the goal of simplifying the share capital structure of Oi, and are to be deliberated during the shareholders’ general meetings, to be held on the same date, and before the start of the period for the Voluntary Exchange of Preferred Shares: (i) merger of AG Telecom Participações S.A. (“AG Tel”) into Pasa Participações S.A. (“PASA”), LF Tel S.A. (“LF”) into EDSP75 Participações S.A. (“EDSP75”), and PASA and EDSP75 into Bratel Brasil S.A. (“Bratel”); (ii) merger of Valverde Participações S.A. into TmarPart; (iii) merger of Venus RJ Participações S.A. (“Venus”), Sayed RJ Participações S.A. (“Sayed”) and PTB2 into Bratel; (iv) merger of Bratel into TmarPart; and finally (v) the merger of TmarPart into Oi.

As previously disclosed in the Material Fact, dated February 20, 2014, the Simplification of Corporate Ownership will be done without diluting the interests of the other shareholders that hold interests in the companies involved, given that the established exchange ratios solely take into account the direct and indirect interests between them and in Oi’s share capital, observing the premise that these companies will not have, with the possible exception of goodwill recorded in relation to their investments, relevant assets or liabilities (or they will have sufficient cash and cash equivalents to fully repay such liabilities). Any goodwill, or other assets, recorded by the companies whose structure will be simplified may be transferred to Oi or to TmarPart, as the case may be, for the benefit of their shareholders, and these amounts will not be considered when establishing exchange ratios.

The TmarPart Shareholders’ Agreements will terminate as a consequence of the Simplification of Corporate Ownership

3. Proposal for New Oi Bylaws

The shareholders of TmarPart approved the proposal for new by-laws of Oi that will be submitted to the Board of Directors and the General Meeting of Oi’s shareholders, which will allow Oi to adopt improved levels of corporate governance, as well as to disperse the right to vote, in accordance with governance pledges made with to market. Oi’s new bylaws will include, among other things, the following main provisions:

(i)                                    A 100% tag along for common shares;

(ii)                                Preferred shares without the right to vote, but would maintain the rights currently held by the preferred shareholders;

(iii)                            Convertibility of the preferred shares, during the time periods and in accordance with the conditions approved by the Board of Directors;

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(iv)                              The voting rights of a single shareholder cannot exceed 15%;

(v)                                  As stipulated by the Regulations of the Novo Mercado, at least 20% of the Directors must be independent;

(vi)                              A collective term of two years for the members of the Board of Directors, with exception to the first Board of Directors, which shall have a term of three years;

(vii)                          Prohibition against the same person holding the positions of Chairman of the Board of Directors and Chief Executive Officer (except during the first three years from adoption of the new Bylaws);

(viii)                      The Board of Directors is obligated to address any public offer to repurchase Oi’s shares;

(ix)                              The requirement to complete an offer to purchase common shares at a price at least equal to the economic value of the shares in the case of termination of the registration or exit from Level 1 Corporate Governance of the BM&F Bovespa, except in the event that Oi enters the Level 2 Corporate Governance or the Novo Mercado segment of the BM&F Bovespa;

(x)                                  Mandatory resolution of disputes or controversies through arbitration in front of the Market Arbitration Chamber (Câmara de Arbitragem do Mercado).

The limitation on voting rights will cease to be in effect in the following events:

(i)                                     capital increase or corporate reorganization that results in a dilution of the current shareholder base of more than 50%;

(ii)                                  as a result of an offer to purchase all outstanding common shares of Oi in which the offeror acquires at least 20% of the outstanding common shares or such offeror or group of shareholders representing the same or related interest of the offeror by voting agreement comes to hold, either individually or together, an interest in excess of 50% of Oi’s voting capital; or

(iii)                            at any time, no shareholder of Oi or group of shareholders representing the same or related interest by voting agreement, holds, individually or together, an interest in excess of 15% of Oi’s voting capital.

4. Commitment to Convert Shares Assumed by the Shareholders of TmarPart

The shareholders of TmarPart that hold shares of Oi, have committed to convert their preferred shares in Oi to common shares pursuant to the approved exchange ratio of 0.9211 common shares for each preferred share issued by Oi. This commitment will remain in effect until the earlier of October 31, 2015 and the end of the 30-day term for the completion of the conversion of Oi’s preferred shares into common shares under the structure for the Voluntary Exchange of Preferred Shares, subject to implementation of the Condition for the Exchange.

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5. Commitment to Merge the Shareholder Bases of Oi and PT SGPS

In addition, TmarPart, Oi and PT SGPS executed on the date hereof an amendment to the Terms of Commitment Agreement, dated September 8, 2014, which requires the parties to use their best efforts and take all reasonable steps to cause the listing of Oi’s shares (or securities backed by the shares of Oi or its successor in the event of a corporate reorganization) on the NYSE Euronext Lisbon (a regulated market), in addition to the New York Stock Exchange and BM&FBovespa, where the shares of Oi are already listed.

6. Amendment to the Option Agreement with PT SGPS

In addition, Oi also adjusted an amendment to the Option Agreement with PT SGPS, in order to allow PT SGPS to assign its call option to purchase Oi’s shares.  In consideration for the foregoing, Oi will have a right of first refusal exercisable prior to such assignment. The effectiveness of the amendment to the Option Agreement is subject to the approval at Oi’s General Shareholders’ Meeting at which holders of preferred shares will be entitled to voteand approval by the CVM, if applicable. Oi’s General Shareholders’ Meeting to deliberate on the amendment to the Option Agreement will be called on or prior to August 31, 2015 and held on or prior September 30, 2015.

The General Shareholders’ Meeting of Oi to approve the amendment to the Option Agreement will take place within the above time frame, and if possible, during the same General Shareholders’ Meeting at which the Preliminary Steps will be approved, unless the decision of the CVM is still pending with respect to the amendment to the Option Agreement. Certain shareholders of TmarPart have agreed to vote their shares in favor of the above amendment during Oi’s General Shareholders’ Meeting that will vote on the amendment to the Option Agreement.

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7. Conditions for Implementation, Approvals and other Information

Within the next few days, Oi and TmarPart’s management, as the case may be, will initiate the appropriate actions, including the preparation of all corporate acts and relevant contracts, for the adoption of the matters described in this Material Fact to be submitted for approval in new Preliminary Meetings of shareholders to be called in due course.

In addition to the relevant corporate approvals, the transactions and matters described in this Material Fact are subject to prior approval of the National Telecommunications Agency (Agência Nacional de Telecomunicações, or “ANATEL”).

The Voluntary Exchange of Preferred Shares and the Preliminary Steps will also be submitted for consent to certain creditors and debenture holders, pursuant to their respective debt instruments, but are not, however, subject to their approval.

The other conditions of the transactions described in this Material Fact, notably the full terms of the merger of TmarPart into Oi, in the form required by CVM Instruction No. 319/99, will be disclosed in the form of a Material Fact after the approval of the transactions by the management of Oi and TmarPart.

8. Expected Timeline

It is estimated that the general meetings which will deliberate regarding the Preliminary Steps, as well as the opening date for the shareholders of Oi’s preferred shares to express their intent to convert their preferred shares into common shares, will be called in approximately 130 days, subject to ANATEL’s prior consent to the implementation of the transactions and matters described in this Material Fact.”

The shareholders also set October 31, 2015 as the deadline for the implementation of the Preliminary Steps.

*            *           *

Consummation of the Exchange

Oi reports that, following the approval by its General Shareholders’ Meeting held on March 26, 2015, the exchange contracted for on September 8, 2014 by Oi, TmarPart, PT SGPS, Portugal Telecom International Finance B.V. (“PT Finance”) and PT Portugal, SGPS, S.A. (“PT Portugal”) was consummated, under which PT SGPS transferred 47,434,872 Oi common shares and 94,869,744 Oi preferred shares to PT Finance; and

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Oi, through PT Finance, in turn, transferred to PT SGPS securities issued by Rio Forte Investments, S.A. in the aggregate principal amount of €897 million, without remainder (the “Exchange”).

As a result of the consummation of the Exchange, PT SGPS’s direct interest in Oi declined from 104,580,393 common shares and 172,025,273 preferred shares, representing 37.66% of the voting capital (ex-treasury) and 32.82% of the total share capital of Oi (ex-treasury), to 57,145,521 common shares and 77,155,529 preferred shares, representing 24.81% of the voting capital (ex-treasury) and 19.17% of the total share capital of Oi (ex-treasury). Oi’s shares received by PT Finance as a result of the Exchange remain in treasury.

Pursuant to the terms of the Option Agreement entered into on September 8, 2014between PT SGPS, PT Finance, PT Portugal, Oi and TmarPart, and amended on the date hereof, the call option to acquire Oi’s shares granted to PT SGPS becomes exercisable from the date hereof for a period of six years, according to the terms and conditions already disclosed to the market.

*            *           *

Oi will maintain its shareholders and the market informed of any developments of relevant events related to the matters described in this Material Fact.

Rio de Janeiro, March 31, 2015.

Oi S.A.

Bayard De Paoli Gontijo

Chief Executive and Financial Officer and Investor Relations Officer

Additional Information and Where to Find It:

This Material Fact is for informational purposes only and is not an offer to purchase or a solicitation of an offer to sell any shares of Oi. The proposed Voluntary Exchange of Preferred Shares described in this Material Fact has not commenced.

Any offer to purchase or the solicitation of an offer to sell preferred shares of Oi will be made only pursuant to an offer to purchase and related materials that Oi intends to file with the SEC upon commencement of this offer. Oi urges shareholders who are eligible to participate in the Voluntary Exchange of Preferred Shares to carefully read the offer to purchase and related materials relating to the Voluntary Exchange of

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Preferred Shares when they become available and prior to making any decisions with respect to the Voluntary Exchange of Preferred Shares as these documents will contain important information about the Voluntary Exchange of Preferred Shares.

Following the filing with the Commission of (1) the offer to purchase and related materials relating to the Voluntary Exchange of Preferred Shares, or (2) any other offer materials related to the Voluntary Exchange of Preferred Shares, shareholders of Oi will be able to obtain the filed documents free of charge on the SEC’s website at www.sec.gov or from Oi.

Special Note Regarding Forward-Looking Statements:

This Material Fact contains forward-looking statements within the meaning of the U.S. Private Securities Litigation Reform Act of 1995 and Brazilian applicable regulation. Statements that are not historical facts, including statements regarding the beliefs and expectations of Oi and TmarPart, business strategies, future synergies and cost savings, future costs and future liquidity are forward-looking statements. The words “will,” “may,” “should,” “could,” “anticipates,” “intends,” “believes,” “estimates,” “expects,” “forecasts”, “plans,” “targets,” “goal” and similar expressions, as they relate to Oi, TmarPart or their respective management, are intended to identify forward-looking statements. There is no guarantee that the expected events, tendencies or expected results will actually occur. Such statements reflect the current views of Oi’s or TmarPart’s management and are subject to a number of risks and uncertainties. These statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, corporate approvals, operational factors and other factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations. All forward-looking statements attributable to Oi, TmarPart or their respective affiliates, or persons acting on their behalf, are expressly qualified in their entirety by the cautionary statements set forth in this paragraph. Undue reliance should not be placed on such statements. Forward-looking statements speak only as of the date they are made. Except as required under the Brazilian and U.S. federal securities laws and the rules and regulations of the CVM, the SEC or of regulatory authorities in other applicable jurisdictions, Oi, TmarPart and their respective affiliates do not have any intention or obligation to update or to publicly announce the results of any revisions to any of the forward-looking statements to reflect actual results, future events or developments, changes in assumptions or changes in other factors affecting the forward-looking statements. You are advised, however, to consult any further disclosures Oi or TmarPart makes on related subjects in reports and communications that Oi and TmarPart file with the SEC.

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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.

Date: April 1, 2015

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.

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