Exhibit 99.1

RESMED INC. ANNOUNCES PLAN TO INITIATE DIVIDEND

AND UPDATE ON CHIEF EXECUTIVE OFFICER SUCCESSION

SAN DIEGO, California, May 17, 2012 – ResMed Inc. (NYSE: RMD) today announced plans to initiate a dividend beginning in fiscal year 2013.

Subject to declaration by the board of directors, ResMed plans to initiate a quarterly dividend of $0.17 per share in the first quarter of its fiscal 2013, which begins on July 1, 2012. ResMed plans to pay the dividend in US currency to holders of its common stock trading on the New York Stock Exchange (NYSE). Holders of Chess Depositary Instruments (CDIs) trading on the Australian Stock Exchange will receive an equivalent amount in Australian currency, based on the exchange rate on the record date, and reflecting the 10:1 ratio between CDIs and NYSE shares. ResMed expects the dividend will be unfranked for Australian tax purposes.

“Over the past several years, we have used some of our cash to invest in our business through increased research and development, market development, acquisitions, and capital expenditures,” said Peter C. Farrell, Ph.D., ResMed’s chairman and chief executive officer. “We have also used some of our cash to repurchase shares. We expect to continue all these activities in the future. Even with these investments, we have sufficient funds for strategic opportunities and to operate our business and therefore, we are initiating a dividend for our shareholders. We are confident about our future and see exciting opportunities ahead.”

Additionally, ResMed’s board of directors has reaffirmed its current process for chief executive officer succession. The board of directors has requested that Dr. Peter Farrell remain as chief executive officer until the end of calendar 2013, which he has agreed to do. In the meantime, potential internal chief executive officer candidates will continue to be evaluated. When the board decides that there are suitable internal candidates for the role, the board plans to compare and contrast those candidates with potential external candidates. The process is expected to be completed by the end of 2013.

About ResMed

ResMed is a global leader in the development, manufacturing and marketing of medical products for the diagnosis, treatment and management of respiratory disorders, with a focus on sleep-disordered breathing. The Company is dedicated to developing innovative products to improve the lives of those who suffer from these conditions and to increasing awareness among patients and healthcare professionals of the potentially serious health consequences of untreated sleep-disordered breathing. For more information on ResMed, visit www.resmed.com.

Further information can be obtained by contacting Constance Bienfait at ResMed Inc., San Diego, at (858) 836-5971; Brett Sandercock at ResMed Limited, Sydney, on (+612) 8884-2090; or by visiting the Company’s multilingual Website at www.resmed.com.

Statements contained in this release that are not historical facts are “forward-looking” statements as contemplated by the Private Securities Litigation Reform Act of 1995. These forward-looking statements, including statements regarding the Company’s future revenue, earnings or expenses, new product development and new markets for the Company’s products, are subject to risks and uncertainties, which could cause actual results to materially differ from those projected or implied in the forward-looking statements. Those risks and uncertainties are discussed in the Company’s Annual Report on Form 10-K for its most recent fiscal year and in other reports the Company files with the U.S. Securities & Exchange Commission. Those reports are available on the Company’s Website.

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