Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND YEAR ENDED JUNE 30, 2008

SAN DIEGO, California, August 5, 2008 - ResMed Inc. (NYSE: RMD) today announced revenue and income results for the quarter ended June 30, 2008. Revenue for the quarter was a record $235.2 million, a 23% increase over the quarter ended June 30, 2007. For the current quarter, income from operations and net income were $37.0 million and $29.6 million, respectively. Diluted earnings per share for the quarter ended June 30, 2008 was $0.38. For the quarter ended June 30, 2008, an additional expense of $3.1 million has been recognized as a charge to cost of sales in relation to the voluntary recall we announced in April 2007 related to our previous series of S8 flow generators. We do not expect any further significant costs in relation to this recall. Excluding product recall expenses, diluted earnings per share was $0.40, an increase of 14% compared to the quarter ended June 30, 2007. Excluding product recall expenses, gross margin was 58.3% mainly as the result of encouraging growth in the U.S. market.

SG&A costs were $77.4 million for the quarter, an increase of $12.2 million, or 19%, over the same period in fiscal 2007. SG&A costs were 33% of revenue in the June quarter, compared to 34% in the same period in fiscal 2007. The increase in SG&A was primarily due to the addition of selling and administration personnel and related expenses to support sales growth. The increase in SG&A was also due to the net appreciation of international currencies against the U.S. dollar.

R&D expenses during the quarter were $17.6 million or approximately 7% of revenue. R&D expenses increased 24% year over year. The increase in research and development outlays reflects the continuing commitment to innovation within our product portfolio, as well as an ongoing commitment to clinical research and product development. The increase in R&D was also due to the net appreciation of international currencies against the U.S. dollar.

Amortization of acquired intangibles of $2.1 million, incurred during the quarter ended June 30, 2008, consisted of amortization of acquired intangible assets associated with our acquisitions of Resprecare, Hoefner, Saime, PulmoMed and PolarMed. Stock-based compensation costs incurred during the quarter ended June 30, 2008, of $5.3 million, consisted of expenses associated with stock options granted to employees and the employee stock purchase plan.

For the year ended June 30, 2008, revenue was a record $835.4 million, an increase of 17% over the $716.3 million for the year ended June 30, 2007. For the year ended June 30, 2008, income from operations and net income were $143.0 million and $110.3 million, respectively. GAAP diluted earnings per share for the year ended June 30, 2008 was $1.40 per diluted share.

Inventory was $158.3 million as of June 30, 2008, a decrease of $11.2 million compared to the March 31, 2008 level of $169.5 million. Accounts receivable days sales outstanding, at 72 days, decreased one day when compared to 73 days for the March 31, 2008 quarter.

Kieran T. Gallahue, Chief Executive Officer, commented, “In the fourth quarter of fiscal 2008, overall sales outside of the Americas totaled $123.0 million, a 32% increase over the prior year quarter. Americas’ sales were $112.2 million, an increase of 14% over the prior year quarter. Operating cash flow for the June quarter was a record $56.8 million and we repurchased $51.7 million in stock, which puts our fiscal year total at $99.5 million representing over 2.6 million shares.”

Mr. Gallahue continued, “We were pleased with the strong and balanced growth achieved by our global operations this past quarter, particularly the accelerated growth experienced in the U.S. market. We are encouraged by the traction gained from our recent product releases: the S8 II series of flow generators and the Swift LT nasal pillows mask.

“Our industry received positive signals that it is poised for continued growth. Home sleep testing took another step forward as both national and local Medicare rulings were released and private insurers, such as the country’s largest insurer, Anthem, issued updated coverage policies. Medicare competitive bidding implementation was delayed 18-24 months, a positive signal for the home medical equipment industry. Lastly, the International Diabetes Federation published an important consensus statement on sleep apnea and diabetes. The diabetes community now has an official recommendation to screen all type 2 diabetes patients suspected of sleep apnea. ResMed is well positioned to deliver strong growth in fiscal year 2009.”

About ResMed

ResMed is a leading manufacturer of medical equipment for the treatment and management of sleep-disordered breathing and other respiratory disorders. We are 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 for the potentially serious health consequences of untreated sleep-disordered breathing. For more information on ResMed, visit www.resmed.com.

ResMed will host a conference call at 1:30 p.m. U.S. Pacific Standard Time today to discuss these quarterly results. Individuals wishing to access the conference call may do so via ResMed’s website at www.resmed.com or by dialing (866) 543-6407 (domestic) or +1 (617) 213-8898 (international) and entering conference I.D. No. 31223107. Please allow extra time prior to the call to visit the website and download the streaming media player (Windows Media Player) required to listen to the Internet broadcast. The online archive of the broadcast will be available approximately 90 minutes after the live call and will be available for two weeks. A telephone replay of the conference call is available by dialing (888) 286-8010 (domestic) and +1 (617) 801-6888 (international) and entering conference I.D. No. 24669616.

Further information can be obtained by contacting Matthew Borer at ResMed Inc., San Diego, at (858) 746-2280; 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, new markets for the Company’s products and the impact of future developments related to the recently announced product recall, are subject to risks and uncertainties, which could cause actual results to materially differ from those projected or implied in the forward-looking statements. The Company cannot be certain that it has accurately predicted the costs of the product recall, which could change in response to additional feedback from ongoing discussions with the FDA and with various foreign regulatory bodies. In addition, the product recall could affect the Company’s reputation. Additional 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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RESMED INC AND SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

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RESMED INC AND SUBSIDIARIES

Consolidated Balance Sheets (Unaudited)

(In US$ thousands except share and per share data)

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