Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND NINE MONTHS ENDED MARCH 31, 2009

SAN DIEGO, California, May 7, 2009 - ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended March 31, 2009. Revenue for the March 2009 quarter was $227.9 million, an 8% increase (a 16% increase on a constant currency basis) over the quarter ended March 31, 2008. For the quarter ended March 31, 2009, income from operations was $52.5 million and net income was $39.2 million, an increase of 40% and 32%, respectively, compared to the quarter ended March 31, 2008. Diluted earnings per share for the quarter ended March 31, 2009 were $0.51, an increase of 34% compared to the quarter ended March 31, 2008.

SG&A expenses were $70.9 million for the March 2009 quarter, an increase of $0.7 million, or 1% (a 13% increase on a constant currency basis) over the same period in fiscal 2008. SG&A expenses were favorably impacted by the appreciation of the U.S. dollar against international currencies. This increase in SG&A was primarily due to expenses necessary to support sales growth. SG&A costs were 31% of revenue in the March 2009 quarter, compared to 33% in the same period in fiscal 2008.

R&D expenses were $13.9 million for the March 2009 quarter, or approximately 6% of revenue. R&D expenses decreased by 7% (a 22% increase on a constant currency basis) compared to the prior year quarter. R&D was also positively impacted by the appreciation of the U.S. dollar against international currencies, particularly the Australian dollar. R&D outlays reflect ResMed’s continuing commitment to innovation within its product portfolio, as well as an ongoing commitment to clinical research and product development.

Amortization of acquired intangibles of $1.7 million ($1.1 million, net of tax) incurred during the quarter ended March 31, 2009, consisted of amortization of assets associated with our acquisitions of Resprecare, Hoefner, Saime and PolarMed. Stock-based compensation costs incurred during the quarter ended March 31, 2009 of $6.7 million ($4.9 million, net of tax) consisted of expenses associated with stock options granted to employees and our employee stock purchase plan.

For the nine months ended March 31, 2009, revenue was $668.8 million, an increase of 11% over the nine months ended March 31, 2008. For the nine months ended March 31, 2009, income from operations and net income were $132.4 million and $101.1 million, an increase of 25% and 25%, respectively, compared to the nine months ended March 31, 2008. Diluted earnings per share for the nine months ended March 31, 2009 were $1.31 per diluted share, an increase of 28% compared to the nine months ended March 31, 2008.

Inventory, at $147.7 million, decreased by $10.6 million compared to June 30, 2008. Accounts receivable days sales outstanding, at 74 days, increased by 2 days compared to June 30, 2008.

Kieran T. Gallahue, President and Chief Executive Officer, commented, “In the third quarter of fiscal 2009, we continued to show strong growth year over year. Our favorable mix of product sales and market share gains led to a 23% increase in the Americas over the prior year quarter resulting in $122.5 million in revenue. As expected, sales outside the Americas were impacted by currency movements, in particular the depreciation of the Euro against the U.S. dollar. As a result, sales outside the Americas decreased by 6% to $105.4 million, but were up 10% in constant currency terms. Cash flow from operations for the March 2009 quarter was a strong $44.2 million.

“Our gross margin also expanded in Q3. This was a result of an increase in sales of our higher margin products, the depreciation of the Australian dollar and continued efforts to leverage cost efficiencies across our global organization. The market continues to respond well to our full range of products. The Easy Breathe motor technology has set a new standard in performance. Our new masks, including the Swift™ LT for Her and the Activa™ LT are well-positioned to improve patient comfort and compliance. Market efforts to improve compliance are also helping to drive sales of our feature-rich flow generators and our one-of-a-kind wireless Restraxx™ data system. We remain encouraged about the prospects for future market growth as the market for sleep disordered breathing therapy remains highly underpenetrated. As is widely known, there is a high prevalence of sleep-disordered breathing/obstructive sleep apnea in such co-morbidities as cardiac disease and diabetes, as well as in the transportation industry, and there is a vital public health need to diagnose and treat the disease in these groups. We remain committed to bringing innovative new products to market, and plan an active introductory schedule over the next 12-18 months.”

ResMed

ResMed is a leading developer, manufacturer, and distributor of medical equipment for treating, diagnosing, and managing 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 of 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 Daylight Time today to discuss these quarterly results. Individuals wishing to access the conference call may do so via ResMed’s Web site at http://investor.resmed.com or by dialing (800) 591-6945 (domestic) or +1 (617) 614-4911 (international) and entering conference I.D. No. 54922515. Please allow extra time prior to the call to visit the Web site 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. 31657251.

Further information can be obtained by contacting Connie Bienfait at ResMed Inc., San Diego, at (858) 746-2736; Brett Sandercock at ResMed Limited, Sydney, on (+612) 8884-2090; or by visiting the Company’s multilingual Web site 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 Web site.

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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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