Exhibit 99.1

RESMED INC ANNOUNCES FINANCIAL RESULTS FOR THE

QUARTER AND NINE MONTHS ENDED MARCH 31, 2008

SAN DIEGO, California, May 1, 2008 - ResMed Inc. (NYSE: RMD) today announced revenue and income results for the quarter ended March 31, 2008. Revenue for the quarter was $211.8 million, a 16% increase over the quarter ended March 31, 2007. For the current quarter, income from operations and net income were $37.4 million and $29.7 million, respectively. Diluted earnings per share for the quarter ended March 31, 2008 was $0.38. Net income and diluted earnings per share both increased by 12% compared to the quarter ended March 31, 2007, excluding voluntary product recall expenses incurred in the March 2007 quarter. Gross margin was 60% for the quarter ended March 31, 2008.

SG&A costs were $70.1 million for the quarter, an increase of $8.8 million or 14% over the same period in fiscal 2007. SG&A costs were 33% of revenue in the March 2008 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 necessary to support our 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 $15.0 million, or approximately 7% of revenue. R&D expenses increased 15% year over year and are expected to remain at approximately 7% of net revenue for the last quarter of 2008. The increase in research and development outlays reflects ResMed’s continuing commitment to innovation within its 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 $2.0 million ($1.3 million net of tax) incurred during the quarter ended March 31, 2008, consisted of amortization of assets associated with our acquisitions of Resprecare, Hoefner, Saime, PolarMed and Pulmomed. Stock-based compensation costs incurred during the quarter ended March 31, 2008 of $5.6 million ($4.3 million net of tax) consisted of expenses associated with stock options granted to employees and with our employee stock purchase plan.

The company also announced several non-routine events that occurred during the quarter. The company donated $2.0 million ($1.3 million net of tax) to the ResMed Foundation. The Foundation was established to promote research into the deleterious medical consequences of untreated sleep-disordered breathing. As previously announced, the company also completed the sale and leaseback of our corporate headquarters in San Diego, and as a result, we recognized a gain on the sale of $5.9 million ($3.7 million net of tax) in the March 2008 quarter. Additionally, the company made the decision to write-down certain at-cost investments by $3.2 million ($2.6 million net of tax) due to a decline in their value and the determination that the impairment was other than temporary. The net after-tax impact of these non-routine transactions was a $0.2 million decrease in net income for the quarter ended March 2008.

For the nine months ended March 31, 2008 revenues were $600.2 million, an increase of 14% over the nine months ended March 31, 2007. For the nine months ended March 31, 2008, income from operations and net income were $106.0 million and $80.7 million, respectively. GAAP diluted earnings per share for the nine months ended March 31, 2008 was $1.02 per diluted share.

Inventory, at $169.5 million, increased by $3.1 million compared to the quarter ended December 2007. Accounts receivable days sales outstanding, at 73 days, decreased by 2 days compared to the quarter ended December 2007.

Kieran T. Gallahue, President and Chief Executive Officer, commented, “In the third quarter of fiscal 2008, overall sales outside of the Americas totaled $112.2 million, a 27% increase over the prior year quarter. Americas sales were $99.6 million, an increase of 5% over the prior year quarter. Cash flow from operations for the March quarter was $33.9 million.”

Mr. Gallahue continued, “As we move into the final quarter of fiscal 2008, we are excited about the Americas launch of our S8 II flow generator platform with Easy-Breathe technology. This technology was launched earlier this year in markets outside the Americas and has been very well received by both patients and clinicians. In addition, we will also launch a redesigned nasal pillows mask during the quarter. The Swift LT will add to our existing nasal pillows franchise, as the Swift II will continue to be sold worldwide.”

“In March, both Medicare and Aetna approved the use of home sleep testing to diagnose patients with sleep-disordered breathing. This decision will complement the existing channel and allow patients the option to be diagnosed in their homes. As the industry adapts to this significant change, we will continue to support our sleep physicians and other partners in the sleep community as they evolve their patient care and business models in response to this ruling. In time, the introduction of home sleep testing as a complement to the current diagnostic pathways should vastly increase patient access to therapy. This new diagnostic pathway will begin to ramp up over the course of the next 12 to 18 months, and it will dovetail nicely with the efforts we have made in developing new markets, including diabetes, occupational health and cardiology.”

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 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 Time today to discuss these quarterly results. Individuals wishing to access the conference call may do so via ResMed’s Web site at www.resmed.com or by dialing (866) 202-4367 (domestic) or +1 (617) 213-8845 (international) and entering conference I.D. No.59350033. 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.22453137.

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 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.

- More -

RESMED INC AND SUBSIDIARIES

Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

- More -

RESMED INC AND SUBSIDIARIES

Consolidated Balance Sheets (Unaudited)

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

- End -