Exhibit 99.1

RESMED INC ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER ENDED SEPTEMBER 30, 2008

SAN DIEGO, California, November 6, 2008 - ResMed Inc. (NYSE: RMD) today announced record revenue and income results for the quarter ended September 30, 2008. Revenue for the quarter was $217.9 million, a 17% increase over the quarter ended September 30, 2007. For the current quarter, income from operations was $36.6 million and net income was $28.0 million, an increase of 15% and 16%, respectively, compared to the quarter ended September 30, 2007. Diluted earnings per share for the quarter ended September 30, 2008 was $0.36, an increase of 16% compared to the quarter ended September 30, 2007.

SG&A costs were $71.3 million for the quarter, an increase of $8.5 million or 13% over the same period in fiscal 2007. The increase in SG&A was primarily due to expenses necessary to support sales growth and the net appreciation of international currencies against the US dollar. SG&A costs were 33% of revenue in the September 2008 quarter, compared to 34% in the same period in fiscal 2007.

R&D expenses during the quarter were $17.3 million, or approximately 8% of revenue. R&D expenses increased 33% year over year. 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 US dollar.

Amortization of acquired intangibles of $1.9 million ($1.3 million net of tax) incurred during the quarter ended September 30, 2008, consisted of amortization of assets associated with our acquisitions of Resprecare, Hoefner, Saime and PolarMed. Stock-based compensation costs incurred during the quarter ended September 30, 2008 of $5.6 million ($3.9 million net of tax) consisted of expenses associated with stock options granted to employees and with our employee stock purchase plan.

Inventory, at $145.6 million, decreased by $12.7 million compared to June 30, 2008. Accounts receivable days sales outstanding, at 75 days, increased by 3 days compared to June 30, 2008.

Kieran T. Gallahue, President and Chief Executive Officer, commented, “In the first quarter of fiscal 2009, we continued to show strong and balanced growth across the globe. Sales outside of the Americas totaled $104.3 million, an 18% increase over the prior year quarter, while sales in the Americas were $113.6 million, an increase of 16% over the prior year quarter. Cash flow from operations for the September quarter was a record $67.9 million. Our robust operating cash flows, in addition to our strong and conservative balance sheet, position us well in the current economic environment.”

Mr. Gallahue continued, “As we move into the second quarter of fiscal 2009, we are well-positioned to grow revenues. We are encouraged by the sales growth of our S8II flow generator platform and Swift LT nasal pillows mask. Our new product release schedule remains active, particularly in both the mask and bilevel categories. We are introducing new masks in both Europe and the US during the second quarter, including the Americas release of Swift LT for Her. This is the first and only nasal pillows product designed and marketed specifically for female patients. Additionally, we released a series of new bilevels in Europe and the VPAP S in the Americas. All of these bilevels utilize our patented Easy-Breathe motor technology, providing unparalleled performance at up to 90% less noise than other leading competitors. We continue to invest aggressively in developing new technologies and products to serve the growing sleep-disordered breathing marketplace, while maintaining prudent fiscal management.”

“Global progress in our efforts to educate and validate the role of sleep-disordered breathing in comorbid patient populations took a major step forward in the last three months. In September, the European Society of Cardiology published guidelines for the diagnosis and treatment of acute and chronic heart failure. For the first time, the guidelines noted that patients with symptomatic heart failure frequently have sleep-related disorders (central or obstructive sleep apnea) and recommended treatment with CPAP for patients diagnosed with obstructive sleep apnea. This follows just three months after the International Diabetes Federation issued a consensus statement on sleep-disordered breathing and type II diabetes, where the substantial value of identifying and treating diabetic patients suffering from sleep-disordered breathing was also recognized and recommended. The increasing awareness among comorbidity specialists augurs well for the efforts and investment we are making in 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. US Pacific 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 (800) 261-3417 (domestic) or +1 (617) 614-3673 (international) and entering conference I.D. No. 49480223. 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. 99471059.

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.

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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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