Exhibit 99.1

RESMED ANNOUNCES RECORD FINANCIAL RESULTS

FOR QUARTER ENDED SEPTEMBER 30, 2005

SAN DIEGO, California, November 2, 2005 - ResMed Inc (NYSE: RMD) today announced record revenue and income results for the quarter ended September 30, 2005. Revenue for the quarter was $127.1 million, a 45% increase over the quarter ended September 30, 2004. Excluding the incremental revenue contribution from acquisitions, revenue was $114.1 million, an increase of 30%. For the September 30, 2005 quarter, income from operations and net income, excluding the impact of stock-based compensation costs, restructuring expenses and acquisition related costs described below, were $30.4 million and $20.7 million, an increase of 33% and 37% respectively. Diluted earnings per share, excluding the impact of stock-based compensation costs, restructuring expenses and acquisition related costs, for the quarter ended September 30, 2005, was $0.28, an increase of 33%, compared to the September 2004 quarter. Net income for the current quarter was $16.4 million or $0.23 per diluted share including after-tax stock-based compensation costs, restructuring expenses and acquisition related costs of $4.3 million. Gross margin was 63% for the quarter ended September 30, 2005.

Selling, general and administration (SG&A) costs for the quarter were $41.8 million, an increase of $15.1 million over the same period in fiscal 2005, excluding stock-based compensation costs. SG&A was 33% of revenue in the September quarter, compared to 30% in the same period in fiscal 2005, due to recent acquisitions, the addition of selling and administration personnel, and infrastructure investment in Europe.

Research and development expenditure during the quarter was $7.9 million, or approximately 6% of revenues, excluding stock-based compensation costs. R&D expense increased 16% during the quarter ended September 30, 2005 from $6.8 million in the quarter ended September 30, 2004 reflecting ResMed’s continuing commitment to clinical research and product development. ResMed intends to continue to spend approximately 6% of revenues on R&D during the rest of fiscal year 2006.

Restructuring expenses incurred during the quarter ended September 30, 2005, of $1.0 million ($0.6 million net of tax) predominantly consisted of expenses associated with the previously-announced integration of the Company’s German operations. Acquisition related expenses of $1.5 million ($1.0 million net of tax) incurred during the quarter ended September 30, 2005, consisted of amortization of acquired intangible assets associated with our acquisitions of Resprecare, Hoefner, Saime and Pulmomed. Stock-based compensation costs incurred during the quarter ended September 30, 2005, of $3.4 million ($2.6 million net of tax) consisted of expenses associated with stock options granted to employees and the employee stock purchase plan. The recognition of these stock-based compensation expenses is in accordance with FASB No. 123(R), which was adopted for the first time in the current quarter.

To accompany the above financial information, the Company is providing tabular reconciliation of GAAP operating income and GAAP net income with operating income (and net income), excluding the impact of stock-based compensation costs, restructuring expenses and amortization of acquired intangibles, for the quarters ended September 30, 2005, and September 30, 2004.

Inventory, at $100.9 million, increased by $11.8 million compared to June 2005 levels primarily to accommodate sales growth, particularly in the domestic market. Accounts receivable days sales outstanding, at 71 days, were consistent with the June 2005 quarter.

Peter C. Farrell, PhD, Chairman and Chief Executive Officer, commented, “In the first quarter of fiscal 2006, domestic sales increased by a very robust 47% over the year ago quarter to $66.9

-More-

million, reflecting strong demand for our new Mirage Swift^™ patient interface and full face mask as well as a favorable reception to the S8^™ flow generator platform. International sales, including incremental revenue contributions from the acquisitions of Resprecare, Hoefner, Saime and Pulmomed, totaled $60.2 million, a 43% increase over last year. Organically, international sales increased to $47.2 million, or 12% growth compared to the September 2004 quarter; and this growth occurred without the S8 platform being fully released within Europe. Net income for the September quarter, excluding stock-based compensation costs, restructuring and acquisition-related expenses, was $20.7 million, an increase of 37% over the same period in 2004, due primarily to strong sales growth. Our operating cash flow for the September quarter was $15.9 million.”

Dr. Farrell further continued, “During the past year, we have expanded our international operations with several strategic acquisitions. The latter have contributed ventilation products, technologies and expertise, as well as management depth, integrated distribution channels, and an expanded reach within Europe. Our team has done an excellent job integrating these acquisitions and positioning ResMed for future growth in Europe. Recently, we also entered into an agreement to acquire PolarMed Holdings AS, a leading Scandinavian distributor with offices in Norway, Sweden and Denmark. We are delighted that Stein Jacobsen, the owner of PolarMed, has agreed to direct ResMed’s operations in this growing market and to contribute his expertise in the ventilation market. Finally, we continue to make headway in the heart failure space and we are particularly happy with the recent FDA approval of VPAP Adapt SV^™, our adaptive servo-ventilation device which treats periodic breathing or Cheyne-Stokes respiration, the major breathing disorder associated with severe congestive heart failure.”

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) 362-4832 (domestic) or +1 (617) 597-5364 (international) and entering conference I.D. No. 58193457. 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. 54530695.

Further information can be obtained by contacting Hillary Theakston at ResMed Inc in San Diego (858) 746-2610; Brett Sandercock at ResMed Limited in Sydney on (+61 2) 9886-5406; 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 US 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)

-More-

Reconciliation of Non-GAAP Financial Measures (Unaudited)

(Dollars in thousands except per share amounts)

In managing its business, ResMed makes use of certain non-GAAP financial measures in evaluating the Company’s results of operations. The measure, “operating income, excluding the impact of stock-based compensation costs, restructuring expenses and amortization of acquired intangible assets” is reconciled with GAAP operating income in the table below:

The measure “net income, excluding the impact of stock-based compensation costs, restructuring expenses and amortization of acquired intangible assets,” is reconciled with GAAP net income in the table below:

ResMed believes that presenting diluted earnings per share, excluding the impact of stock-based compensation costs, restructuring expenses and amortization of acquired intangible assets, is an additional measure of performance that investors can use to compare operating results between reporting periods. Management of the Company uses non-GAAP information internally in planning, forecasting and evaluating the Company’s results of operations in the current period and in comparing it to past periods. The Company also uses these non-GAAP measures in evaluating management performance for compensation purposes. Management believes that this information also provides investors better insight in evaluating the Company’s earnings performance from core operations, and provides consistency in financial reporting.

The Company initially adopted FASB No. 123(R) on July 1, 2005 using the modified prospective method, which resulted in stock-based compensation expenses being recognized during the quarter ended September 30, 2005 without corresponding expenses in the quarter ended September 30, 2004. In addition, the events giving rise to the restructuring expenses are not associated with the Company’s normal operating business and are expected to result in future market opportunities, cost savings, and other benefits.

Management believes disclosure of non-GAAP earnings has economic substance because the excluded expenses represent non-cash expenditures, or relate to transactions that are variable in nature between reporting periods.

Our use of non-GAAP earnings is intended to supplement, and not to replace, our presentation of net income and other GAAP measures. Like all non-GAAP measures, non-GAAP earnings are subject to inherent limitations because they do not include all the expenses that must be included under GAAP. We compensate for the inherent limitations of non-GAAP measures by not relying exclusively on non-GAAP measures, but rather by using such information to supplement GAAP financial measures.

-More-

Reconciliation of Basic and Diluted Earnings per Share (Unaudited)

(Dollars in thousands except per share amounts)

-End-