Exhibit 99.1

RESMED INC. ANNOUNCES RECORD FINANCIAL RESULTS FOR THE

QUARTER AND TWELVE MONTHS ENDED JUNE 30, 2013

SAN DIEGO, August 1, 2013—ResMed Inc. (NYSE: RMD) today announced record revenue and income for the quarter ended June 30, 2013. Revenue for the quarter ended June 30, 2013 was $414.6 million, an 11% increase (also an 11% increase on a constant currency basis) over the quarter ended June 30, 2012. For the quarter ended June 30, 2013, GAAP income from operations was $86.2 million, while GAAP net income was $73.0 million or $0.50 per diluted share. These results were impacted by a $24.8 million ($17.7 million, net of tax) charge for our previously announced Sydney University education, research and settlement expenses. For the quarter ended June 30, 2013, non-GAAP operating income and non-GAAP net income were $110.9 million and $90.7 million, an increase of 24% and 18%, respectively, compared to the quarter ended June 30, 2012 (non-GAAP measures exclude the impact of the charge for Sydney University education, research and settlement expenses, as described below). Non-GAAP diluted earnings per share for the quarter ended June 30, 2013 were $0.62, an increase of 17% compared to the quarter ended June 30, 2012.

SG&A expenses were $115.1 million for the quarter ended June 30, 2013, an increase of $9.1 million, or 9% (also a 9% increase on a constant currency basis) compared to the quarter ended June 30, 2012. SG&A costs were 27.8% of revenue in the quarter ended June 30, 2013, compared to 28.5% for the quarter ended June 30, 2012.

R&D expenses were $31.4 million for the quarter ended June 30, 2013, or 7.6% of revenue. R&D expenses increased by 12% (a 14% increase on a constant currency basis) compared to the quarter ended June 30, 2012. R&D expenses were favorably impacted by the depreciation of the Australian dollar against the U.S. dollar.

The company amortized acquired intangibles of $2.5 million ($1.9 million, net of tax) during the quarter ended June 30, 2013. Stock-based compensation costs incurred during the quarter ended June 30, 2013 of $10.5 million ($6.6 million, net of tax) consisted of expenses associated with stock options, restricted stock units, and our employee stock purchase plan.

As disclosed in our May press release, we reached an agreement with the University of Sydney (“University”) to pay $24.8 million for the establishment of two perpetual academic chairs, the funding of future research in the fields of sleep medicine and biomedical engineering and the settlement of legal proceedings between the parties. We have expensed the full amount of $24.8 million ($17.7 million, net of tax) in the current quarter within our operating expenses and we have separately disclosed the amount as an education, research and settlement charge.

For the year ended June 30, 2013, revenue was $1.5 billion, an increase of 11% over the year ended June 30, 2012 (a 12% increase on a constant currency basis). For the year ended June 30, 2013, GAAP net income was $307.1 million, an increase of 21% compared to the year ended June 30, 2012. GAAP diluted earnings per share for the year ended June 30, 2013 were $2.10, an increase of 23% compared to the year ended June 30, 2012. For the year ended June 30, 2013, non-GAAP operating income and non-GAAP diluted earnings per share were $379.6 million and $2.22, an increase of 29% and 30%, respectively, compared to the year ended June 30, 2012.

Additionally, the Board of Directors has today declared a quarterly dividend of $0.25 per share, which will have a record date of August 20, 2013, and be payable on September 17, 2013. The dividend will be paid in U.S. currency to holders of ResMed’s common stock trading on the New York Stock Exchange (NYSE). Holders of CHESS Depositary Instruments (CDIs) trading on the Australian Securities Exchange (ASX) will receive an equivalent amount in Australian currency, based on the exchange rate on the record date, and reflecting the 10:1 ratio between CDIs and NYSE shares. Because the two exchanges have different settlement and transfer procedures, the ex-dividend date will be August 14, 2013 for CDI holders and August 16, 2013 for common stock holders. As a result of these differences, ResMed has received a waiver from the ASX’s settlement operating rules, which will allow ResMed to defer processing conversions between its common stock and CDI registers from August 14, 2013 through August 20, 2013, inclusive.

Mick Farrell, chief executive officer, commented, “In the fourth quarter of fiscal 2013 we showed strong year-over-year growth on both top and bottom lines. Revenue in the Americas increased by 11% over the prior year’s quarter to $230.3 million for Q4. Revenue in Europe and Asia-Pac combined reached $184.3 million, an increase of 12% (an 11% increase on a constant currency basis) over the prior year’s quarter. Non-GAAP operating profit for the June quarter was $110.9 million, cash flow from operations was a record $123.9 million, while gross margin was 62.7%, all demonstrating excellent operating performance. We have also announced today that our quarterly dividend has increased by 47% to $0.25 per share. Additionally, during the quarter, we repurchased 1.5 million shares, at a cost of $72.7 million. The increased dividend and the ongoing share buy-back program demonstrate our commitment to a robust capital management program.

“We had many other accomplishments this quarter to report. The Serve-HF heart failure trial is fully enrolled with over 1,325 patients. In addition, we have finalized the protocol for our U.S. heart failure trial, CAT-HF and intend to begin enrollment this fall. We introduced VPAP™ COPD, a first-of-its-kind respiratory product for those suffering from chronic obstructive pulmonary disease (COPD), and it is already doing well. We launched the Quattro™ Air full face mask globally. This new mask is the lightest full face mask on the market, weighing in at just 3.3 ounces, making it 45 percent lighter than its predecessor and the current #1 seller in the U.S., the Mirage Quattro™. During the quarter, we also launched ResMed’s SleepSeeker – which is an online tool to increase patient engagement in therapy for sleep-disordered breathing. With SleepSeeker, patients will be able to view their own therapy data, including time on therapy, any apnea or hypopnea events, and any mask leaks during the night. Our aim is to improve therapy compliance through better patient engagement. These solutions will help in the management and control of various chronic diseases associated with both COPD and untreated sleep-disordered breathing.”

About ResMed

ResMed is a global leader in the development, manufacturing and marketing of medical products for the diagnosis, treatment and management of respiratory disorders, with a focus on sleep-disordered breathing. The company is 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 website at www.resmed.com or by dialing 847-585-4405 (domestic) or +1 847-585-4405 (international) and entering conference pass code no. 35164091. 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 30 minutes after the live call and will be available for two weeks. A telephone replay of the conference call is available by dialing 630-652-3042 (domestic) and +1 630-652-3042 (international) and entering conference I.D. No. 35164091.

Further information can be obtained by contacting Constance Bienfait at ResMed Inc., San Diego, at (858) 836-5971; 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 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 Website.

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RESMED INC AND SUBSIDIARIES

Condensed Consolidated Statements of Income (Unaudited)

(In US$ thousands, except per share data)

	Three Months Ended June 30,					Twelve Months Ended June 30,
	2013			2012		2013			2012
Net revenue	$	414,607		$	371,929	$	1,514,457		$	1,368,515
Cost of sales		154,759			145,460		573,800			547,780
Gross profit		259,848			226,469		940,657			820,735
Operating expenses:
Selling, general and administrative		115,057			105,909		430,802			402,621
Research and development		31,390			27,911		120,124			109,733
Education, research and settlement charge (1)		24,765			—		24,765			—
Amortization of acquired intangible assets		2,471			2,919		10,142			13,974
Total operating expenses		173,683			136,739		585,833			526,328
Income from operations (1)		86,165			89,730		354,824			294,407
Other income (expenses), net:
Interest income (expense), net		7,439			7,326		32,486			29,080
Other, net		(5,777	)		1,454		(2,191	)		8,458
Total other income (expenses), net		1,662			8,780		30,295			37,538
Income before income taxes		87,827			98,510		385,119			331,945
Income taxes		14,814			21,663		77,986			77,095
Net income (1)	$	73,013		$	76,847	$	307,133		$	254,850
Basic earnings per share	$	0.51		$	0.54	$	2.15		$	1.75
Diluted earnings per share (1)	$	0.50		$	0.53	$	2.10		$	1.71
Non-GAAP diluted earnings per share, excluding the impact of the education, research and settlement charge (1)	$	0.62		$	0.53	$	2.22		$	1.71
Basic shares outstanding		142,669			142,788		142,954			145,901
Diluted shares outstanding		146,115			146,099		146,410			149,316

⁽¹⁾  See reconciliation of non-GAAP financial measures in table at end of press release.

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RESMED INC AND SUBSIDIARIES

Condensed Consolidated Balance Sheets (Unaudited)

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

	June 30, 2013			June 30, 2012
ASSETS
Current assets:
Cash and cash equivalents	$	876,048		$	809,541
Accounts receivable, net		318,349			283,160
Inventories		145,847			174,351
Prepayments, deferred income taxes and other current assets		108,605			94,099
Total current assets		1,448,849			1,361,151
Property, plant and equipment, net		411,433			434,363
Goodwill		274,829			256,209
Other intangibles		49,639			54,827
Deferred income taxes and other non-current assets		25,971			31,319
Total non-current assets		761,872			776,718
Total assets	$	2,210,721		$	2,137,869
LIABILITIES AND STOCKHOLDERS’ EQUITY
Current liabilities:
Accounts payable		60,688			55,006
Accrued expenses		137,674			127,381
Deferred revenue		44,953			41,563
Income taxes payable		30,090			27,777
Deferred income taxes		627			1,073
Current portion of long-term debt		300,017			52
Total current liabilities		574,049			252,852
Non-current liabilities:
Deferred income taxes		9,895			8,843
Deferred revenue		11,928			14,384
Income taxes payable		3,564			3,380
Non-current portion of long-term debt		769			250,783
Total non-current liabilities		26,156			277,390
Total liabilities		600,205			530,242
Stockholders’ Equity:
Common stock		568			568
Additional paid-in capital		1,025,064			899,717
Retained earnings		1,576,641			1,366,712
Treasury stock		(1,083,845	)		(895,826	)
Accumulated other comprehensive income		92,088			236,456
Total stockholders’ equity		1,610,516			1,607,627
Total liabilities and stockholders’ equity	$	2,210,721		$	2,137,869

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Reconciliation of Non-GAAP Financial Measures (Unaudited)

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

The measure, “non-GAAP operating income” is reconciled with GAAP income from operations in the table below:

	Three Months Ended June 30,				Year Ended June 30,
	2013		2012		2013		2012
GAAP income from operations		86,165		89,730		354,824		294,407
Education, research and settlement charge (A)		24,765		—		24,765		—
Non-GAAP operating income (excluding the impact of the education, research and settlement charge)		110,930		89,730		379,589		294,407

The measure, “non-GAAP net income” and “non-GAAP diluted earnings per share” are reconciled with GAAP net income and GAAP diluted earnings per share in the table below:

	Three Months Ended June 30,				Year Ended June 30,
	2013		2012		2013		2012
GAAP net income		73,013		76,847		307,133		254,850
Education, research and settlement charge, net of tax (A)		17,707		—		17,707		—
Non-GAAP net income (excluding the impact of the education, research and settlement charge)		90,720		76,847		324,840		254,850
Diluted shares outstanding		146,115		146,099		146,410		149,316
GAAP diluted earnings per share	$	0.50	$	0.53	$	2.10	$	1.71
Non-GAAP diluted earnings per share (excluding the impact of the education, research and settlement charge)	$	0.62	$	0.53	$	2.22	$	1.71

^(A)  The education, research and settlement charge relates to an agreement with the University of Sydney (“University”) to pay A$25 million (US$24.8 million) for the following.

• A$10 million for the establishment of two perpetual academic chairs called the ResMed Chair of Sleep Medicine for sleep-disordered breathing with a focus on chronic disease and the ResMed Chair of Biomedical Engineering with an emphasis on bioinformatics research.

• A$5 million in equal installments, over five years, to be used by the University to support research in the fields of sleep medicine and biomedical engineering.

• A$10 million in settlement of proceedings between the parties, including A$1.25 million for the release from the proceedings and A$8.75 million for royalties payable under the license agreement.

ResMed believes that presenting diluted earnings per share, excluding the impact of the charge for Sydney University education, research and settlement expenses is an additional measure of performance that investors can use to compare operating results between reporting periods. We believe the expenses are not associated with the Company’s normal operating business.

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. 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. 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.

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