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RESMED NAMED TO FORTUNE’S 2004 LIST
OF AMERICA’S FASTEST GROWING COMPANIES

Sydney, Australia, September 8, 2004 – ResMed Inc. (NYSE: RMD) announced today that it has
been named to FORTUNE’s annual list of America’s Fastest Growing Companies based on
annual growth in sales and earnings over the past three years and total stock market return. The
complete list and state-by-state database of the companies appeared in the September 6, 2004,
issue of FORTUNE Magazine. In June of this year, ResMed marked its 37th consecutive quarter
of growth. The company grew its sales by 24 percent over the prior year to reach $339.3 million
in revenues for the fiscal year ended June 30, 2004. Net income for the year rose 25 percent to
$57.3 million and earnings per fully diluted share were $1.63, a 23 percent increase over the prior
year. Operating income was $85.4 million, an increase of 27 percent over the prior year, and
shareholders’ equity increased 26 percent to $361.5 million.

“As pleased as I am with the results we have achieved so far, I believe we are just starting on the
journey,” stated Peter C. Farrell, PhD, Chairman and Chief Executive Officer. “ResMed has been
a consistent pioneer in the sleep business, from its entry into the market in 1989, and we continue
to innovate. We are committed to waking people up to sleep and to improving patients’ lives, by
leading the industry in both clinical education and product development. Until we have succeeded
in educating physicians and the public about the importance of healthy sleep, ignorance will
remain our biggest competitor in this industry.