EXHIBIT 32.1

The following certifications are being furnished solely to accompany the Report pursuant to 18 U.S.C. § 1350 and in accordance with SEC Release No. 33-8238. These certifications shall not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, nor shall they be incorporated by reference in any filing we make under the Securities Act of 1933, as amended, whether made before or after the date hereof, regardless of any general incorporation language in such filing.

Certification of Chief Executive Officer

Pursuant to 18 U.S.C. § 1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of ResMed Inc., a Delaware corporation (the “Company”), hereby certifies, to his knowledge, that:

(i) the accompanying Annual Report on Form 10-K of the Company for the year ended June 30, 2012 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 13, 2012

/s/ PETER C. FARRELL

Peter C. Farrell

Chairman, chief executive officer and president

(principal executive officer)

A signed original of this written statement required by Section 906 has been provided to ResMed Inc. and will be retained by ResMed Inc. and furnished to the Securities and Exchange Commission or its staff upon request.

Certification of Chief Financial Officer

Pursuant to 18 U.S.C. § 1350, as created by Section 906 of the Sarbanes-Oxley Act of 2002, the undersigned officer of ResMed Inc., a Delaware, corporation (the “Company”), hereby certifies, to his knowledge, that:

(i) the accompanying Annual Report on Form 10-K of the Company for the year ended June 30, 2012 (the “Report”) fully complies with the requirements of Section 13(a) or Section 15(d), as applicable, of the Securities Exchange Act of 1934, as amended; and

(ii) the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: August 13, 2012

/s/ BRETT A. SANDERCOCK

Brett A. Sandercock

Chief financial officer

A signed original of this written statement required by Section 906 has been provided to ResMed Inc. and will be retained by ResMed Inc. and furnished to the Securities and Exchange Commission or its staff upon request.