PART II - OTHER INFORMATION EXHIBIT 32.1

RESMED INC. AND SUBSIDIARIES

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

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 Quarterly Report on Form 10-Q of the Company for the period ended September 30, 2008 (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.

November 6, 2008

/s/ KIERAN T. GALLAHUE

Kieran T. Gallahue

Chief 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. This certification will not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, or otherwise subject to the liability of that section, nor will this certification be deemed to be incorporated by reference into any filing under the Securities Act of 1933, as amended, or the Securities Exchange Act of 1934, as amended, except to the extent that the registrant specifically incorporates it by reference.

RESMED INC. AND SUBSIDIARIES

CERTIFICATION OF CHIEF FINANCIAL OFFICER

PURSUANT TO SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002

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 Quarterly Report on Form 10-Q of the Company for the period ended September 30, 2008 (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.

November 6, 2008

/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. This certification will not be deemed “filed” for purposes of Section 18 of the Securities Exchange Act of 1934, as amended, or otherwise subject to the liability of that section, nor will this certification be deemed to be incorporated by reference into any filing under the Securities Act of 1933, as amended, or the Securities Exchange Act of 1934, as amended, except to the extent that the registrant specifically incorporates it by reference.