A runflat tire system comprises a pneumatic tire, a wheel rim on which the pneumatic tire is mounted, and a support ring made of elastic material and disposed in a cavity surrounded by an inner surface of the rim and an inner surface of the tire mounted thereon, wherein the support ring comprises an annular body extending in a circumferential direction of the tire and provided with a plurality of hollows opening at the cavity, and at least one noise damper made of sponge material having apparent density of 0.1 g/cm.sup.3 or less and disposed in the hollow such that the noise damper does not protrude into the cavity from an inlet surface of the hollow.