A run-flat tire-wheel assembly having, in an inside cavity of the tire/rim, a run-flat support formed by a ring-shaped metal shell and rubber elastic members or a ring-shaped metal shell and rubber elastic members composed of a rubber composition containing 100 parts by weight of a peroxide cross-linkable rubber and 1 to 30 parts by weight of a peroxide cross-linking agent, wherein the contact surfaces of the ring-shaped metal shell with the rubber elastic members are subjected to an electrolytic polymerization with 6-mono- or di-allylamino-1,3,5-triazine-2,4-dithiol or its mono- or di-salt, whereby the bondability between the ring-shaped metal shell and rubber elastic members is improved.