A sulfur vulcanizing system rubber composition comprises EPDM, zinc as a vulcanization accelerator activator, at least one thiazole type vulcanization accelerator serving to control the dissolution of zinc from the composition, and at least one ultra-accelerator of the thiuram or dithiocarbamate type, these accelerators being preferably combined under specified quantitative limitations. The hose using this rubber composition is particularly suitable for use in a cooling system for an automobile engine, since the dissolution of zinc into a coolant is prevented, thereby preventing the formation of any zinc compound causing the blocking of the hose, or the leakage of the coolant through the seal between the hose and any pipe connected therewith.