Pneumatic run-flat radial tire

A pneumatic run-flat radial tire comprising a carcass layer;

• a main belt;
• a tread portion;
• a side wall portion;
• and a reinforcing rubber layer, wherein the carcass layer includes at least one radial carcass ply with cords that are substantially radially arranged between a pair of bead cores embedded respectively in a pair of bead portions, the main belt is arranged on an outer periphery of a crown portion of the carcass and includes at least two inclined belt layers each containing cords extending in parallel in an inclined direction with respect to an equatorial plane of the tire, the tread portion is reinforced by the main belt, the side wall portion connects between the tread portion and the bead portions, and the reinforcing rubber layer is arranged in an inner face of the carcass extending at least to the side wall portion and has a substantially crescent cross section,
• wherein a cord having a difference in thermal shrinkage stress between at 30° C. and at 80° C. of 3.0×10−2 cN/dtex or more is used as the cords constituting the at least one carcass ply of the carcass layer, wherein the slope a of decreasing rate (%) of the dynamic storage modulus of elasticity E′ of the reinforcing rubber layer from 30° C. to 50° C. satisfies the following condition:
• α≦−3.0×10−2[%]/[deg], and
• wherein the slope β of decreasing rate (%) of the dynamic storage modulus of elasticity Et of the reinforcing rubber layer from 50° C. to 80° C. satisfies the following condition:
• β≧−8.0×10−2[%]/[deg].