The curable composition of the present invention contains (A1) a silyl-containing ethylene/.alpha.-olefin/non-conjugated polyene random copolymer rubber which has a structural unit derived from a norbornene compound as the non-conjugated polyene with at least one specific vinyl group at the terminal and contains a specific hydrolyzable silyl group, and (B) a compound, other than the rubber (A1), having a hydroxyl group and/or a hydrolyzable group, e.g., (B1) a compound having a silanol group and/or a compound which can react with moisture to form a compound having a silanol group in the molecule.This compound improves elongation of the cured product and residual surface tackiness, and, at the same time, is high in curing speed and capable of giving the cured product of high resistance to weather. It is suitable for, e.g., adhesives, tackifiers, paints, sealants, waterproof materials, spray materials, shaping materials and casting rubber materials.