A resin composition comprises (a) 100 parts by weight of at least one compound selected from the group consisting of phenol resins and brominated phenol resins, (b) 20 to 500 parts by weight of a crystalline olefin resin, provides that copolymers of ethylene with unsaturated carboxylic acid ester or vinyl acetate are precluded, and (c) 0 to 300 parts by weight of a non-aromatic softening agent for rubber. The resin composition is easy to handle in dynamic cross-linking of rubber or a thermoplastic elastomer to give uniform cross-linking. A cross-linked rubber composition or thermoplastic elastomer composition has improved compression set and moldability.