A thermoplastic elastomer composition comprised of (a) a thermoplastic resin selected from the group consisting of polyphenylene ether, polypropylene, polyethylene, and polystyrene, (b) a block copolymer selected from the group consisting of styrene-ethylene butylene-styrene, styrene-ethylene propylene-styrene, hydrogenated polybutadiene, hydrogenated polyisoprene, hydrogenated styrene-isoprene random copolymer, styrene-ethylene propylene block copolymer, styrene-ethylene ethylene propylene-styrene and hydrogenated styrene-butadiene random copolymers, (c) a core-shell polymer comprised of a polymeric core and a polymeric shell with the proviso that the polymeric core and/or the polymeric shell may be crosslinked, and (d) an oil.