Abstract: The present invention relates to a thermoplastic elastomer composition having a durometer hardness (ASTM D2240) of Shore A 30 to 90 comprising: a) 100 parts by weight of a hydrogenated styrenic block copolymer comprising at least two blocks (A) of a polymer containing 50% wt or more monovinyl aromatic hydrocarbon units, and at least one selectively hydrogenated block (B) of a polymer containing 50% wt or more conjugated diene units, wherein the monovinyl aromatic hydrocarbon content is in the range of from 10 to 50 wt %, based on the total weight of block copolymer, wherein the vinyl content in the initially prepared poly(conjugated diene) block (B) is in the range of from 30 to 80%, and wherein the hydrogenated styrenic block copolymer has a degree of hydrogenation of at least 30% with respect to the residual olefinic unsaturation in the block (B), which block copolymer optionally may be mixed with a diblock copolymer having one poly(monovinyl aromatic hydrocarbon) block and one poly(conjugated diene) block