A thermoplastic elastomer composition prepared by partially crosslinking a composition comprising the following components (A), (B) and (C):
(A) 30-70 parts by weight of an ethylene/α-olefin copolymer prepared by copolymerizing ethylene and an α-olefin having 3 to 12 carbon atoms in the presence of a catalyst comprising a solid component and an organoaluminum compound which solid component contains at least magnesium and titanium, said ethylene/α-olefin copolymer having the following properties (I) to (IV):
(I) Melt index      0.01-100 g/10 min (II) Density      0.860-0.910 g/cm³ (III) Maximum peak temperature as measured according to a differential scanning calorimetry (DSC)      not lower than 100°C (IV) Insolubles in boiling
n-hexane      not less than 10 wt.% (B) 70-30 parts by weight of a propylene polymer; and (C) 70-200 parts by weight, based on 100 parts by weight of the components (A) and (B), of an ethylene/­α-olefin copolymer rubber.