Thermoplastic elastomer composition, comprising an thermoplastic polyolefin and an dynamically vulcanized elastomer comprising monomer units of ethylene, an .alpha.-olefin and optionally one or more non-conjugated polyenes and oil, having an oil/elastomer ratio of at least 2/1, having a content of thermoplastic polyolefin of less than 10 wt. % relative to the total weight of the thermoplastic elastomer composition, granulate of the composition having the capability of flowing out of a cylinder, held in vertical position, within 120 seconds, after being kept in that cylinder under a pressure of 465 kg/m2, at a temperature of 50.degree. C., for a period of 1 hour, that cylinder having an internal diameter of 95.3 millimeter (mm) and a length of 356 mm and being filled for a length of between 326 and 338 mm.