A partly cross-linked thermoplastic elastomer polyolefin composition intended to be converted by any plastics processing technique into a molded part, such as a cover for housing a vehicle's safety airbag, comprises an olefin polymer of polypropylene type, at least one copolymer of ethylene-alpha-olefin type, at least one cross-linking agent and a free radicals formation agent characterized in that a) the olefin polymer of polypropylene type is chosen from the group of polypropylene/ethylene or polypropylene/α-olefin copolymers and selected from those having an impact resistance of at least 40 kJ/m2 when measured using the notched Izod impact resistance test at 23° C. in accordance with ISO standard 180. b) at least one copolymer of the ethylene-α-olefin type is selected from the group formed by those having a density at least equal to 0.870 g/cm3 in accordance with ISO standard 1183. c) at least one thermoplastic elastomer is introduced into the composition.