A thermoplastic material has a) from 5% weight to 95% by weight, preferably from 10% by weight to 60% by weight, of vulcanized rubber in a subdivided form; b) from 5% by weight to 95% by weight, preferably from 40% by weight to 90% by weight, of at least one heterophase copolymer having a thermoplastic phase made from a propylene homopolymer or copolymer and an elastomeric phase made from a copolymer of ethylene with an α-olefin, preferably with propylene; c) from 0% by weight to 90% by weight, preferably from 0% by weight to 50% by weight, of at least one α-olefin homopolymer or copolymer different from b); the amounts of a), b) and c) being expressed with respect to the total weight of a)+b)+c). The thermoplastic material shows improved mechanical properties, in particular, improved elongation at break.