The mixture of the invention contains, for 100 parts by weight: (A) 10 to 90 parts in weight of at least one copolymer grafted to polyamide blocks, said copolymer comprising a polyolefin trunk and at least 1.3 polyamide grafts on said trunk in average, and having a nanostructured organization, wherein said grafts are attached to the trunk by the rest of an unsaturated monomer (X) having a function capable of reacting with a polyamide with an amine end; the rest of said monomer (X) being attached on the trunk by grafting or copolymerization from its double bond thereof, (A) optionally including at least one non-grafted polyolefin in a proportion such that the nano-structured organization of the compound (A) is preserved; and (B) 90 to 10 parts in weight of a formulation of at least one elastomer having unsaturated double bonds and capable of reacting with a crosslinking or vulcanization agent, said formulation containing a crosslinking or vulcanization system of said elastomer(s), at least one plasticizer and the standard additives present in elastomer formulations.