Abstract: The invention relates to is a crosslinked composition containing in parts by weight: 20 to 100 parts of at least one elastomer (I), 2 to 50 parts of at least one core/shell copolymer (II), and 0 to 100 parts of at least one thermoplastic polymer (III). The invention also relates to a method of producing one such crosslinked composition, which is characterized in that it consists in: mixing an elastomer and a core/shell copolymer optionally in the presence of: a grafted polyolefin, a plasticizer, fillers and/or additives, and a suitably-selected crosslinking system, and subsequently crosslinking said mixture at a suitable temperature. In a preferred embodiment of the invention, the mixture is crosslinked at a temperature of between 150 and 320° C. The invention method be carried out in an internal mixer, or, alternately, in a twin-screw extruder or a Buss®-type co-kneader. Depending on the case, the resulting mass is calendared or extruded, cooled and subsequently granulated.