Abstract: The invention relates to a cross-linked elastomer composition including: an ethylene/alpha-olefin multiblock copolymer comprising polymerized ethylene and alpha-olefin units, an elastomer including a block copolymer having at least two, identical or different, aromatic blocks which are separated by at least one elastomer block, and a cross-linkable polymer, for example, a diene elastomer. The invention also relates to a product including the composition, and to the use of such a product as a seal.