A thermoplastic elastomer composition comprises a blend of a thermoplastic component with a cured elastomer component characterised in that the elastomer component prior to curing comprises a major proportion of a main elastomer and a minor proportion of a high molecular weight reactive polymer which shows a higher crosslinking efficiency in free-radical induced vulcanisation than the main elastomer. Preferably, the high molecular weight reactive polymer comprises from (3) to (15), and more preferably (4) to (10), parts by weight per one hundred parts of the total elastomer component of the composition. The use of the high molecular weight reactive polymer in the composition improves the low temperature performance of the composition and gives improvements to the processing behaviour, the resistance to stiffening at low temperatures and recovery/relaxation properties. Preferably, the high molecular weight reactive polymer is miscible with the main elastomer in the elastomer component. The thermoplastic elastomer composition may be made by mixing the thermoplastic component and an elastomer component comprising a main elastomer and a high molecular weight reactive polymer at a temperature to cause melting of the thermoplastic component to give a melt blend of the components, and subjecting the elastomer component in the melt blend to cure in the presence of at least one curative free-radical source.