A process for preparing a cured copolyetherester elastomeric composition comprising following steps I and II:Step I: melt-extruding an uncured linear copolyetherester elastomeric composition of [A] and [B] to follow:[A] a linear copolyetherester elastomer composed of(A-1) a hard segment consisting of(i) an acid component of which at least 70 mol % is an aromatic dicarboxylic acid and(ii) a diol component having an average molecular weight of up to 350 and(A-2) a soft segment consisting of(iii) a polyalkylene glycol having an average molecular weight of from 500 to 5,000 in an amount of from 10 to 80% by weight based on the elastomer [A]; and[B] a compound having an unsaturated aliphatic moiety other than unsaturated conjugated moieties, said compound [B] being copolymerized or blended with said elastomer [A], wherein said unsaturated aliphatic moiety is chemically inert at the melt-extruding temperature, the amount of said moiety being 0.001 to 0.5 equivalent per 100 grams of said elastomer [A]Step II: curing the resulting extrudate by irradiation of actinic light.