In a process for functionalizing an .alpha.-olefin/diene copolymer, a copolymer comprising units derived from at least one .alpha.-olefin and units derived from at least one diene, which copolymer contains at least one double bond, is contacted in a reaction medium with an alkyl hydroperoxide in the presence of a catalyst comprising a metal of Group 5 or 6 of the Periodic Table or a compound thereof, under reaction conditions which promote formation of an oxirane ring or hydroxyl groups at the site of the double bond.