Provided are new functionalized nitrile rubbers, which may optionally also be in partially or wholly hydrogenated form, and also a process for preparing them by metathesis of nitrile rubbers in the presence of a metathesis catalyst and at least one functionalized allyl compound. The new functionalized nitrile rubbers are suitable for producing vulcanizable mixtures and allow the production of vulcanizates having very stable networks. Also made possible, in particular, is the synthesis of block copolymers.