Novel hydrogenated nitrile rubbers are provided, which, as well as having reduced contents of phosphines and/or diphosphines, include phosphine oxides and a specific content of halogens, and which enable access to vulcanizable mixtures and corresponding vulcanizates that possess improved moduli and compression set values and good values for heat buildup under dynamic stress. These novel hydrogenated nitrile rubbers are obtained by a specific production process, in the course of which the hydrogenated nitrile rubbers are reacted with at least one specific oxidizing agent.
