A novel process produces a novel hydrogenated nitrile rubber (B) which features a very narrow molecular weight distribution and a correspondingly low value for the polydispersity index. The preparation process encompasses the treatment of a hydrogenated nitrile rubber (A) with ultrasound, whereupon the resultant hydrogenated nitrile rubber (B) has a lower weight-average molecular weight (M.sub.w) than the hydrogenated nitrile rubber (A). The resultant hydrogenated nitrile rubber (B) has excellent suitability for the production of mouldings via processing by extrusion processes or by injection-moulding processes.