The present disclosure relates to novel polyurethanes comprising cationic units, of diisocyanates and of nonionic units derived from polyolefins comprising at least 10 mol % of units comprising at least one residual carbon-carbon double bond.The present disclosure also relates to cosmetic or pharmaceutical compositions comprising the polyurethanes, and also to a cosmetic treatment process, for example for shaping and/or holding the hair, comprising the application of such a composition.