Copolymers are described, containing a) 20.0-99.9% by weight of one or more structural units resulting from polymerizable substances of the following structural formula (I) in which R2 is a linear or branched saturated alkyl radical having 6 to 200 carbon atoms or a linear or branched, mono- or polyunsaturated alkenyl radical having 6 to 200 carbon atoms, and R1, Y, n and m are each as defined in claims 1, b) 0.1-20.0% by weight of one or more structural units resulting from polymerizable quaternary ammonium compounds, and c) 0-60.0% by weight of one or more nonionic structural units resulting from one or more further polymerizable substances. The copolymers are advantageously suitable, for example, for the production of cosmetic, dermatological or pharmaceutical formulations.