The invention relates to the use of at least one copolymer obtainable by (i) free-radically initiated copolymerization of a monomer mixture comprising (a) 1 to 99.99% by weight of at least one monomer chosen from N-vinylimidazoles and diallylamines optionally in partially or completely quaternized form; (b) 0 to 98.99% by weight of at least one neutral or basic water-soluble monomer which is different form (a); (c) 0 to 50% by weight of at least one unsaturated acid or unsaturated anhydride, (d) 0 to 50% by weight of at least one free-radically copolymerizable monomer which is different from (a), (b) or (c); and (e) 0.01 to 10% by weight of at least one monomer which acts as crosslinker and has at least two ethylenically unsaturated, nonconjugated double bonds; and (ii) subsequent partial or complete quaternization or protonation of the polymer in the case where the monomer (a) is unquaternized or only partially quaternized, as additive for skin cosmetic and dermatological preparations.