Abstract: A cosmetic composition comprising water-soluble copolymer, which as characteristic structural elements comprises a) vinylcarboxamide units of the general formula I where R1 and R2 independently of one another are H, alkyl, cycloalkyl, aryl or aralkyl, and b) units of the general formula II where A is a chemical bond or an alkylene group, the radicals R3 independently of one another are H, alkyl, cycloalkyl, aryl or aralkyl, or together with the nitrogen atom to which they are bonded, form an unsubstituted, mono- or polysubstituted, five- to seven-membered, heterocyclic, aromatic or nonaromatic ring, which if appropriate contains one or two further heteroatoms, selected from among O, N and S, it being possible for the heterocyclic ring to be fused to a further five- or six-membered, aromatic or nonaromatic ring, R4 is H, alkyl or aralkyl.