The present invention relates to a cosmetic composition which comprises at least one water-soluble or water-dispersible copolymer which is obtainable by free-radical copolymerization of at least one N-vinyllactam, at least one anionogenic monomer and optionally further .alpha.,.beta.-ethylenically unsaturated compounds copolymerizable therewith, in the presence of a polymer component with repeat units which have ether groups or which are derived from vinyl alcohol.