The invention provides water-soluble or water-swellable copolymers obtained by free-radical copolymerization of A) acryloyldimethyltaurine and/or acryloyldimethyltaurates, B) optionally, one or more other olefinically unsaturated, noncationic, optionally crosslinking comonomers containing at least one oxygen, nitrogen, sulfur or phosphorus atom and possessing a molecular weight of less than 500 g/mol, C) one or more mono- or polyolefinically unsaturated, optionally crosslinking macromonomers each possessing at least one oxygen, nitrogen, sulfur or phosphorus atom and having a number-average molecular weight of greater than or equal to 200 g/mol, and D) one or more olefinically unsaturated, cationic comonomers containing at least one oxygen, nitrogen, sulfur or phosphorus atom and possessing a molecular weight of less than 500 g/mol, the copolymerization E) taking place in the presence or absence of at least one polymeric additive having number-average molecular weights of from 200 g/mol to 10.sup.9 g/mol.The water-soluble or water-swellable copolymers of the present invention are useful in formulating cosmetics.