Water-soluble or water-swellable polymers are described, containing a) 20.0 to 98.99 mole percent of one or more independently recurring structural units of the formula (1) and b) 1.0 to 79.99 mole percent of one or more independently recurring structural units of the formula (2), and c) 0.01 to 8.0 mole percent of one or more independently recurring cross-linking structural units, which are obtained from one or more monomers having at least two olefinic double bonds. The polymers are suitable, for example, as thickeners or yield point formers, in particular in cosmetic, dermatological or pharmaceutical compositions.