The invention relates to water-soluble or water-swellable polymers the repeating structural units of which consist of a) 90.0 to 99.99 mole-% of one or more repeating structural units originating from special monomers with sulfonic acid groups or the salts thereof such as for example 2-acrylamido-2-methyl-propanesulfonic acid or the salts thereof and b) 0.01 to 10.0 mole-% of one or more repeating structural units originating from special cross-linking agents with at least three polymerizable double bonds. The polymers for example have an advantageous sensory property profile and are highly suitable as thickening agents even in salt-containing compositions. They are furthermore advantageously suitable for producing cosmetic, dermatological or pharmaceutical compositions.