The present invention relates to polymer ic thickener compositions comprising at least one water-swellable crosslinked copolymer, a process for preparing such compositions and their use as a thickener, e.g., in cosmetic, dermatologic, pharmaceutical or veterinary formulations. The water-swellable crosslinked copolymer according to the present invention is prepared from a mixture comprising (a) acrylamide, (b) an acrylamidoalkylsulfonic acid and/or a salt thereof and (c) an amine-based polyfunctional crosslinking agent comprising at least three allylic functions.