Superabsorbent polymers based on partly hydrolysed homopolymers and/or copolymers of acrylonitrile which are cross-linked through the incorporation of polyfunctional monomers, wherein 30 to 80 mol-% of the nitrile groups are converted into carboxylate groups, 20 to 70 mol-% of the nitrile groups are converted into carbonamide groups and 0 mol-% to 20 mol-% of the nitrile groups are unchanged, and the said cross-linked polymers possess a swelling capacity of 700 g/g in water and of up to 60 g/g in physiological saline and a gel strength of from 20 g to 100 g, their preparation and their use.