The present invention relates to powdery, insoluble, water-swellable, cross-linked polymers absorbing water, aqueous or serous liquids, which are formed of a) 55-99.9%-wt. polymerized unsaturated, polymerizable acid-groups--comprising monomers which are neutralized to the extent of at least 25 mol-%, b) 0-40%-wt. polymerized unsaturated monomers which are co-polymerizable with a), c) 0.1-5.0%-wt. of a cross-linking agent, and d) 0-30%-wt. of a water-soluble polymer, with the weight amounts of a) to d) being relative to anhydrous polymer, and the polymer powder is heated with an at least bifunctional compound reactive with acid groups to a temperature of 150.degree. C.-250.degree. C. under cross-linkage of the surface, and the polymer powder that is thus already surface-cross-linked is subjected to a repeated surface-cross-linking treatment using an at least bifunctional compound reactive with acid groups at a temperature of 150.degree. to 250.degree. C. The present invention further relates to a process for the production of these polymers and to their use as absorbents for water and aqueous liquids, in particular in constructions for the absorption of body fluids, and in current-conducting or light-transmitting cables, as component in packing materials, as soil improver, and as artificial soil for plant breeding.