Water-absorbing foamlike crosslinked polymers which are obtainable by (I) foaming a polymerizable aqueous mixture which consists of (a) monoethylenically unsaturated monomers containing acid groups, which are at least 50 mol % neutralized, (b) with or without other monoethylenically unsaturated monomers, (c) crosslinker, (d) initiators, (e) from 0.1 to 20% by weight of at least one surfactant, (f) with or without one or more solubilizers and (g) with or without thickeners, foam stabilizers, polymerization regulators, fillers and/or cell nucleating agents, the foaming being performed by dispersing fine bubbles of a gas inert to free radicals, and (II) polymerizing the foamed mixture with formation of a foamed hydrogel, with or without adjusting the water content of the foamed polymer to from 1 to 60% by weight, processes for their preparation and their use in sanitary articles which are used for absorbing body fluids and in dressing materials for covering wounds are described.