A process for the production of a water-swellable, cross-linked, particulate polymer having a porous structure and a high absorption rate for water and/or aqueous liquids, comprising polymerizing or copolymerizing in aqueous solution a monomer selected from the group consisting of acrylic acid, methacrylic acid acrylamido methylpropane sulfonic acid, acrylamide and methacrylamide or copolymerizing said monomer with a water-soluble monomer and optionally a monomer only partially water-soluble or water-insoluble in amounts of up to 20%-wt., relative to the total monomer quantity, in the presence of at least one cross-linking di- or polyfunctional monomer, and optionally oligosaccharides and/or polysaccharides and/or polyvinyl alcohol, characterized in that the aqueous monomer solution comprises as polymerization initiator and blowing agent one or several azo compounds having a half-life of at least 10 hours at a temperature of 30.degree. to 120.degree. C., with the concentration of polymerization initiator and blowing agent, relative to the total monomer solution, amounting to 0.1 to 5.0%-wt., and that the polymer gel is crumbled, dried at 100.degree. to 240.degree. C., and ground.