The present invention relates to improved hydrogel-forming polymer compositions which can be used as absorbents in absorbent structures and absorbent articles such as diapers, sanitary napkins and the like. Such hydrogel-forming polymer compositions are substantially water-insoluble, slightly cross-linked, partially neutralized polymers which are prepared from unsaturated polymerizable, acid group-containing monomers and cross-linking agents. These hydrogel-forming polymer materials, upon imbibing fluids, form hydrogels. Such polymer materials have relatively high gel volume and relatively high gel strength as measured by shear modulus of the hydrogel which forms therefrom. Such polymer materials also contain relatively low levels of extractable polymer material which can be extracted therefrom by contact with synthetic urine. Preferred hydrogel-forming polymers having these characteristics can be prepared by polymerizing the acid group-containing monomers in their free acid form at relatively low monomer concentrations, preferably using relatively low polymerization temperatures. Absorbent structures and absorbent articles containing these dried hydrogel-forming polymer materials are also disclosed.