The present invention relates to a process for producing water-absorbing sheet-like materials which consist of a water-absorbent polymer and a prefabricated nonwoven fabric, wherein the prefabricated nonwoven fabric is impregnated with a solution comprising partially neutralized acrylic acid and at least one cross-linking agent and is squeezed to a certain coating amount, and the monomer solution thus applied is characterized in that the polymerization is carried out in the presence of radical initiators which cannot be activated thermally and at least one thermally activatable radical former used in addition. The additional use of a thermally activatable radical former in the polymerization results in products having a low residual monomer content, an improved water absorption under load, and a higher retention, with a production method being employed which is technically simple and economically efficient at the same time. The thermally activatable initiator portion may either be added to the monomer solution or applied to the substrate in an amount of 0.01 to 0.5 mole percent, relative to the monomer to be polymerized.