A process for preparing water-soluble homo- or copolymers comprising (meth)acrylamide by free-radical polymerization of an aqueous solution of ethylenically unsaturated monomers comprising at least (meth)acrylamide in the presence of at least one stabilizer for prevention of polymer degradation by molecular oxygen, which is a gel polymerization and wherein the process comprises at least the following steps: providing an aqueous monomer solution comprising at least • water, • 25 to 45% by weight - based on the amount of all the components of the aqueous solution - of ethylenically unsaturated monomers, where at least 70% by weight of the monomers are monoethylenically unsaturated, hydrophilic monomers having a solubility in water at room temperature of at least 50 g/l, with the proviso that at least one of the monomers is (meth)acrylamide, • 0.1 to 2% by weight - based on the sum total of all the monomers - of at least one stabilizer for prevention of polymer degradation by molecular oxygen, selected from the group of sulfur compounds, sterically hindered amines, N-oxides, nitroso compounds, aromatic hydroxyl compounds and ketones, • an azo initiator having a 10 h t 1/2 of 40°C to 75°C, where the aqueous monomer solution • has a pH of < 7, • has been cooled to a temperature of < 5°C and • has been inertized, adding at least one redox initiator for the free-radical polymerization to the monomer solution which has been cooled to less than 5°C, polymerizing the aqueous monomer solution under essentially adiabatic conditions, no heat being supplied to the reactor from the outside during the polymerization and the reactor not being cooled during the polymerization, and the initiation temperature of the polymerization being less than 5°C and the mixture being heated under the influence of the heat of polymerization which develops to a temperature of 60°C to 100°C, forming a polymer gel, and drying the polymer gel obtained. providing an aqueous monomer solution comprising at least • water, • 25 to 45% by weight - based on the amount of all the components of the aqueous solution - of ethylenically unsaturated monomers, where at least 70% by weight of the monomers are monoethylenically unsaturated, hydrophilic monomers having a solubility in water at room temperature of at least 50 g/l, with the proviso that at least one of the monomers is (meth)acrylamide, • 0.1 to 2% by weight - based on the sum total of all the monomers - of at least one stabilizer for prevention of polymer degradation by molecular oxygen, selected from the group of sulfur compounds, sterically hindered amines, N-oxides, nitroso compounds, aromatic hydroxyl compounds and ketones, • an azo initiator having a 10 h t 1/2 of 40°C to 75°C, where the aqueous monomer solution • has a pH of < 7, • has been cooled to a temperature of < 5°C and • has been inertized, • water, • 25 to 45% by weight - based on the amount of all the components of the aqueous solution - of ethylenically unsaturated monomers, where at least 70% by weight of the monomers are monoethylenically unsaturated, hydrophilic monomers having a solubility in water at room temperature of at least 50 g/l, with the proviso that at least one of the monomers is (meth)acrylamide, • 0.1 to 2% by weight - based on the sum total of all the monomers - of at least one stabilizer for prevention of polymer degradation by molecular oxygen, selected from the group of sulfur compounds, sterically hindered amines, N-oxides, nitroso compounds, aromatic hydroxyl compounds and ketones, • an azo initiator having a 10 h t 1/2 of 40°C to 75°C, • has a pH of < 7, • has been cooled to a temperature of < 5°C and • has been inertized, adding at least one redox initiator for the free-radical polymerization to the monomer solution which has been cooled to less than 5°C, polymerizing the aqueous monomer solution under essentially adiabatic conditions, no heat being supplied to the reactor from the outside during the polymerization and the reactor not being cooled during the polymerization, and the initiation temperature of the polymerization being less than 5°C and the mixture being heated under the influence of the heat of polymerization which develops to a temperature of 60°C to 100°C, forming a polymer gel, and drying the polymer gel obtained.