A process for preparing water-soluble homo- or copolymers comprising (meth)acrylamide by free-radical polymerization of an aqueous solution of monoethylenically unsaturated monomers comprising at least (meth)acrylamide in the presence of at least one stabilizer for prevention of polymer degradation by molecular oxygen. The stabilizer is preferably one selected from the group of sulfur compounds, sterically hindered amines, N-oxides, nitroso compounds, aromatic hydroxyl compounds and ketones, more preferably 2-mercaptobenzothiazole or a salt thereof.