Aqueous self-crosslinking copolymer dispersions ABC obtainable by free-radically initiated copolymerization in the first stage of a monomer mixture A comprising olefinically unsaturated monomers A1 having carbonyl groups, unsaturated carboxylic acids or monoesters of unsaturated dicarboxylic acids A2, monomers A3 selected from vinylaromatic compounds, n-butyl methacrylate and also alkyl esters of unsaturated carboxylic acids or dialkyl esters of unsaturated dicarboxylic acids, esters A4 selected from alkyl esters of unsaturated carboxylic acids of dialkyl esters of unsaturated dicarboxylic acids, and other free-radically polymerizable monomers A5, and subsequent addition of a second monomer mixture B and further polymerization in the second stage, the mixture B comprising olefinically unsaturated monomers B1 corresponding to A1, esters B2 corresponding to A4, and monomers B3 corresponding to A5, and subsequently adding compounds C having hydrazine or hydrazide groups.