The microcapsules containing bleaching agents are obtainable by polymerizing monomer mixtures which comprise5-100% by weight of at least one ethylenically unsaturated carboxylic anhydride (a),0-95% by weight of at least one monoethylenically unsaturated monomer (b) different from the monomers of group (a),0-80% by weight of crosslinking monomers (c) which have at least two nonconjugated monoethylenic double bonds in the molecule, and0-20% by weight of water-soluble monoethylenically unsaturated monomers (d),where the total of components (a) to (d) is 100% by weight. The polymerization takes place in the oil phase of a stable oil-in-water emulsion in the presence of free-radical polymerization initiators, where the temperature of the polymerizing reaction mixture is, where appropriate, increased continuously or periodically during the polymerization. The oil phase contains or consists of the bleaching aid.