Process for the production of a peroxyester comprising the following steps: a) producing a mixture comprising one or more peroxyesters and one or more carboxylic acid salts or adducts by reacting an anhydride with the formula R 1 -C(=O)-O-C(=O)-R 2 with an organic hydroperoxide of the formula R 3 n in the presence of a base, wherein R 1 is selected from linear and branched alkyl, cycloalkyl, aryl, and arylalkyl groups with 1-17 carbon atoms, optionally substituted with oxygen- and/or halogen-containing substituents, R 2 is selected from linear and branched alkyl, cycloalkyl, aryl, and arylalkyl groups with 2-17 carbon atoms, optionally substituted with oxygen- and/or halogen-containing substituents, R 3 is a tertiary alkyl group with 3-18 carbon atoms, optionally substituted with oxygen- and/or halogen-containing groups and/or unsaturated groups, and n is an integer in the range 1-3, b) separating the one or more carboxylic acid salts or adducts from the mixture produced in step a), c) liberating the carboxylic acid from the salt or adduct, d) optionally producing an additional amount of carboxylic acid by reacting an aldehyde of the formula R 2 -C(=O)H with oxygen, e) reacting the carboxylic acid obtained in step c) and optionally an additional amount of carboxylic acid of the formula R 2 -C(=O)OH - said additional amount of carboxylic acid being obtained from step d) and/or obtained in another way - with an acid anhydride or a ketene of the formula C(R 4) 2 =C=O, each R 4 being independently selected from H and CH 3, preferably with acetic anhydride, to form an anhydride with the formula R 1 -C(=O)-O-C(=O)-R 2, and f) recycling at least part of the anhydride formed in step e) to step a). a) producing a mixture comprising one or more peroxyesters and one or more carboxylic acid salts or adducts by reacting an anhydride with the formula R 1 -C(=O)-O-C(=O)-R 2 with an organic hydroperoxide of the formula R 3 n in the presence of a base, wherein R 1 is selected from linear and branched alkyl, cycloalkyl, aryl, and arylalkyl groups with 1-17 carbon atoms, optionally substituted with oxygen- and/or halogen-containing substituents, R 2 is selected from linear and branched alkyl, cycloalkyl, aryl, and arylalkyl groups with 2-17 carbon atoms, optionally substituted with oxygen- and/or halogen-containing substituents, R 3 is a tertiary alkyl group with 3-18 carbon atoms, optionally substituted with oxygen- and/or halogen-containing groups and/or unsaturated groups, and n is an integer in the range 1-3, b) separating the one or more carboxylic acid salts or adducts from the mixture produced in step a), c) liberating the carboxylic acid from the salt or adduct, d) optionally producing an additional amount of carboxylic acid by reacting an aldehyde of the formula R 2 -C(=O)H with oxygen, e) reacting the carboxylic acid obtained in step c) and optionally an additional amount of carboxylic acid of the formula R 2 -C(=O)OH - said additional amount of carboxylic acid being obtained from step d) and/or obtained in another way - with an acid anhydride or a ketene of the formula C(R 4) 2 =C=O, each R 4 being independently selected from H and CH 3, preferably with acetic anhydride, to form an anhydride with the formula R 1 -C(=O)-O-C(=O)-R 2, and f) recycling at least part of the anhydride formed in step e) to step a).