O.Z. 0050/41496 The preparation of isoxazole4,5-dicarboxylic diesters of the formula I (I) where R1 is any organic radical which is inert under the reaction conditions, and R2 and R3 are each alkyl, cycloalkyl or benzyl, entails reacting an aldoxime of the formula II (II) with a diester of maleic or fumaric acid, of the formula III R2OOC-C=C-COOR3 (III) where R2 and R3 are identical or different and have the abovementioned meanings, in the presence of an aqueous solution of a hypohalite which is present in excess relative to II.