A method is described for the preparation of optically active hydroxamic acids of the general formula wherein R1, R2 and R3 are different and are a cyclic or linear, aliphatic or aromatic, substituted or unsubstituted hydrocarbon radical which can optionally contain heteroatoms, said method being characterized in that a racemate of chiral amides, carboxylic acid esters or carboxylic acids of the general formula wherein R1, R2 and R3 are as defined above and X is —NH2, —OR or —OH, R being any organic radical, is reacted with hydroxylamine, NH2OH, in the presence of an acyltransferase, and the optically active hydroxamic acid (I) formed is then separated from the unconverted enantiomer of general formula (II). The resulting optically active hydroxamic acid can be converted to the corresponding optically active primary amines by a Lossen rearrangement.