Optically active amines of the formula I 1 where R1 and R2 are different and R1, R2, R3 are alkyl, cycloalkyl, arylalkyl, aryl, heteroaryl and heterocyclic radicals and R3 may also be hydrogen (H), with the radicals being able to bear substituents selected from the group consisting of alkyl, cycloalkyl, alkoxy, aryloxy, amino, alkylamino and dialkylamino, are racemized by reacting the optically active amine I in the presence of hydrogen and a hydrogenation or dehydrogenation catalyst at elevated temperature, wherein the catalyst comprises the active components copper and zinc oxide and a support material.