Optically active amines of the formula I ##STR1## where R.sup.1 and R.sup.2 are different and R.sup.1, R.sup.2, R.sup.3 are alkyl, cycloalkyl, arylalkyl, aryl, heteroaryl and heterocyclic radicals and R.sup.3 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.