Abstract: Asymmetric hydrogenation of prochiral N-arylketimines to give optically active secondary amines at a temperature from -40.degree. to 80.degree. C., under a hydrogen pressure of 10.sup.6 to 10.sup.8 Pa and with the addition of catalytic amounts of a rhodium compound of the formula III or IIIa ##STR1## in which X is 2 olefin ligands or a diene ligand, Y is a chiral diphosphine in which the secondary phosphine groups are linked by 2-4 C atoms and which, together with the Rh atom, forms a 5-membered, 6-membered or 7-membered ring, or Y is a chiral disphosphinite in which the phosphinite groups are linked via 2 C atoms and which, together with the Rh atom, forms a 7-membered ring, Z is Cl, Br or I and A.sup.- is the anion of an oxygen acid or complex acid.