Processes for preparing an amine, which processes comprise: reacting a reactant selected from the group consisting of primary alcohols, secondary alcohols, aldehydes, ketones, and mixtures thereof, with hydrogen and a nitrogen compound selected from the group consisting of ammonia, primary amines, secondary amines and mixtures thereof, in the presence of a zirconium dioxide-, copper- and nickel-containing catalyst; wherein the catalyst comprises a catalytically active composition which comprises, before reduction with hydrogen, oxygen compounds of zirconium, copper, and nickel, and 0.2 to 40% by weight of an oxygen compound of cobalt, calculated as CoO, 0.1 to 5% by weight of an oxygen compound of iron, calculated as Fe2O3, and 0.1 to 5% by weight of at least one oxygen compound of lead, tin, bismuth or antimony, calculated as PbO, SnO, Bi2O3 and Sb2O3 respectively.