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, nickel and tin, and 0.5 to 8.0% by weight of an oxygen compound of cobalt, calculated as CoO, and wherein the catalytically active composition does not comprise any ruthenium.