Processes for preparing an amine, the processes comprising: 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, 1.5 to 4.5% by weight of an oxygen compound of cobalt, calculated as CoO, and 0.2 to 5.0% by weight of at least one oxygen compound of niobium, sulfur, phosphorus, gallium, boron, lead or antimony, calculated in each case as Nb2O5, H2SO4, H3PO4, Ga2O3, B2O3, PbO and Sb2O3 respectively, and wherein the catalytically active composition does not comprise any molybdenum.