Process for the continuous preparation of an amine by reaction of a primary or secondary alcohol, aldehyde and/or ketone with hydrogen and a nitrogen compound selected from the group consisting of ammonia, primary and secondary amines at a temperature in the range from 60 to 300° C in the presence of a copper-containing catalyst, wherein the catalytically active composition of the catalyst prior to reduction with hydrogen comprises from 20 to 85% by weight of aluminum oxide (Al2O3), zirconium dioxide (ZrO2), titanium dioxide (TiO2) and/or silicon dioxide (SiO2), from 1 to 70% by weight of oxygen-containing compounds of copper, calculated as CuO, from 0 to 50% by weight of oxygen-containing compounds of magnesium, calculated as MgO, oxygen-containing compounds of chromium, calculated as Cr2O3, oxygen-containing compounds of zinc, calculated as ZnO, oxygen-containing compounds of barium, calculated as BaO, and/or oxygen-containing compounds of calcium, calculated as CaO, and less than 30% by weight of oxygen-containing compounds of nickel, calculated as NiO, based on the oxygen-containing compounds of copper, calculated as CuO, and the reaction is carried out isothermally in the gas phase in a tube reactor.