Abstract: A process for preparing an amine by reacting an aldehyde and/or ketone with a nitrogen compound selected from the group consisting of ammonia and primary and secondary amines, and subsequent hydrogenation of the resulting reaction product in the liquid phase and in the presence of hydrogen and a heterogeneous copper oxide hydrogenation catalyst at a temperature of 20 to 230° C., wherein the aldehyde and/or ketone is reacted with the nitrogen compound either together with the hydrogenation in the liquid phase and in the presence of the hydrogen and of the catalyst (alternative 1) or in a step preceding the hydrogenation (alternative 2), and wherein the catalytically active composition of the catalyst, prior to reduction thereof with hydrogen, comprises at least 24% by weight of oxygen compounds of copper, calculated as Cu.