Catalysts whose active material contains, in addition to from 20 to 85% by weight, calculated as ZrO.sub.2, of oxygen-containing zirconium compounds, from 1 to 30% by weight, calculated as CuO, of oxygen-containing compounds of copper and from 1 to 40% by weight each, calculated as CoO or NiO, respectively, of oxygen-containing compounds of cobalt and of nickel are used for the amination of alcohols under hydrogenating conditions.