An improved method of preparing amines by reaction of alcohols with ammonia or primary or secondary amines at elevated temperature and superatmospheric pressure in the presence of hydrogen and a hydrogenation catalyst containing cobalt, nickel and copper, the improvement comprising using a catalyst which contains (calculated on the metal content of the catalyst) from 70 to 95% by weight of a mixture of cobalt and nickel and from 5 to 30% by weight of copper, the ratio by weight of cobalt to nickel being from 4:1 to 1:4. The amines prepared in this way are suitable for the production of emulsifying agents, plant protection agents and vulcanization accelerators.