A process for preparing secondary amines of the formula I in which R 1 and R 2 are each independently selected from the group of hydrogen, linear or branched aliphatic radicals having 1 to 15 carbon atoms, cycloaliphatic radicals having 5 to 10 carbon atoms, aralkyl radicals and phenyl radicals which may be o-, m- and/or p-substituted by aliphatic radicals having 1 to 4 carbon atoms, and R 3 is selected from the group of linear or branched aliphatic radicals having 1 to 15 carbon atoms, cycloaliphatic radicals having 5 to 10 carbon atoms, aralkyl radicals and phenyl radicals which may be o-, m- and/or p-substituted by aliphatic radicals having 1 to 4 carbon atoms, I) by aminating alcohols of the formula II in which R 1 and R 2 are each as defined above II) with primary amines of the formula III R 3 -NH 2 III in which R 3 is as defined above III) and hydrogen in the liquid phase in the presence of hydrogenation catalysts, comprising the following steps: (i) feeding alcohols of the formula II, primary amines of the formula III, hydrogen and optionally solvent into the hydrogenation reactor, the molar ratio of alcohol II to primary amine III being 1 to 20:1, (ii) performing the hydrogenation at temperatures of 150 to 210°C and pressures of 1 to 300 bar in the presence of a hydrogenation catalyst comprising copper on oxidic supports. R 1 and R 2 are each independently selected from the group of hydrogen, linear or branched aliphatic radicals having 1 to 15 carbon atoms, cycloaliphatic radicals having 5 to 10 carbon atoms, aralkyl radicals and phenyl radicals which may be o-, m- and/or p-substituted by aliphatic radicals having 1 to 4 carbon atoms, and R 3 is selected from the group of linear or branched aliphatic radicals having 1 to 15 carbon atoms, cycloaliphatic radicals having 5 to 10 carbon atoms, aralkyl radicals and phenyl radicals which may be o-, m- and/or p-substituted by aliphatic radicals having 1 to 4 carbon atoms, I) by aminating alcohols of the formula II in which R 1 and R 2 are each as defined above II) with primary amines of the formula III R 3 -NH 2 III in which R 3 is as defined above III) and hydrogen in the liquid phase in the presence of hydrogenation catalysts, comprising the following steps: (i) feeding alcohols of the formula II, primary amines of the formula III, hydrogen and optionally solvent into the hydrogenation reactor, the molar ratio of alcohol II to primary amine III being 1 to 20:1, (ii) performing the hydrogenation at temperatures of 150 to 210°C and pressures of 1 to 300 bar in the presence of a hydrogenation catalyst comprising copper on oxidic supports. I) by aminating alcohols of the formula II in which R 1 and R 2 are each as defined above II) with primary amines of the formula III R 3 -NH 2 III in which R 3 is as defined above III) and hydrogen in the liquid phase in the presence of hydrogenation catalysts, comprising the following steps: (i) feeding alcohols of the formula II, primary amines of the formula III, hydrogen and optionally solvent into the hydrogenation reactor, the molar ratio of alcohol II to primary amine III being 1 to 20:1, (ii) performing the hydrogenation at temperatures of 150 to 210°C and pressures of 1 to 300 bar in the presence of a hydrogenation catalyst comprising copper on oxidic supports. (i) feeding alcohols of the formula II, primary amines of the formula III, hydrogen and optionally solvent into the hydrogenation reactor, the molar ratio of alcohol II to primary amine III being 1 to 20:1, (ii) performing the hydrogenation at temperatures of 150 to 210°C and pressures of 1 to 300 bar in the presence of a hydrogenation catalyst comprising copper on oxidic supports.