2 most preferably from 0 3 to 0 6 the major advantage of the process of the present invention is therefore that the heat of reaction obtained in the hydrogenation even at low temperatures can be used for the separation of water from the amine and water containing reaction mixture that is produced this is made possible by the distillation at absolute pressures of lt 1 bar in which the water is largely removed from the tda in only a single step as a result it is possible as illustrated by means of the example to carry out the distillation with amounts of external steam of less than 0 6 kg of steam per kg of water separated off in the example 0 45 kg of heating steam per kg of water are separated off external steam means steam that is not obtained from the heat of reaction of the hydrogenation this represents a saving of more than 50 as compared with the prior art processes this savings was not possible with the processes according to the prior art because the separation of water by distillation has conventionally been carried out at normal or excess pressure and accordingly at high temperatures and the temperature level of the steam produced at low hydrogenation temperatures of from 100 to 200 u00b0 c is not sufficient in the only known process in which a reduced pressure is used for the distillation it is necessary according to the teaching of ep a 1602640 to combine a plurality of mutually connected distillation columns which are however likewise operated without the use of the heat from the hydrogenation according to the teaching of ep a 1602640 the evaporator of the column operated at low pressures and accordingly.