Abstract: Aliphatic amines are obtained by continuous addition of ammonia to C2- to C8-alkenes in the presence of a heterogeneous or homogeneous catalyst at a pressure of 2 to 8 MPa, a temperature of 220 to 320° C. and a molar ratio of ammonia to the alkene of 1.5 to 20, while the gaseous reaction mixture which leaves the second section, is cooled to a temperature near the dew point, it is led to the enrichment part of the first section, where it is sprayed in counterflow with a liquid mixture consisting of the starting substances. The unreacted starting substances thus disposed of the most of the amine formed are recycled under pressure in gaseous state to the second section, the liquid mixture in the impoverishment part of the section gets rid of the unreacted starting substances, and from the bottom of the first section the concentrate is conducted to further processing.