A process for the preparation of alkyleneimines by subjecting sulfuric acid monoesters of aminoalkanols to an at least two-stage reaction with aqueous bases at a temperature of at least 110° C. under pressure, relieving the pressure of the reaction mixture and distilling off the alkyleneimines from the reaction mixture after each reaction stage, wherein the conversion in the first stage is from 40 to 90% and that in the second stage is from more than 90% to 99.99%.