Preparation of ethyleneamines by reacting monoethanolamine (MEOA) with ammonia in the presence of a catalyst in a reactor (1) and separating the resulting reaction product, where ethylenediamine (EDA) obtained in the separation is reacted in a separate reactor (2) in the presence of a catalyst to give diethylenetriamine (DETA), and the resulting reaction product is passed to the separation of the reaction product resulting from reactor 1.