The present invention describes a process for the preparation of triethylenediamine by reacting piperazine over a zeolite catalyst which, in addition to SiO₂, contains an oxide of at least one further divalent, trivalent or tetravalent metal M, wherein the zeolite has a molar Si/M ratio of 100. In particular, a zeolite of the ZSM-5 type is used. The use of the zeolites permits suppression of the undesired formation of the byproduct 2-ethylpiperazine and hence considerable simplification of the working-up, in combination with high piperazine conversions and a small excess of water.