Process for the preparation of a mono-N-alkylpiperazine of the formula I in which R1 is C1- to C5-alkyl or 2-(2-hydroxyethoxy)ethyl, by reacting diethanolamine (DEOA) of the formula II with a primary amine of the formula H2N—R1 (III) in the presence of hydrogen and a supported, metal-containing catalyst, where the catalytically active mass of the catalyst, prior to its reduction with hydrogen, comprises oxygen-containing compounds of aluminum, copper, nickel and cobalt and, in the range from 0.2 to 5.0% by weight, oxygen-containing compounds of tin, calculated as SnO, and the reaction is carried out in the liquid phase at an absolute pressure in the range from 95 to 145 bar.