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 catalyst molding, where the reaction is carried out in the liquid phase at an absolute pressure in the range from 150 to 250 bar and the amination is carried out by means of a catalyst molding, the precursor of which can be prepared according to a process in which (i) an oxidic material comprising copper oxide, aluminum oxide and lanthanum oxide is provided, (ii) pulverulent metallic copper and/or copper flakes and optionally graphite is added to the oxidic material, (iii) the mixture resulting from step ii is shaped to give a molding, where the oxidic material is obtainable by simultaneous or successive precipitation of the component copper oxide, of the component aluminum oxide and of the component lanthanum oxide and subsequent drying and calcination and, after the shaping according to step iii, the catalyst molding is calcined again.