Preparation of N-(2-hydroxyethyl)-piperazine by reacting triethanolamine with ammonia in the presence of hydrogen at from 100.degree. to 500.degree. C. and from 10 to 500 bar over a heterogeneous catalyst in which the catalytically active material contains from 20 to 85% by weight of ZrO.sub.2 or Al.sub.2 O.sub.3 or mixtures thereof, from 1 to 30% by weight of at least one copper oxide, calculated as CuO, and from 1 to 60% by weight of at least one oxide of cobalt, nickel or molybdenum, calculated as CoO, NiO and MoO.sub.3, respectively.