In a process for preparing diamines from aminoalcohols and nitrogen compounds selected from the group consisting of ammonia and primary and secondary amines at from 80.degree. to 250.degree. C. and pressures of from 1 to 400 bar using hydrogen in the presence of a zirconium, copper, nickel catalyst, the catalytically active composition comprises from 20 to 85% by weight of oxygen-containing zirconium compounds, calculated as ZrO.sub.2, from 1 to 30% by weight of oxygen-containing compounds of copper, calculated as CuO, from 30 to 70% by weight of oxygen-containing compounds of nickel, calculated as NiO, from 0.1 to 5% by weight of oxygen-containing compounds of molybdenum, calculated as MoO.sub.3, and from 0 to 10% by weight of oxygen-containing compounds of aluminum and/or manganese, calculated as Al.sub.2 O.sub.3 and MnO.sub.2 respectively.