A process for preparing primary amines which have at least one functional group of formula (—CH2—NH2) and at least one further primary amino group by alcohol amination, the process comprising reacting a starting material having at least one functional group of formula (—CH2—OH) and at least one further functional group (—X), where (—X) is selected from a hydroxyl group and a primary amino group, with ammonia with elimination of water, wherein the reacting is homogeneously catalyzed in the presence of at least one complex catalyst comprising an element selected from groups 8, 9 and 10 of the Periodic Table and also a donor ligand.