Process for the preparation of polyalkylenepolyamines by homogeneously catalyzed alcohol amination, in which aliphatic amino alcohols are reacted with one another or aliphatic diamines or polyamines are reacted with aliphatic diols or polyols with the elimination of water in the presence of a homogeneous catalyst and in the presence of hydrogen gas. Polyalkylenepolyamines obtainable by such processes and polyalkylenepolyamines comprising hydroxy groups, secondary amines or tertiary amines. Uses of such polyalkylenepolyamines as adhesion promoters for printing inks, adhesion promoters in composite films, cohesion promoters for adhesives, crosslinkers/curing agents for resins, primers for paints, wet-adhesion promoters for emulsion paints, complexing agents and flocculating agents, penetration assistants in wood preservation, corrosion inhibitors, immobilizing agents for proteins and enzymes.