Process for the preparation of alkoxylated polyalkylenepolyamines, comprising the following steps (a) homogeneously catalyzed alcohol amination, where 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 to give polyalkylenepolyamines, (b) reaction of these polyalkylenepolyamines with alkylene oxides to give alkoxylated polyalkylenepolyamines. Specific alkoxylated polyalkylenepolyamines obtainable by such processes and alkoxylated polyalkylenepolyamines and processes for their preparation. Uses of alkoxylated polyalkylenepolyamines as detergent additives, dispersants, textile auxiliaries, wood protectants, corrosion inhibitors.