In a method of preparing polyalkyleneimines from alkyleneimines in the presence of a liquid solvent, and a catalyst, the preparing is effected semi-discontinuously in one reaction container. The preparing is optionally effected in the presence of further additives.Polyalkyleneimines obtained by such methods and formulations thereof likewise form part of the subject matter of the invention, especially those having a low proportion of chloride-containing compounds. Such polyalkyleneimines have uses in the field of medical technology, printing media, wastewater treatment, surface treatment, cosmetics, laundry detergents, biotechnology, packaging, electronics, paper, building construction chemistry, textiles, chromatography, ion exchangers, oil industry, ceramics, glass, membrane technology, catalysts, electroplating, biocides or wood protection. Further possible uses include as corrosion inhibitor, dispersant, additive in oils, for formulation of drugs, haircare products, scents and aromas, for preparing gene vectors, for functionalizing and modifying surfaces in electroplating and medical technology or for preparing cleaning systems for the semiconductor industry and lithium batteries.