The present invention provides polyalkylamines and a method for synthesising these compounds. These polyalkylamines have good properties as transfection agents. The method is an economic versatile two-step synthesis allowing the combination of various polyalkylamines, thus leading to the assembly of a combinatorial library of transfection agents. Moreover, the present invention provides polyalkylamine particles (polymersomes) containing said polyalkylamines and their use for delivering bioactive agents into cells. The invention also encompasses the use of lipid particles containing the cationic polyalkylamines as a medicament.