Abstract: The present invention deals with the synthesis of multifunctional dendrimeric and hyperbranched polymers for application as drug delivery systems of bioactive pharmaceutical compounds and as gene delivery systems (carriers of genetic material), the latter through condensation with genetic material. Specifically, the present invention deals with the synthesis of multifunctional compounds based on appropriate dendrimeric or hyperbranched polymers at the terminal surface of which have been introduced functional groups X, Y, Z. In addition, for gene delivery to cells these multifunctional systems will become cationic for the formation of complexes with negatively charged genetic material. The functional groups render the delivery systems recognizable by complementary cell receptors. Furthermore they render the systems stable in the biological milieu and facilitate their transport through cell membranes.