Two series of hyperbranched polymers (HP), polyurethanes and polyureas, with aromatic and aliphatic structures, are synthesized in one-pot method using commercially available monomers. The obtained HP samples were characterized by H-1 Nuclear Magnetic Resonance (NMR) spectroscopy, Gel Permeation Chromatography (GPC), Differential Scanning Calorimetry (DSC) and Thermal Gravimetric Analysis (TGA) measurements. Molecular dynamics in these systems were investigated by combining Thermally Stimulated Depolarization Currents (TSDC) and broadband Dielectric Relaxation Spectroscopy (DRS) techniques. High conductivity contribution in dielectric loss does not allow the study of the segmental a relaxation associated with the glass transition. In the glassy state two secondary relaxation mechanisms have been investigated, the gamma and the beta mechanism. The gamma relaxation mechanism, at low temperatures/high frequencies, is attributed to motions of the end groups (-OH for polyurethanes and -NH2 for polyureas), and has been found faster in the hyperbranched polyureas. in addition, our results reveal that gamma relaxation mechanism in both series depends on the chemical structure, being faster for aliphatic structures. The beta relaxation mechanism, at higher temperatures/lower frequencies, is attributed to the motions of branched ends with polar groups. Our study suggests that this mechanism may be a typical relaxation process for hyperbranched polyurethanes structures, not existed in the linear counterparts. All the systems exhibit dc conductivity at temperatures higher than T-g which shows Arrhenius-like temperature dependence and is characterized by rather high activation energies (in the order of 200 kJ/mol). At temperatures lower than T-g all the systems studied exhibit remarkably high charge mobility. In particular, aliphatic hyperbranched polyureas exhibit dc conductivity which has been found to be of VTF type concerning the temperature dependence. This result implies that the conduction mechanism is coupled with molecular motions in the glassy state of the polymer. (C) 2009 Elsevier Ltd. All rights reserved.