Dielectric spectroscopy (10(-2) Hz to 10(6) Hz) was employed to investigate the molecular dynamics of hyperbranched polyesters where the number of the generation is systematically varied from 2 to 5. As a first result, the dielectric properties depends strongly on the generation of the hyperbranched polymers. For higher generations (3 to 5) at temperatures below T-g two relaxation processes are observed, a gamma-process at lower temperatures and a beta-process at higher ones. The apparent activation energies are around 100 kJ/mol which seems to be too high for truly localized processes. For the Generation 2, only the gamma-process is observed. For all investigated polymers the dielectric alpha-relaxation could not be observed because of strong conductivity effects. Therefore, the conductivity is systematically analyzed which obeys the peculiarities found to be characteristic for semiconducting disordered materials. Especially, the Barton/Nakajima/Namikawa relationship is found to be valid. 2009 Wiley Periodicals, Inc. J Appl Polym Sci 113: 2477-2484, 2009