Dielectric permittivity and loss have been measured over the frequency range 10(-2) Hz - 10 kHz between 100 K and 350 K for samples of 50/50 mixtures of each of two hyperbranched polyesters, one five-generation hydroxy functional (5G-OH) and one three-generation alkyl-terminated polymer (3G), with dielectrically inactive linear polyethylene. The thermal transitions of the hyperbranched polymers were studied with differential scanning calorimetry. Three relaxation transitions were found in 5G-OH : alpha, the glass-rubber transition and two subglass processes denoted beta and gamma showing Arrhenius temperature dependence both with an activation energy of 96+/-2 kJ mol-1. The low temperature process could be assigned to motions of the terminal hydroxyl groups whereas beta is due to reorientation of the ester groups. Sample 3G showed only a glass transition and one subglass process being assigned to reorientation of the ester groups. The high activation energy (202 kJ mol-1) of this process indicates that the ester groups are highly constrained in this polymer.