Two epoxy systems with molecules having different topologies and functionalities, i.e. bifunctional linear and trifunctional star-like molecules, are characterized by means of both dielectric and mechanical spectroscopy methods in order to detect segmental and molecular relaxation rates as functions of temperature. The dielectric method is also used to determine the ionic conductivity effects in both systems. An effect of pressure at a constant temperature on the segmental relaxation times and on the conductivity is also investigated. We also examined coupling between the dc-conductivity relaxation process and α-relaxation process. As a result it was found that the dependence of the dc-conductivity relaxation time on the α-relaxation time can be described by means of the fractional Debye-Stokes-Einstein power-law relation. Like for our previous high-pressure results on other glass formers, it turns out that the pressure dependence of the α-relaxation time systematically deviates from the exponential form on approaching the glassy state.