This paper presents a novel approach to the characterization of dielectrics exhibiting dispersion with frequency and the derivation of their equivalent circuits. The approach is based on the utilization of generalized relaxation time distribution (GRTD) facilitated by the analysis of dispersion in the dielectric constant complex plane. New parametric characterizations are introduced leading to a direct derivation of a distributed resistance-capacitance (R-C) network. The validity of this new methodology is examined by comparing reported measurements of a.c. resistivity and permittivity of zinc oxide (ZnO) varistors with those obtained from distributed parameter predictions. A discrete form of the equivalent network is also derived consisting of 16 R-C branches. The results of the distributed parameters and discrete equivalent network will be shown to agree satisfactorily with measurements over the frequency range of 30 Hz to 10 MHz. Remarkable agreement was also obtained between measured dispersion and network predictions for a perfluoropolyether microemulsion polymer over the frequency range of about 100 kHz up to 100 MHz using 18 R-C branches.