A series of glyceryl monoolein/water liquid crystal systems containing 15%, 20%, 30%, and 35% w/w water have been investigated using dielectric spectroscopy over a frequency range of 10(-3)-10(6) Hz and a temperature range of 20-90 degrees C in order to facilitate association of the lyotropic and thermotropic phase behavior with the dielectric response. The phase boundaries of the mixes were determined independently using hot stage microscopy; The frequency-dependent dielectric spectra of systems containing lamellar, cubic, and hexagonal phases are reported and have been modeled using circuits corresponding to generalized Maxwell-Wagner responses. More specifically, the systems were found to correspond to a parallel bulk capacitance and conductance in series with a Maxwell-Wagner blocking capacitance, which was associated with an adsorbed layer at the electrode surfaces. An additional dispersion was observed corresponding to a series RC circuit, which was associated with charge transport across the lipid bilayers. It is proposed that the dielectric responses of the lamellar, cubic, and hexagonal phases exhibited by these systems may be described in terms of equivalent circuit models, which may in turn be related to specific structural features of the sample.