Four lamellar based phases in the lecithin/water/oil phase system have been prepared and examined by low-frequency dielectric spectroscopy in the frequency range 3 x 10(-5) to 3 x 10(+5) Hz. The dielectric properties of the lamellar and liquid crystal phases have been determined over ranges of temperature, and measurements are reported for mixed phase systems. From this information the physical basis for the observed responses has been determined and is reported. Two broad patterns of dielectric response have been found, The ordered micellar and liquid crystal phases do not support dc conductances, even at the lowest frequencies used, The dispersions in these well-defined phases are of the fractional power law form, (iw)(-s), in frequency with 1 > s > 0.5 at the lowest frequencies and 0.5 > s > 0 in the hertz and kilohertz ranges, On the addition of decane, or by using a formulation that lies close to the lamellar/liquid crystal phase boundary, de conduction is observed, but in both cases the charge transport is blocked by electrode barrier layers and the generalized Maxwell-Wagner response is found. When the conductance is brought about by the addition of the oil, a large dipolar-like dispersion is observed in the frequency range below the inverse of the bulk relaxation time of the system, This dispersion has been associated with the discrete oil globules within the lamellar structure.