The widely observed phenomenon of low-frequency dispersion is interpreted in terms of an electrochemical process in which ionic charge carriers migrating under the action of an external field combine to form neutral molecules, thereby eliminating charges which would be necessary to sustain the very high capacitances at low frequencies. Both charging and discharging currents are almost independent of time with the discharge currents consistently lower than the charging currents. The neutral molecules provide a reservoir of charge and of energy which become released on discharging the system after step-function charging, most of the charge and energy being dissipated in what is a highly lossy system. The frequency-domain response is then interpreted using the new concept of "energy criterion" which is particularly suited to the analysis of fractional power-law dependence on frequency. This provides a self-consistent and realistic theory of low-frequency dispersion and enables the connection to be made between time and frequency-domain responses, despite the fact that the strong non-linearity of the response makes the Fourier transformation of limited usefulness.