A continuum theory of dielectric relaxation within liquid crystal materials is described and used to model the response of dual frequency materials to single pulse voltage waveforms. The equations governing the anisotropic axis (director) angle, electric field, and induced polarizations are solved numerically to investigate pulsed addressing of a model zenithally bistable liquid crystal device. By suitably tailoring the voltage pulse, it is found to be possible to switch between both bistable states. For short pulses the high frequency components of the leading edge of the voltage pulse excites the perpendicular polarization and forces the director to lie parallel to the cell substrates. For longer voltage pulses the constant dc component of the voltage pulse excites the parallel polarization causing the director to lie perpendicular to the substrates. It is also found that reducing rotational viscosity and increasing the achievable dielectric anisotropies (particularly the high frequency value) can significantly reduce the operating voltages of such a device.