The time, voltage, and temperature dependencies of transient polarization currents are reported for two types of varistors (i.e., ZnO and a SiC composite). The current transients exhibit a power-law time response to a step change in voltage (i.e., I≊I0/tm, where m is slightly less than unity) that persists over a time scale exceeding 10−8–104 s. The polarization current increases linearly with low applied voltage, but at more than a linear rate for higher voltage. The temperature dependence of the polarization current in medium voltage ZnO varistors is described by an Arrhenius plot with a change of slope near 200 K, which suggests thermal activation energies of about 160 and 10 meV. The time dependence of the polarization currents is confirmed and extended to short times by the ac admittance measured as a function of frequency. Transient changes in the ac admittance accompany the transient polarization currents, and exhibit time and temperature dependencies that reveal their close relationship to the polarization currents. By comparing transient admittance data to predictions of the Mott–Schottky theory of a barrier, it is concluded that the theory gives an inadequate account of the ac conductance, even though the voltage dependence of the capacitance is predicted well. Theoretical explanations of the polarization currents that are based upon a distribution of exponential relaxation times are examined. A reasonable account of the polarization current is provided, but the origin of the distribution is uncertain. Possible origins are a distribution of thermal activation energies or electron hopping among randomly distributed donors.