The thermionic emission enhanced by barrier lowering and the Zener tunnelling in ZnO varistors are discussed. Capacitance versus voltage, reverse current versus temperature, and 1/fnoise measurements have been performed on commercial varistors. A model is proposed from which follows a diffusion voltageVDwhich is consistent both with the 1/C2vsVplot and with the thermal activation energy obtained from the reverse current versus 1/T. The empirical law &bgr;=d logV/dlogI= constant, is explained by Zener breakdown. The 1/fcurrent noise is proportional to the square of the current and independent of the conduction mechanism across reversely biased barriers.