A new degradation analysis of ZnO-based varistors by AC impedance measurements is presented. From these measurements, which have been achieved on samples as a response to a small signal in the frequency range 10^-3 to 10⁵ Hz, at room temperature, the distribution function of the relaxation time constant has been deduced. The heterogeneity factor beta characterizing the barriers constituting the ZnO-based varistors has been used as a measure of degradation. Our data reveal that the grain boundaries are not identical, in good agreement with the numerical/experimental current(I)-voltage(V) characteristics of various single-grain junctions.