Zinc oxide ceramics composed of (mol%) 97·5 ZnO, 1 Sb2O3, 0·5 Bi2O3, 0·5 Co3O4, 0·5 MnO2 were investigated in the scanning electron microscope by voltage-contrast and voltage-current characteristic methods. Electron beam bombardment increases the conductivity of an active grain boundary. Oxygen ambient atmosphere plays an important role in the establishment and degradation of potential barriers in zinc oxide ceramics. This material is highly inhomogeneous due to the distribution of electrical properties of the individual grain boundaries. Electric current in zinc oxide ceramics flows through parallel paths of complex geometry. Every path contains active grain boundaries connected in series. The electronic properties of grain boundaries and the topology of the electrical network of active grain boundaries are two main features of non-ohmic zinc oxide ceramics.