The local field effects on voltage contrast in the scanning electron microscope (SEM) mean that local fields generated by a non-uniform potential distribution on specimen surface cause a variation in the secondary electron (SE) detector current. It causes some errors in the voltage measurement. The authors present a theory to calculate the SE detector current in the presence of the local fields. In the calculation, they assume that the field distribution above the specimen surface (metal electrodes with 8 mu m width and 12 mu m separation) is two-dimensional. Analysed models are a conventional SEM detector system (model A), a retarding-field energy analyser with an extraction field (model B) and a high-resolution energy analyser with an extraction field (model C). The results show that the local field effects could not be neglected even in models B and C with strong extraction fields. The calculated values of local field effects in models A and B agree well with the experimental ones. The dependence of local field effects on the electrode geometry is equivalent to that on the extraction field, though this dependency is not so strong.