According to the electrode theory widely accepted, the polarization resistance (R-p) of SOFC oxygen electrodes should be independent of the electrolyte resistivity (rho). This is a natural consequence from the usual theory, since it assumes that R-p is only determined by the interaction between the electrode and gas phase, However, it has been recently found that R-p increases with rho. This observation suggests that the R-p-determining factor should involve an electrolyte factor. This paper is an attempt to explain the R-p vs. rho relationship as being due to the locally variable polarization resistance of the electrode. Since the actual electrode makes discrete contacts with the electrolyte surface and the polarization resistance is more or less locally variable, it can be regarded as an assembly of many electrode elements having various local performances. When a load current is applied to such an electrode, an interfacial resistance (r(i)) arises due to a geometrical effect of the discrete contacts. By taking the effect of r(i) into account, it was predicted that R-p increases with increasing r(i). The validity of the theory was tested by checking whether or not the r(i) increases with increasing rho. The r(i) was measured by extrapolating the resistance of the electrolyte vs. sample length to zero length. In fact, r(i) increases with increasing rho. To obtain experimental evidence for the locally variable polarization, we measured the decay curves as a function of pO(2). The slope of the decay curve increases with increasing pO(2) suggesting that there is a local difference of polarization which drives an interfacial ionic current through the short-circuit pathway. We also tested this mechanism by an artificial nonuniform electrode which had a substructure consisting of two electrode elements, Ag and Au pastes electrodes. A polarization difference between the two electrode elements was found to increase with increasing rho of the electrolyte, as expected from the local current mechanism. This theory involves no mechanism of the local polarization resistance, therefore, being compatible with any known polarization mechanism as far as the R-p vs. rho relation is concerned.