The present study was aimed to reveal the mechanisms of electrical conductivity of the perfluorosulfonic membrane (MF-4SK) in the proton-substituted form and an effect of Tb ions modified this matrix on these mechanisms. The frequency dependences of the complex permittivity at a temperature of 293 K and the temperature dependences of it at a frequency of 1 kHz for samples of the both forms have been measured. An increase in the permittivity ε´ value with decreasing frequency and increasing temperature was brought out. The maxima of the dielectric loss factor were obtained for the layers of the studied systems at different temperatures. The obtained experimental data allowed us to assume that there were distributions over relaxation times for relaxation oscillators. A transition from classical to quantum mechanical charge transfer was discovered and interpreted for the original and modified membranes.