The parameters of an extended three-wire model of ion-exchange materials conductivity, which characterize the current particles flowing through various structural fragments of the ion exchanger, are calculated based on the concentration dependence of the sulphocationite KU-2 resin electrical conductivity in electrolyte solutions of different nature. It is shown that most of the current in the resin is transferred through the channel with a consecutive arrangement of conducting gel and solution phases regardless of the counterion nature. The differences in model parameters for the resin in the salt and proton form, related to the specific mechanism of proton transfer, confirm the adequacy of the applied approach to the estimation of the counterion nature effect on the current transfer in resin.