The experimental results of the study of the concentration dependence of the electrical conductivity and diffusion permeability of ion-exchange membranes which are in contact with solutions of weak electrolytes ( carboxylic acids) are provided for the first time. An attempt was made to correlate the observed properties of the membrane to their structure, based on the microheterogeneous model. Some features have been revealed that differentiate the behavior of membranes in solutions of strong and weak electrolytes. For example, for anion-exchange membranes, the dependence of the electrical conductivity on the equilibrium solution concentration disappears in the concentration above 0.05 M, and there is an insignificant increase in the electrical conductivity in lower concentrations. An explanation for the observed effects is suggested which takes into account that the electrical conductivity of the gel phase is much higher than the electrical conductivity of an electrically neutral solution. An equation is proposed which connects the electrical conductivity of a membrane with its ion-exchange capacity and mobility of the counterion in the gel phase. Recommendations on the practical aspect of electrodialysis technology for the treatment of weak electrolytes are given. From a fundamental point of view, it is concluded that for a full description of the transport-structural organization of ion-exchange membranes which are in a solution of a weak electrolyte, the knowledge of the concentration dependence of the electrical conductivity and diffusion permeability only is not enough, and other experimental methods are required.