It has been found that after 300 h of operation of AMX and AMX-Sb anion-exchange membranes (Astom, Japan) in overlimiting current regimes in the process of electrodialysis desalination of 0.02 M NaCl, NH4Cl, NaH2PO4, and KC4H5O6 (KHT) solutions, the limiting currents, $$i_{{\lim }}^{{\exp }}$$ , determined by graphic processing of current–voltage curves increase in the order NaCl < NaH2PO4 < KHT. Their increments relative to those for the “fresh” membrane are 33, 90, and 128%, respectively. The growth in $$i_{{\lim }}^{{\exp }}$$ is accompanied by an increase in the thickness of the samples occurring in the NaH2PO4 and KHT solutions. In the case of NH4Cl, the values of $$i_{{\lim }}^{{\exp }}$$ decrease. It has been shown that a small decrease in counterion transport numbers during membrane operation has almost no effect on the values of limiting currents. The main contribution to the increase in $$i_{{\lim }}^{{\exp }}$$ is apparently made by electroconvection, which develops according to the mechanism of electroosmosis of the first kind. Its development is facilitated by the growth in the number and size of free-standing micrometer-sized cavities on the surface of anion-exchange membranes, the area and linear dimensions of which increase in the order NaCl < NaH2PO4 < KHT. These cavities are formed as a result of enhancement of electrochemical degradation of the ion-exchange material and the inert filler polyvinyl chloride at the membrane/solution interface in ampholyte solutions.