In this paper chronopotentiometric measurements are described to study the overlimiting ion transport through a Neosepta CMX cation and AMX anion exchange membrane. This technique is used to characterise the fluctuations in membrane voltage drop observed in the overlimiting region of current-voltage curves and to investigate the structural inhomogeneity of the aforementioned membranes. Above the limiting current the measurements show large voltage drop fluctuations in time indicating hydrodynamic instabilities. The amplitude of these fluctuations is increasing with increasing applied current density. The fluctuations also occur when a set-up is used where there is no forced convection and the depleted diffusion layer is stabilised by gravitation. Experimental transition times are found to be smaller than calculated for an ideally permselective membrane and indicate a reduced permeable membrane area. The results can be related to the theory of electroconvection due to an inhomogeneous membrane structure.