We explore here the chronopotentiometric responses of pure electrolytes with anion-exchange Donnan exclusion membranes (IEDEM). As these electrolytes are locally depleted at the membrane surface in the absence of background electrolyte, electrical migration cannot be neglected. Yet, a linear relationship between the signal readout (square root of the transition time, τ0.5) and the electrolyte concentration is observed, albeit with much larger apparent diffusion coefficients than expected. We develop here a simplified migration–diffusion model based on the Nernst–Planck equation to explain the experimental data. As the flux of the counterion at the membrane surface must be zero for a permselective membrane, electrical migration is understood to precisely counteract the contribution of diffusional mass transport. This results in a simplified understanding of the mass transport processes at such membranes. Numerical simulations are performed to compare the predicted and experimental data. Based on these mechanistic and practical insights, permselective anion-exchange membranes are shown to respond to a range of ions in a similar fashion in the concentration range of 0.1–10 mM. The membranes are able to sustain significantly high current densities of 0.4 mA mm−2 and may become useful as ion detectors or counter electrode separation materials.