We have studied theoretically the effects of pH on the ion transport through amphoteric polymer membranes composed of weak polyelectrolytes where the charged groups are randomly distributed along the axial direction of the membrane. This system serves as a simplified model for the pH controlled ion transport and drug delivery through membranes of biological interest. The theoretical approach employed is based on the Nernst-Planck equations. The complete system of electrical charges formed by : (i) the pH dependent, amphoteric membrane fixed charge, and (ii) the four mobile charges (the two salt ions and the hydrogen and hydroxide ions) have been taken into account without any additional assumption. The model predictions show that the ionic fluxes and the membrane potential are very sensitive to the external pH, and the potential utility of these predictions for the analysis of experiments involving pH dependent passive transport through membranes is emphasized.