The performance of ion-exchange membranes for protein purification is analyzed using numerical solutions of different mathematical models. The models incorporate nonlinear sorption isotherms and mass-transfer coefficients based on either the overall or local solid-phase and liquid-phase driving forces. The numerical solutions are compared to analytical solutions which use overall mass-transfer coefficients only and, in general, are theoretically incorrect for nonlinear isotherms. The numerical solutions are fit to experimental breakthrough curves from the literature. The models allow the determination of the rate-controlling mass-transfer phenomena and solid-phase concentration, and prediction of the operating and membrane-design parameters needed to obtain sharp breakthrough curves.