For chemical-engineering design purposes, it is useful, where possible, approximately to characterize the equilibrium between an ion-exchange material and any two exchangeable ion species involved by a constant selectivity coefficient. This can be done with the ideal or empirically modified mass-action law, but the application of even this simplified model to systems involving more than two exchangeable ion species, some of which differ in their valences, can lead to extremely cumbersome calculations. To overcome this difficulty, a successive-approximation algorithm is presented here, and specifically applied in the form of a program for a small electronic calculator.Within the limitations of the model, the program can compute the exchanger-phase composition of up to 10 ion species from the counterionic composition of the fluid phase, and vice versa. In addition to the given composition, a set of indepedent selectivity-coefficient and valence values is accepted as input. Instead of the valences, empirical, noninteger powers may be used where this improves the fit to experimental data.A method for bringing the data into a form suitable for direct solution is given, and the calculation procedure is illustrated with examples.Even in cases for which closed-form algebraic solutions can be developed, the present method, as implemented with the relatively slow, handheld electronic calculator, is fast enough to warrant its preferment, often even for the simplest binary ion-exchange calculations.