Multivalent ion exchange is proposed as a generally applicable formalism to describe the non-linear chromatographic adsorption of biopolymers. Single- and multi-component isotherms are calculated that explicitly account for the influence of the mobile phase modulator concentration. Three regions of binding (strong, intermediate, and weak) are distinguished on the basis of strength of interaction, and the potential advantages of operating in the strong region for preparative purposes are pointed out. The inapplicability of the Langmuir isotherm in this region is demonstrated, and separation schemes that take advantage of the characteristic features of biopolymeric adsorption are described. The rectangular single-component ion-exchange isotherms are shown to reduce in the presence of competition to reversible concave-down forms.