A new theoretical model for travelling wave cycling zone adsorption is developed based on equations derived from the continuous flow, equilibrium staged model of chromatography. The model includes zone spreading effects and can use Langmuir, Freundlich, or linear adsorption equilibrium relationships. Inherent in the model is the ability to use temperature, concentration, or pH as cyclic thermodynamic variables and these cyclic variables can be input to the model as either square or ramp waves in the traveling wave mode. The equations are solved numerically on a computer utilizing a modified fourth order Runge-Kutta integration scheme. The theoretical predictions are compared with experimental results for single and multicomponent separations. Good agreement is observed between theory and experiments when accurate equilibrium data are available. When approximate equilibrium data in the form of linear isotherms or superimposed isotherms for multicomponent systems are used, the model gives qualitative but not quantitative agreement with the experimental results. Columns operating as cycliing zone adsorbers have considerably fewer stages than when used in elution chromatography.