Material balance for the reactant in a fixed-bed adsorption-reaction system is formulated to give a quasilinear partial differential equation of first-order. The equation is then solved analytically by applying the method of characteristics and the theory of mathematical shock. Freundlich isotherm is adopted for the equilibrium relationship whereas the reaction considered takes place in the fluid phase, being of first-order and irreversible. From the adsorption system without reaction the system behavoir is investigated when the adsorbate feed concentration undergoes a change of a step, a square wave, or an impulse. Concerning the adsorption-reaction system, it is assumed that only the reactant is adsorbable and the system behavoir is analyzed when the reactant feed concentration undergoes a change of a step or a square wave. The result shows that the reactant conversion is improved while partial separation between the reactant and the product is accomplished.