Simple wave theory is applied to the problem of adiabatic adsorption and desorption in a fixed bed. The heat and temperature dependence of the adsorption isotherm produce effects that are of importance in analysing the performance of exchange columns. Thus in elution a plateau of only partial desorption moves ahead of the zone of complete desorption. During the saturation of a bed a shock is formed and the heat released by adsorption moves ahead as a kinematic temperature wave.