Equilibrium theory is applied to the analysis of the periodic performance of an isothermal pressure swing adsorber in which the bed is composed of two layers of different adsorbents. The feed consists of a single adsorbable component in inert gas, and the purge is pure inert gas. The adsorbents differ in capacities for the adsorbable species and in the shapes of isotherms, which can be linear or concave downward. We solve for the periodic concentration profile and for the depth of penetration of the shock into the second layer during the feed step. The solution is analytical and relies on the theory of characteristics. The periodic state is determined directly, without iteration. Examples consider the effects of isotherm shapes and capacities, the direct determination of the periodic states, and the optimum layering of beds.