Local equilibrium theory allows us to determine many interesting features involving the application of pressure swing adsorption for purification, enrichment, and solvent recovery. In this paper, a simple local equilibrium model is constructed and solved analytically for the periodic state and its development. A single component is adsorbed and the adsorption isotherm is nonlinear. We consider the effect of isotherm nonlinearity, the minimum bed depths required for operation at the critical volumetric purge-to-feed ratio and at higher purge-to-feed ratios, the direct determination of periodic states, the development of periodic states, and the extent of accumulation of adsorbate in beds for favorable isotherms.