The periodic behavior of an adsorption bed that is alternatively fed with a binary mixture in inert gas and purged countercurrently, but incompletely, with pure inert gas is analyzed using local equilibrium theory. The bed is isothermal with the two adsorbable components present in trace amounts and adsorption equilibrium described by a binary Langmuir isotherm. The purge step ends as soon as one of the components has been completely removed from the bed. For this nonlinear system, the periodic state is found analytically, without iteration, and feed and purge times are obtained directly. Both separation and purification problems are analyzed. A system is completely defined by three parameters : the constant separation factor for each component and the ratio of partition ratios of the components as pure feeds. Different combinations of these parameters yield wave interactions among simple waves and shocks, which are resolved numerically, and corresponding bed profiles that are quite dissimilar.