A theoretical study of multicomponent pressure swing adsorption (PSA) in which the system is considered to be one-dimensional, isothermal, locally at equilibrium with linear adsorption isotherms, and is considered to have negligible diffusion effects and axial total pressure variation is presented in this paper. The resulting mathematical model for multicomponent PSA is a set of first-order quasilinear hyperbolic partial differential equations. The similarities between this model and the model for multicomponent elution chromatography are used to define regions of constant state in the physical plane of time and distance and to obtain the solution in these regions semianalyticaly. Simple relations in terms of algebraic and ordinary differential equations which provide quick and simple estimation of the maximum product purity, maximum productivity, and maximum feed and purge times for PSA processes with an arbitrary number of components are derived. The application of the theory is illustrated by the construction of solutions for a four-step PSA process.