In a previous study (Webley, P. A.; He, J. Fast solution-adaptive Finite Volume Method for PSA/VSA Cycle Simulation. 1. Single Step Simulation. Comput. Chem. Eng. 2000, 23, 170 1), a fast, solution-adaptive finite-volume technique for the simulation of a single adsorption step for a variety of boundary conditions was described. In this study, we apply this method to the simulation of nonisothermal PSA/VSA cycles of general complexity. Using successive substitution, stage-wise node refinement, and control algorithms, rapid cyclic steady state can be achieved even for problems with very long dynamics. We illustrate the advantages of node refinement as a useful tool for accelerating convergence to cyclic steady state. Simultaneous incorporation of control techniques into the successive substitution framework allows for rapid convergence of the PSA process to design specifications. We compare the results of our simulator to experimental data for a two-bed VSA process and find good agreement in pressures, flows, and temperatures.