We present two novel algorithm features for the transient simulation of cyclic processes that exhibit cyclic steady state (CSS). In principle, the algorithm could be used for many cyclic process. Air separation using rapid pressure swing adsorption (RPSA) is used as an illustration. The first feature of the algorithm is an a priori rational stopping criterion to determine the CSS unambiguously. The stopping criterion ensures that neither is progress towards CSS truncated prematurely nor is computer time wasted by simulating an unnecessarily large number of cycles. The second feature of the algorithm is a reduction of the number of cycles required to reach the CSS while ensuring that the CSS is certainly determined. The conditions where these two novel algorithm features are applicable have been clearly identified. These two features could be employed regardless of the numerical methods used to solve the mathematical models, and regardless of the process in question, as long as certain desired conditions are fulfilled.