A pulsed cyclic membrane process, originally proposed by Paul for gas separations, has been investigated through a simulation and optimization study. For carbon dioxide hydrogen separation, it is shown that cyclic operation, based on an already reported material, could potentially compete with the most selective, still virtual, polymers, both in terms of selectivity and productivity. The use of asynchronous cycling operation, unexplored up to now, has been more specifically investigated. This mode of operation offers an extended range of performances from the point of view of the selectivity-productivity trade-off. A dedicated optimization study based on either nonlinear or genetic algorithm approach shows that, for this system, synchronous operation offers the best performances. These results have been confirmed by multiobjective optimization by means of the genetic algorithm.