Pressure swing adsorption (PSA) and membrane-based gas separation processes are two different alternatives for effective, continuous bulk gas separation at the industrial scale. Both these processes possess characteristics that render them advantageous over conventional cryogenic processes, and they can be combined into a Hybrid Separation System (HSS). Dynamic simulation and optimisation of a HSS must rely on all mathematical equations describing the dynamic behaviour of PSA and membrane permeation modules in a single flowsheet. The mathematical model is a set of Partial Differential and Algebraic Equations (PDAE) and has been used to investigate two HSS classes, considering the case of air separation. The paper considers two HSS concepts (for same and opposite separation selectivity), and presents dynamic simulation and optimisation results, focusing on the performance of the HSS flowsheet and demonstrating significant improvements over the standalone PSA and membrane processes.