A pressure swing adsorption (PSA) system using two or more valves for controlling the flow of gases entering or exiting a bed of adsorbents is disclosed, where the two or more valves are opened sequentially (i.e., in at least two actions separated by a delay in time). The sequential opening of the valves may increase the degree to which adsorbed species are purged from the bed, and also facilitates more rapid execution of certain time steps of the PSA cycle, thus increasing adsorbent productivity The sequential opening of the valves may also allow for verification of valve operation by measuring either the absolute value, the slope (derivative) or the rate of change of derivative of the pressure, either in the adsorbent bed, in the downstream manifold, or in a volume of gas held in a buffer vessel.