An innovative membrane-based process for the separation of gaseous streams has been developed and tested at lab-scale. The new process can be conveniently carried out on the same modules currently employed for conventional gas separation membrane systems, and it relies on periodic swing of the downstream pressure, while upstream conditions are kept constant. Such new unit operation is run with no need of switching streams, and it allows to process constant flow rate and composition of both feed and retentate, while permeate is collected at assigned frequency, resulting in an overall on-average steady state process. An on-off control strategy over time of permeate collection produces alternate sorption/desorption steps in the membrane, associated to increase/decrease cycles of downstream pressure in the process, in a similar fashion to pressure swing adsorption (PSA). Indeed, consistently with the hybrid nature of the new process, the specific dynamic control of downstream pressure allows the exploitation of both resistive (permeation) and capacitive (adsorption) properties of the membrane, and the associated characteristics in terms of selectivity. By changing the duration of pressure swing period, the resistive or capacitive properties of the membrane can be conveniently tuned in order to explore different performances of the process, in terms of key component recovery and separation factor.