In the present paper, selective composite membranes containing sulfonated poly(ether ether ketone) (SPEEK) layers on top of a hydrophobic, polypropylene support are applied as absorber and desorber in a gas¿liquid membrane contactor system for the separation of paraffins and olefins. The water present in the absorption liquid swells the hydrophilic polymer sufficiently, making the membranes olefin-selective. As a result, even at high liquid velocities where the membrane determines the selectivity of the process, high selectivities can be obtained in combination with high productivities. Continuous contact between the absorption silver nitrate solution and the SPEEK layer prevents the layer from drying out and subsequent loss of selectivity. Previously, unknown high ethylene/ethane selectivities (>2700) are obtained in combination with reasonable ethylene productivities (7.6×10¿10 cm3/cm2 s Pa (1×10¿6 cm3/cm2 s cmHg)).