The application of olefin-selective membrane materials in gas-liquid membrane contactors for the separation of paraffins and olefins using a silver nitrate solution as the absorption liquid turned out to be very successful, especially with respect to the olefin/paraffin selectivity obtainable. Composite hollow-fiber membranes with a top layer of a highly permeable block copolymer of poly(ethylene oxide) (PEO) and poly(butylene terephthalate) (PBT) are prepared and applied in a gas-liquid membrane contactor for the separation of paraffins and olefins using a silver nitrate solution as the absorption liquid. The water present in the absorption liquid swells the hydrophilic polymer sufficiently. This prevents drying out of the layer and enables the partitioning of silver ions into the polymer matrix, making it olefin-selective. Ethylene permeabilities obtained are comparable to the values found for membranes with nonselective, elastomeric top layers (40-50 barrer). Selectivities, however, are more than 20 times higher. Independent of the liquid flow rate, a selectivity of 165 is obtained for PEO/PBT-coated membranes. This makes the application of olefin-selective membranes in a membrane contactor for olefin/paraffin separations very attractive.