A two-stage gas-separation membrane system includes two identical membrane modules held within a single casing. A feed gas is directed into the first module, so as to produce permeate and retentate streams. One of the latter streams then becomes the feed gas for the second module, and reaches the second module through a core tube located within the module. The product of the second module is the product gas for the system. The gas streams entering the two modules flow in mutually opposite directions. This arrangement makes it feasible to provide a two-stage system while using only the number of ports that would be needed for a single stage.