A process has been developed for spinning asymmetric hollow fiber membranes from a polyarylate-polyarylate block copolymer having a separation factor for pure gases in the oxygen-nitrogen pair of alpha(O-2/N-2) = 6.3 and an oxygen permeance coefficient of 2.4 Barrer. The effect of the polymer molecular weight, the composition of the dope solution, and the spinning parameters on the gas transport properties of the hollow fiber membrane and its geometry has been studied. The use of a polymer with a molecular weight of 67 kDa, as well as the introduction of surfactants into the dope solution, has made it possible to prepare samples of defect-free membranes with an oxygen permeance of 120 L(STP)/(m(2) h bar) and a separation factor of alpha(O-2/N-2) = 6.5, which correspond to the selective layer thickness of 60 nm.