A polysulfone/polyethersulfone annular hollow-fiber (cube) membrane was prepared using a phase-inversion process, which is useful for further preparation of an internally staged permeator (ISP) for gas separation. This study focused on the techniques of fabricating the polysulfone/polyethersulfone annular-hollow-fiber membranes and its membrane permeators for gas enrichment. Two homogeneous polymer solutions comprising polysulfone/DMAc and polyethersulfone/NMP/water, respectively, were prepared and extruded with a triple-orifice spinneret into an annular-hollow-fiber membrane that possesses two distinct skin layers and is capable of providing two separation stages internally for gas separation. The performance of the ISP fabricated from the prepared annular hollow-fiber membrane was evaluated theoretically and experimentally under co/countercurrent and countercurrent flow patterns for various binary gas mixtures. The mathematical models generally describe satisfactorily the observed experimental results. A parametric study reveals that while, in general, better separation is available at lower values of overall stage cuts, highly purified permeate products could be achieved at higher values of overall stage cuts if the concentration of a permeating component in the feed stock is relatively high.