Ce0.8Sm0.2O1.9−La0.8Sr0.2Cr0.5Fe0.5O3−δ (SDC-LSCrF) composite hollow fiber membranes were prepared by phase inversion followed by sintering. Average oxygen fluxes of 0.5 cm3·cm−2·min−1 (STP) were measured, at 950 °C, by feeding either He or CO2 (30 mL·min−1) into the lumen of the hollow fiber (with length 48 mm), while exposing the shell side to ambient air. The oxygen flux at given conditions increases to 4.8 cm3·cm−2·min−1 (STP) when the reactive sweep gas CO is employed. The profound lowering of the activation energy for the oxygen flux relative to that observed upon using He and CO2 as sweep gas suggests that rate limitations by the surface exchange reaction occur when using the latter sweep gases. The developed hollow fiber membranes show excellent stability over the 750 h duration of the tests and therefore hold promise for application in oxyfuel combustion processes and membrane reactors.