NOVELTY - A hybrid membrane structure (300) comprises monolithic inorganic porous support (302) comprising first end (310), second end (312), and several inner channels (314) having surfaces defined by porous walls and extending through the support from the two ends; optionally, at least one porous inorganic intermediate layer (306) coating the inner channel surfaces of the inorganic porous support; and oxygen-ion conducting ceramic membrane (304).    USE - As a hybrid membrane structure useful for separating oxygen from gas stream (claimed); in the conversion of coal to liquid fuel and in the conversion of natural gas to liquid fuels and chemicals; for accomplishing first half of the transition from natural gas to syngas to hydrogen fuel to provide pure hydrogen for transportation; and to provide oxygen or oxygen-rich combustion for high efficiency and lower pollution, especially for low nitrogen oxides (NOx) burning.    ADVANTAGE - The membrane structure can solve the significant separation problems in processing industries such as O2 separation. In the hybrid membrane structures, the inorganic porous support structure can provide a backbone for surface area, mechanical strength, and durability, while providing surface area packing density comparable to the pure polymeric membranes. In the hybrid membrane structures, the inorganic porous support can have a uniform pore structure on the inorganic porous support channel surfaces. This can enable deposition of a thin and durable oxygen-ion conducting ceramic membrane layer; and the thin oxygen-ion conducting ceramic membrane layer can offer high permeation flux. The hybrid membrane structures can thus provide a large potential advantage in manufacturing cost relative to the cost of manufacturing prior art inorganic membranes. The monolithic oxygen-ion conducting ceramic membrane products of small channel sizes also offer surface area packing density nearly one order of magnitude higher than conventional tubular membrane of comparable body diameter. This can lead to dramatic reduction of both the membrane cost per surface area and the engineering costs to assembly large surface areas of membrane modules. The multiple-layered membrane structures enable the use of support structures of large pores (i.e. high permeability through the bare support) and enable deposition of thin ion-conductive membrane layers (i.e. high membrane permeation flux). As a result of enhancement to both support and membrane permeability, the membrane-layer design enables achievement of high membrane permeation flux.    DETAILED DESCRIPTION - A hybrid membrane structure (300) comprises a monolithic inorganic porous support (302) comprising first end (310), second end (312), and several inner channels (314) having surfaces defined by porous walls and extending through the support from the first end to the second end; optionally, at least one porous inorganic intermediate layer (306) coating the inner channel surfaces of the inorganic porous support; and an oxygen-ion conducting ceramic membrane (304). When the hybrid membrane structure does not comprise the porous inorganic intermediate layer, the oxygen-ion conducting ceramic membrane coats the inner channel surfaces of the inorganic porous support. When the hybrid membrane structure comprises the porous inorganic intermediate layer, the oxygen-ion conducting ceramic membrane coats the surface of the porous intermediate layer. INDEPENDENT CLAIMS are included for the following:    (1) a method for separating oxygen (O2) from a gas stream involving either introducing a feed gas stream comprising O2 into the first end of the hybrid membrane structure, and collecting a permeate gas stream from the hybrid membrane structure that is higher in O2 content than the feed gas; or introducing a feed gas stream comprising O2 into the first end of the monolithic inorganic porous membrane, and collecting at the second end of the monolithic inorganic porous membrane an oxygen-rich gas stream from the channels plugged at the first end;    (2) a method for making (M1) a hybrid membrane structure involving providing the monolithic inorganic porous support; optionally applying the porous inorganic intermediate layer to the inner channel surfaces of the inorganic porous support; and applying the oxygen-ion conducting ceramic membrane;    (3) a monolithic inorganic porous membrane comprising first end, second end, and several inner channels having surfaces defined by porous walls and extending through the support from the first end to the second end, where the monolithic inorganic porous membrane comprises a mixed-conductive material.    DESCRIPTION OF DRAWING(S) - The figure shows a longitudinal cross-sectional view of the hybrid membrane structure.    Hybrid membrane structure (300)    Inorganic porous support (302)    Oxygen-ion conducting ceramic membrane (304)    Porous inorganic intermediate layer (306)    Inner channels (314)