The present invention provides a composite body having, on a porous substrate and in the interstices of the substrate that includes fibers, preferably of an electrically nonconductive material, a porous layer (1) composed of oxide particles bonded to one another and partly to the substrate that include at least one oxide selected from oxides of the elements Al, Zr, Ti and Si, preferably selected from Al2O3, ZrO2, TiO2 and SiO2, and having, at least on one side, a further porous layer (2) including oxide particles bonded to one another and partly to layer (1) that include at least one oxide selected from oxides of the elements Al, Zr, Ti and Si, preferably selected from Al2O3, ZrO2, TiO2 and SiO2, where the oxide particles present in layer (1) have a greater median particle size than the oxide particles present in layer (2), which is characterized in that the median particle size (d50) of the oxide particles in layer (1) is from 0.5 to 4 μm and the median particle size (d50) of the oxide particles in layer (2) is from 0.015 to 0.15 μm, preferably 0.04 to 0.06 μm, a process for producing corresponding composite bodies and for the use thereof, especially in gas separation.