Ceramic hollow fibre membranes have been prepared out of aluminium-oxide and silicon-nitride. The fibres have been produced in a three stage process. A polymer filled with ceramic material has been prepared in a blender, a hollow fibre precursor has been made by extrusion of the melt with a spinneret and the precursor is transformed in a ceramic fibre by means of heat treatment at 1200-1650 degrees C. The outer diameter of the ceramic fibres is 800-2700 mu m depending on the diameter of the spinneret used. The hollow fibres are microporous and show gas flues of about 4-15 X 10(-8) m(3)/m(2) s Pa. In a final step alumina fibres have been modified by coating them with a gamma-alumina top-layer. The composite fibres have gas fluxes of about 4 X 10(-8) m(3)/m(2) s Pa and are gas selective. The selectivity is close to the value predicted by the Knudsen diffusion theory. So it is possible to produce a defect free ceramic composite hollow fibre membrane, This membrane can serve as a basis for a high selective membrane.