A process for producing a ceramic membrane in the form of a hollow fibre, which process comprises: forming a suspension by mixing inorganic oxide precursor particles with a solution of a polymer binder dissolved in a solvent for the binder; feeding the suspension through a spinneret to form hollow fibres; passing the fibres through an air gap and into a coagulant to solidify the fibres; heating the fibres to remove the polymer binder; and sintering the fibres to render them gas tight, wherein the polymer binder is selected so that it may be removed from the fibres by heating without leaving any residual species within the ceramic that will impair the oxygen permeability of the fibres.