The invention relates to an oxidation reactor and process suited to operate the said reactor which houses a multitude of gas-tight and oxygen conductive membrane elements the external surfaces of which are arranged on the side of a reaction chamber to be filled with catalyst and which constitute, in conjunction with the membrane elements penetrable by oxygenous gas, a connection between the distribution chamber and a collection chamber and/or discharge section of the reactor. The reactor is characterised in that one or several spacer pieces establish a defined minimum distance between the external surface of a membrane element and the catalyst in the reaction chamber.