The invention relates to a reactor for carrying out heterogeneously catalyzed gas-phase reactions, having an internal element (11, 35) or a plurality of internal elements (11, 35) which are arranged in succession in the flow direction of the gas mixture of the heterogeneously catalyzed gas-phase reaction through the reactor (10), where the internal elements extend over the entire reactor cross section, wherein the one or more internal elements (11, 35) is/are at least partly made of a fiber composite ceramic material.