Reactors are described for the continuous reaction of gaseous substances on fixed bed catalysts with continuous temperature control and with the aid of a heat transport medium. These reactors are characterised by the design of the catalyst bed in the form of one or more regularly shaped sheet-like layers having a thickness of 0.01-50 cm, the surface of the catalyst layers being covered by a gas-permeable layer and this surface, on the starting material intake side and/or on the product outlet side, facing a likewise regularly shaped wall at a distance of 0.1 to 10 cm, which wall separates the space for the substances to be reacted or reacted substances from the space for the heat transport medium. The reactors are further characterised by the substances to be reacted being directed so as to flow through the catalyst bed approximately or completely perpendicularly to the sheet-like catalyst layers.