A process for partial oxidation in the gas phase of C3 and/or C4 precursor compounds to (meth)acrolein and/or (meth)acrylic acid in the presence of a heterogeneous particulate catalyst in a reactor having - one or more cuboidal thermoplate modules which are each formed from two or more rectangular thermoplates arranged parallel to each other while in each case leaving a gap which is filled with the heterogeneous particulate catalyst and is flowed through by the fluid reaction mixture, the heat of reaction being absorbed by a heat carrier which flows through the thermoplates and thus at least partly evaporating, and also having - a predominantly cylindrical shell (4, 15, 16) which releases the pressure at the thermoplate modules, completely surrounds them and comprises a cylinder jacket and hoods (15, 16) which seal it at both ends and whose longitudinal axis is aligned parallel to the plane of the thermoplates, and also having - one or more sealing elements (7, 23) which are arranged in such a way that the fluid reaction mixture, apart from flowing through the reactor interior spaces bounded by the hoods (15, 16), only flows through the gap, - wherein a gas pressure is applied to the intermediate space between the thermoplate modules and the predominantly cylindrical shell, in that the application of pressure is constant and is effected by pressure-regulated feed and removal of nitrogen or in that the pressure is applied with continuous feeding of a gas which is inert or intrinsic to the process, particularly of nitrogen or cycle gas, through the intermediate space, - or wherein, in addition to the application of pressure, the intermediate space between the thermoplate modules and the predominantly cylindrical shell is filled with an inert bed material consisting of a chemically inert and sufficiently mechanically and thermally stable material. - one or more cuboidal thermoplate modules which are each formed from two or more rectangular thermoplates arranged parallel to each other while in each case leaving a gap which is filled with the heterogeneous particulate catalyst and is flowed through by the fluid reaction mixture, the heat of reaction being absorbed by a heat carrier which flows through the thermoplates and thus at least partly evaporating, and also having - a predominantly cylindrical shell (4, 15, 16) which releases the pressure at the thermoplate modules, completely surrounds them and comprises a cylinder jacket and hoods (15, 16) which seal it at both ends and whose longitudinal axis is aligned parallel to the plane of the thermoplates, and also having - one or more sealing elements (7, 23) which are arranged in such a way that the fluid reaction mixture, apart from flowing through the reactor interior spaces bounded by the hoods (15, 16), only flows through the gap, - wherein a gas pressure is applied to the intermediate space between the thermoplate modules and the predominantly cylindrical shell, in that the application of pressure is constant and is effected by pressure-regulated feed and removal of nitrogen or in that the pressure is applied with continuous feeding of a gas which is inert or intrinsic to the process, particularly of nitrogen or cycle gas, through the intermediate space, - or wherein, in addition to the application of pressure, the intermediate space between the thermoplate modules and the predominantly cylindrical shell is filled with an inert bed material consisting of a chemically inert and sufficiently mechanically and thermally stable material.