A catalytic reactor comprises a plurality of sheets defining flow channels between them. Within each flow channel is a foil of corrugated material whose surfaces are coated with catalytic material. Flow channels for a first gas extend in oblique directions relative to the flow channels for a second gas. The reactor incorporates header chambers to supply gas mixtures to the flow channels, the headers communicating with adjacent channels being separate. The reactor enables different gas mixtures to be supplied to adjacent channels, which may be at different pressures, and the corresponding chemical reactions are also different. Where one of the reactions is endothermic while the other reaction is exothermic, heat is transferred through the sheets separating the endothermic reaction. When the catalyst in one set of flow channels becomes spent, it can be replaced by removing a header.