A catalytic reactor comprises a plurality of fluid-impermeable plates defining side-by-side flow channels between them. Tight fitting within each flow channel is a sheet of corrugated material whose surfaces are coated with catalytic material. At each end of the flow channels there may be headers for 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 wall of the tube separating the adjacent channels, from the exothermic reaction to the endothermic reaction. The provision of side=by-side flow channels provides for structural strength and for enhanced heat transfer.