A catalytic reactor comprises a stack of sheets defining flow channels between them. Within each flow channel is a flexible wire structure whose surfaces are coated with catalytic material. Flow channels for a first gas extend along S-shaped curved paths whereas the flow channels for a second gas are straight. The reactor incorporates header chambers to supply gas mixtures to the flow channels, each header chamber being a rectangular cap attached to a face of the stack. The reactor enables different gas mixtures to be supplied to adjacent channels, which nay 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 adjacent channels, from the exothermic reaction to the endothermic reaction. When the catalyst in one set of flow channels becomes spent, it can be replaced by removing a header.