A compact catalytic reactor defines a multiplicity of first and second flow channels arranged alternately in the reactor, for carrying first and second fluids, respectively, wherein at least the first fluids undergo a chemical reaction. Each first flow channel containing a removable gas-permeable catalyst structure (20) incorporating a metal substrate, the catalyst structure defining flow paths therethrough, with catalytic material on at least some surfaces of each such path. The catalyst structure also incorporates a multiplicity of projecting resilient lugs (22) which support the catalyst structure (20) spaced away from at least one adjacent wall of the channel (17).