Abstract: A set of prefabricated tube bundle reactor subassemblies is proposed which are adapted to be assembled at a construction site to provide a tube bundle reactor for carrying out catalytic gas and/or liquid phase reactions. In accordance with the invention, the reactor shell and the reactor heads, on the one hand, and the tube bundle and the tube sheets, on the other hand, form separate subassemblies, more specifically at least one shell/head subassembly, at least one head subassembly, and at least one tube bundle subassembly. The subassemblies comprise means for vertically supporting the tube bundle subassembly and for pressure tightly connecting the shell/head subassembly to the tube sheets without requiring heat treatment during assembly of the subassemblies. Likewise proposed are a tube bundle reactor for carrying out catalytic gas and/or liquid phase reactions and an arrangement of the kind of tube bundle reactors mentioned.