Reactions between at least two fluid reactants are performed in a reactor comprising wall elements (1), slot-shaped reaction spaces (3) and cavities (5) for conducting a fluid heat-carrier through. Depending on the process and throughput, a modular structural design is chosen wherein an arbitrary number of wall elements (1) are assembled to a right-parallelepipedal block (24), the reaction spaces (3) are formed between lateral surfaces (2) of right-parallelepipedal wall elements (1), the reactants are introduced into the reaction spaces (3) from edge regions of one side of the block (24) and are conducted through the reaction spaces (3) in parallel flows and the fluid heat-carrier is conducted through the tubular cavities (5) extending in the interior of the wall elements (1).