A multi-tubular reactor system for catalytically reacting a fluid reactant mixture to form a fluid product comprising a shell and a plurality of reactor tubes housed therein. The reactor system is adapted to allow heat-exchange fluid to flow between the shell and the external surface of the reactor tubes. A reactor tube comprises a reaction zone, and also a heating zone and/or a cooling zone. The reaction zone is positioned downstream of the heating zone. The cooling zone is positioned downstream of the reaction zone. The reactor tube contains a bed of solid particulate catalyst in the reaction zone. The reactor tube additionally contains a heat-exchanging essentially rod-shaped insert having a length of from 1 to 20%, preferably 1 to 5%, of the total length of the reactor tube in the heating zone and/or the cooling zone.