The present invention is directed to a combination reactor system for exothermic reactions comprising a trickle-bed reactor and a shell-and-tube reactor. This combination allows the system to efficiently remove heat while also providing the ability to control both the temperature and/or reaction progression. The trickle-bed reactor removes heat efficiently from the system by utilizing latent heat and does not require the use of a cooling or heating medium. The shell-and-tube reactor is used to further progress the reaction and provides a heat exchanger in order to introduce fluid at the desired temperature in the shell-and-tube reactor. Also, additional reactant or reactants and/or other fluids may be introduced to the shell-and-tube section of the reactor under controlled temperature conditions.