The present invention provides a process of producing unsaturated aldehydes and unsaturated acids from olefins by fixed-bed catalytic partial oxidation in a shell-and-tube heat exchanger-type reactor. In this process, the reactor comprises a first-step reaction zone of mainly producing the unsaturated aldehydes, a second-step reaction zone of mainly producing the unsaturated acids, or both the two zones. The first-step reaction zone is divided into two or more zones by a partition. Each of the divided shell spaces is filled with a heat transfer medium, and the heat transfer medium in each shell space is maintained at isothermal temperature or a temperature difference of 0-5 ° C. The temperatures of the heat transfer media in each of the divided shell spaces are set to increase in the moving direction of reactants. In order to facilitate the removal of heat generation at a location where the partition is placed, a reaction inhibition layer is disposed in the first-step reaction zone. Also, in order to protect the catalyst layer from a highly exothermic reaction, the process is performed at a limited temperature difference between the temperature in a hot spot and the temperature of a molten salt. If the improved heat control system according to the present invention is used, the heat stability of the catalyst layer will be secured and the yields of intermediate and final products can be increased.