A method for producing unsaturated aldehydes and unsaturated carboxylic acids corresponding to a raw material in which at least one compound selected from propylene, isobutylene, t-butyl alcohol, and methyl-t-butyl ether is added as the raw material and subjected to gas phase contact oxidation with molecular oxygen or a molecular oxygen-containing gas, using a fixed-bed multistage heat medium circulating type of multi-tubular shell-and-tube reactor filled with a catalyst, wherein the multistage heat medium circulating type of multi-tubular shell-and-tube reactor includes a cylindrical shell, a tube sheet for separating the inside of the shell into two independent spaces, a baffle for dividing each of the two independent spaces inside the shell into two spatially continuous zones, and reaction tubes fixed to the inside of the shell while penetrating through the tube sheet and the baffle, wherein, in the two independent spaces inside the shell, heat transfer to the reaction tubes is performed independently at a temperature of 280 to 400 °C by the flow of an independent heat medium, and wherein the inside of the shell is separated into first and second independent spaces in the direction from an inlet to an outlet of the reaction tubes by the tube sheet, and the temperature of the first heat medium flowing through the first space is adjusted to be lower than the temperature of the second heat medium flowing through the second space, wherein at least four spatially continuous fixed catalyst layer zones corresponding to the spatially continuous zones formed by the baffle exist in the reaction tube, and the fixed catalyst layer zones have increased activity in the direction from an inlet to an outlet of the reaction tube, characterized in that the first fixed catalyst layer zone exhibits activity which is 75 to 85 % of the catalytic activity of the fourth fixed catalyst layer zone, the second fixed catalyst layer zone exhibits activity which is 85 to 95 % of the catalytic activity of the fourth fixed catalyst layer zone, and the third fixed catalyst layer zone exhibits activity which is 95 to 98 % of the catalytic activity of the fourth fixed catalyst layer zone. wherein the multistage heat medium circulating type of multi-tubular shell-and-tube reactor includes a cylindrical shell, a tube sheet for separating the inside of the shell into two independent spaces, a baffle for dividing each of the two independent spaces inside the shell into two spatially continuous zones, and reaction tubes fixed to the inside of the shell while penetrating through the tube sheet and the baffle, wherein, in the two independent spaces inside the shell, heat transfer to the reaction tubes is performed independently at a temperature of 280 to 400 °C by the flow of an independent heat medium, and wherein the inside of the shell is separated into first and second independent spaces in the direction from an inlet to an outlet of the reaction tubes by the tube sheet, and the temperature of the first heat medium flowing through the first space is adjusted to be lower than the temperature of the second heat medium flowing through the second space, wherein at least four spatially continuous fixed catalyst layer zones corresponding to the spatially continuous zones formed by the baffle exist in the reaction tube, and the fixed catalyst layer zones have increased activity in the direction from an inlet to an outlet of the reaction tube, characterized in that the first fixed catalyst layer zone exhibits activity which is 75 to 85 % of the catalytic activity of the fourth fixed catalyst layer zone, the second fixed catalyst layer zone exhibits activity which is 85 to 95 % of the catalytic activity of the fourth fixed catalyst layer zone, and the third fixed catalyst layer zone exhibits activity which is 95 to 98 % of the catalytic activity of the fourth fixed catalyst layer zone.