A process for producing acrolein and acrylic acid or methacrolein and methacrylic acid by subjecting propylene or at least one kind selected from isobutylene and tertiary butanol to vapor-phase catalytic oxidation with a gas containing molecular oxygen using a fixed bed multitubular reactor, the process comprising: A) providing a plurality of catalyst layers formed by division into N, where N represents an integer of 2 or more, in a raw material gas flow direction of reaction tubes and regarding the catalyst layer present closest to the reaction gas inlet side among the catalyst layers as Z in and the catalyst layer present closest to the reaction gas outlet side among the catalyst layers as Z out; and B) packing a catalyst so that activity of the catalyst packed in Z out becomes higher than activity of the catalyst packed in Z in to satisfy the following expression: 0.5 ≤ C max − C crs ≤ 5 C max: the raw material conversion rate at which the yield of the objective products becomes maximum; and C crs: the raw material conversion rate at which, when the maximum temperature of the catalyst layer Z in is regarded as T in, the maximum temperature of the catalyst layer Z out is regarded as T out, and the raw material conversion rate is changed, the high and low correlation between T in and T out is reversed, wherein the catalyst is represented by the following general formula: MO a Bi b Ni c CO d Fe f X g Y h O x wherein Mo, Bi, Ni, Co and Fe represent molybdenum, bismuth, nickel, cobalt and iron, respectively; X represents at least one element selected from tungsten, antimony, tin, zinc, chromium, manganese, magnesium, silica, aluminum, cerium and titanium; Y represents at least one element selected from potassium, rubidium, thallium and cesium; and a, b, c, d, f, g, h and x represent the numbers of atoms of molybdenum, bismuth, nickel, cobalt, iron, X, Y and oxygen, respectively, such that a=12, b=0.1 to 7, c+d=0.5 to 20, f=0.5 to 8, g=0 to 2, h=0.005 to 2, and x is a value determined by the oxidation state of the individual elements. A) providing a plurality of catalyst layers formed by division into N, where N represents an integer of 2 or more, in a raw material gas flow direction of reaction tubes and regarding the catalyst layer present closest to the reaction gas inlet side among the catalyst layers as Z in and the catalyst layer present closest to the reaction gas outlet side among the catalyst layers as Z out; and B) packing a catalyst so that activity of the catalyst packed in Z out becomes higher than activity of the catalyst packed in Z in to satisfy the following expression: 0.5 ≤ C max − C crs ≤ 5 C max: the raw material conversion rate at which the yield of the objective products becomes maximum; and C crs: the raw material conversion rate at which, when the maximum temperature of the catalyst layer Z in is regarded as T in, the maximum temperature of the catalyst layer Z out is regarded as T out, and the raw material conversion rate is changed, the high and low correlation between T in and T out is reversed, C max: the raw material conversion rate at which the yield of the objective products becomes maximum; and C crs: the raw material conversion rate at which, when the maximum temperature of the catalyst layer Z in is regarded as T in, the maximum temperature of the catalyst layer Z out is regarded as T out, and the raw material conversion rate is changed, the high and low correlation between T in and T out is reversed,