An exhaust gas purifying catalyst structure, comprising: a catalyst layer containing the exhaust gas purifying catalyst (5, 15, 25), the catalyst layer having a single-layer structure; and a fire-resistant inorganic substrate supporting the catalyst layer therein, wherein the fire-resistant inorganic substrate is a honeycomb substrate, the exhaust gas purifying catalyst, comprising: plural catalyst units containing: noble metal particles; and anchor particles serving as an anchor material of the noble metal particles and supporting the noble metal particles thereon, wherein the noble metal particles are at least one element selected from the group consisting of platinum, palladium and rhodium, and the anchor particles contain at least one compound selected from the group consisting of aluminum oxide, cerium oxide, zirconium oxide, yttrium oxide and neodymium oxide as a main component, the main component being a component of which content in the particle is greater than or equal to 50% by mole; and an enclosure material enclosing the plural catalyst units and separating the catalyst units from one another, wherein the enclosure material contains Al 2 O 3 or SiO 2 as the main component, wherein the anchor particles and the enclosure material both contain either one alkali element or one alkaline-earth element, and wherein the total content of the alkali element and the alkaline-earth element in the enclosure material with respect to the content of the noble metal particles is in a range from 0.5 to 2.0 in terms of a molar ratio. a catalyst layer containing the exhaust gas purifying catalyst (5, 15, 25), the catalyst layer having a single-layer structure; and a fire-resistant inorganic substrate supporting the catalyst layer therein, wherein the fire-resistant inorganic substrate is a honeycomb substrate, the exhaust gas purifying catalyst, comprising: plural catalyst units containing: noble metal particles; and anchor particles serving as an anchor material of the noble metal particles and supporting the noble metal particles thereon, wherein the noble metal particles are at least one element selected from the group consisting of platinum, palladium and rhodium, and the anchor particles contain at least one compound selected from the group consisting of aluminum oxide, cerium oxide, zirconium oxide, yttrium oxide and neodymium oxide as a main component, the main component being a component of which content in the particle is greater than or equal to 50% by mole; and an enclosure material enclosing the plural catalyst units and separating the catalyst units from one another, wherein the enclosure material contains Al 2 O 3 or SiO 2 as the main component, wherein the anchor particles and the enclosure material both contain either one alkali element or one alkaline-earth element, and wherein the total content of the alkali element and the alkaline-earth element in the enclosure material with respect to the content of the noble metal particles is in a range from 0.5 to 2.0 in terms of a molar ratio. plural catalyst units containing: noble metal particles; and anchor particles serving as an anchor material of the noble metal particles and supporting the noble metal particles thereon, wherein the noble metal particles are at least one element selected from the group consisting of platinum, palladium and rhodium, and the anchor particles contain at least one compound selected from the group consisting of aluminum oxide, cerium oxide, zirconium oxide, yttrium oxide and neodymium oxide as a main component, the main component being a component of which content in the particle is greater than or equal to 50% by mole; and an enclosure material enclosing the plural catalyst units and separating the catalyst units from one another, wherein the enclosure material contains Al 2 O 3 or SiO 2 as the main component, wherein the anchor particles and the enclosure material both contain either one alkali element or one alkaline-earth element, and wherein the total content of the alkali element and the alkaline-earth element in the enclosure material with respect to the content of the noble metal particles is in a range from 0.5 to 2.0 in terms of a molar ratio.