An exhaust gas purifying catalyst capable of exerting excellent NO.sub.x purifying capability even at high exhaust gas temperatures, exceeding 500.degree. C., is provided.The catalyst is an absorption reduction-type NO.sub.x purifying catalyst comprising an NO.sub.x absorbent obtained by loading at least one alkali metal or alkaline earth metal on a crystalline ZrO.sub.2 composite oxide having added thereto at least one trivalent rare earth metal or divalent alkaline earth metal. Preferably, aluminum is further supported on the ZrO.sub.2 composite oxide. The NO.sub.x absorbent is considered to have an NO.sub.x absorption mechanism that an electron released from the alkali metal or the like enters into an oxygen vacancy part of the crystalline ZrO.sub.2 and this oxygen vacancy part functions as a strong base site for donating an electron to an electrophilic component such as NO.sub.x.