To clean a ternary component of nitrogen oxide, hydrocarbon and carbon monoxide contained in exhaust gas by alternately oscillating the treatment atmosphere of exhaust gas between the oxygen excess atmosphere and the reduction atmosphere.

A cleaning method for exhaust gas comprises (1) a first step where exhaust gas is brought into contact with a first catalyst consisting of at least one kind of element selected from Rh and Ir, and (2) a second step where the exhaust gas is brought into contact with a catalyst having a two layer structure which is composed of an outer layer consisting of at least one kind of element selected from Pt, Rh, and Ir, and an inner layer consisting of (a) at least one kind of oxide or multiple oxide selected from an alkali metal, an alkaline earth metal, aluminum, and a rare earth element, and (b) at least one kind of element selected from Pt, Rh, and Ir.