An exhaust aftertreatment system that includes a suitable combination of particulate catalyst materials is used to effectively reduce an amount of NOX to N2 and water in a high-oxygen content exhaust flow from an engine that is controlled to operate by cyclically burning lean and rich mixtures of air and fuel. The catalyst materials of the exhaust aftertreatment system comprise (1) lanthanum-based perovskite oxide particles to oxidize NO to NO2, (2) barium oxide particles to temporarily store NO2, (3) copper oxide nanoparticles chemically deposited onto particles of cerium oxides to reduce NOX to N2 and to generate NH3, and (4) particles of a selective reduction catalyst to temporarily store NH3 and to reduce any residual NOX to N2 and water before the exhaust flow from the engine is discharged to the atmosphere.