An exhaust system for a diesel engine, which engine being operable in a plurality of modes including an idling mode, wherein the engine emits a relatively cool exhaust gas, and a running mode, wherein the engine emits a relatively hot exhaust gas, includes a solid NOx absorbent, whereby NOx is absorbed by the NOx absorbent during the idling mode and is desorbed and passed to atmosphere during the running mode and/or during acceleration from idling to running as the temperature of the exhaust gas increases, wherein during all modes the engine runs lean and the exhaust gas composition is lambda>1.