Exhaust gas purification system and method for internal combustion engine

A high-temperature NOx trap for trapping NOx in a lean condition in a high temperature range is so located as to trap NOx released from a low-temperature NOx trap for trapping NOx in the lean exhaust condition in a low temperature range. A sensor is provided for monitoring an NOx release condition of the low-temperature NOx trap. A controller controls the exhaust air-fuel ratio of an engine to a lean side during the release of NOx from the low-temperature NOx trap, and controls the exhaust air-fuel ratio to a rich side temporarily after the release of NOx from the low-temperature NOx trap.