During operation with part load, a gasoline internal combustion engine is operated with a lean air / fuel mixture by auto-ignition. During operation with full load, spark-ignition is used to operate the engine. The internal combustion engine is operated in three auto-ignition combustion modes depending upon magnitude of a predetermined operating parameter. The operating parameter is indicative of the engine load or the engine speed. The three auto-ignition combustion modes are a gasoline reform auto-ignition combustion mode, an auto-ignition stratified charge combustion mode, and an auto-ignition homogeneous charge combustion mode. In the gasoline reform auto-ignition combustion mode that may be selected during operation with low part load, a first fuel injection during an exhaust gas retaining phase produces sufficient amount of active fuel radicals for promotion of auto-ignition of air / fuel mixture produced by a second fuel injection during the subsequent compression phase. In the auto-ignition stratified charge combustion mode that may be selected during operation with intermediate part load, a fuel injection during compression phase supports auto-ignition. In the auto-ignition homogeneous charge combustion mode that may be selected during operation with high part load, a fuel injection during intake phase supports auto-ignition.