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The Controlled Auto-Ignition (CAI) combustion, also known as Homogeneous Charge Compression Ignition (HCCI) can be achieved by the negative valve overlap method in conjunction with direct injection in a four-stroke gasoline engine. A multi-cycle 3D engine simulation program has been developed and applied to study the effect of injection timing on CAI operations with lean and stoichiometric mixtures. The combustion models used in the present study are based on the modified Shell auto-ignition model and the characteristic-time combustion model. A liquid sheet breakup spray model was used for the droplet breakup processes. Based on the parametric studies on injection timing and equivalence ratio, the major difference between stoichiometric and lean-burn CAI operations is due to the fact that fuel injections take place during the negative valve overlap period.