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The objective of this article is to clarify the effect of thermal and equivalence ratio stratification on Homogeneous Charge Compression Ignition (HCCI) combustion under several conditions with three-dimensional computational fluid dynamics (3D CFD). Reynolds Averaged Navier-Stokes (RANS) simulation was used to calculate in-cylinder fluid dynamics. The 3D CFD simulation is also coupled with detailed chemical reaction to calculate HCCI combustion. First, the study with a simple engine model reveals that thermal stratification is more effective for prolonged combustion duration, which is a key factor for a high load limit of HCCI combustion, than equivalence ratio stratification. Thermal stratification has two-stage combustion: the combustion propagates from hot region slowly at first and then ignites in the entire in-cylinder region. Owing to this phenomenon, thermal stratification is more effective to mitigate HCCI combustion.