The characteristics of auto-ignition in HCCI engines in the presence of charge stratification is studied theoretically using activation energy asymptotics. The analysis accounts for the effects of pressure rise due to piston motion and heat release, and the consequent compression-heating of the charge. The chemical kinetics are approximated using a single reaction step with a large activation energy and the compression-heating effects are accounted for through an entropy variable. The resultant model is simple and suitable for extensive parametric studies of HCCI engine combustion. Some preliminary results on the effects of mixture and composition stratification on the duration of burning are presented using a presumed Gaussian PDF for the initial temperature distribution. The effects of mixture stratification on the feasible operating conditions is demonstrated using simple criteria to delineate the knocking and incomplete end-gas combustion regimes.