Homogeneous Charge Compression Ignition (HCCI) also known as Controlled Auto-Ignition (CAI) combustion, has recently emerged as a viable alternative combustion process to the conventional spark ignition (SI) gasoline and compression ignition (CI) Diesel engines, due to its potential for extremely low emissions and good fuel economy. One of the most important means of achieving and controlling HCCI combustion is to use recycle burned gases (EGR). In order to understand better the effects of recycled burned gases on such combustion process, detailed analytical studies were performed. Since HCCI combustion is a process dominated by chemical kinetics of the fuel-air mixture, an engine simulation model with detailed chemical kinetics has been developed and applied to a four-stroke gasoline engine fuelled with isooctane. After calibration and validation, the engine simulation mode was used to investigate the effects of EGR on HCCI combustion in a four-stroke gasoline engine. The characteristics of HCCI combustion investigated include the autoignition timing, the partial burning and knocking combustion, and NO emission. The heat capacity, dilution, chemical, and charge heating effects on the HCCI combustion process were studied individually by means of a series of analytical studies. When isothermal EGR is used, such as in HCCI combustion with diesel type fuels, the heat capacity has the largest effect on extending the combustion duration and slowing down the rate of the combustion. The larger heat capacity of EGR gases tends to retard the start of autoignition. The dilution of oxygen by EGR has little effect on autoignition but it has a similar effect on extending the combustion duration to that of the dilution effect. The dilution effect of EGR on lowing heat release rate is only noticeable at high concentrations. Finally, the chemical effect of CO2 and H2O was found to be negligible. When hot EGR is used in HCCI combustion, the charge heating effect of EGR has much greater effect on ignition timing and some less significant effect on the combustion duration and heat release rate than the other effects.