Two-dimensional and three-dimensional numerical simulations, which take into account both the low-temperature and high-temperature kinetics and yield correct induction times for hydrocarbon autoignition, are presented. The development of the autoignition is tightly connected to the formation of hot spots that evolved from the nonuniformities caused by pressure waves emitted by the propagating flame. It is shown that there is a considerable feedback: the propagating flame is accelerated by the temperature increase due to development of the cool flames in the end gas, and development of the autoignition is enhanced by the flame acceleration. Knocking onset is the self-ignition of the end-gas, which occurs as a result of combined effects of the end-gas compression by the moving piston during the compression stroke and by the propagating flame together with expanding combustion products. The calculated dependence of the temperature and pressure in the end gas on crank angle and predicted time of the autoignition onset for different engine operation conditions, in particular, for different percentage of EGR are found in a good agreement with the experimental data.