A numerical study was performed to elucidate the link between cyclic combustion variations in spark-ignition engines and instabilities in the non-linear processes occurring during the combustion. The instabilities in combustion were investigated by examining the response of a two-zone phenomenological combustion models to small deviations of mixture and flow conditions in the cylinder, such as the turbulence intensity at ignition, the overall equivalent ratio and the local equivalent ratio around the ignition site. The predicted combustion characteristics were validated and in good agreement with experimental data obtained from a single-cylinder research engine. The study suggested that the main deficiency of combustion in spark-ignition engines is the point-source ignition: it gives rise to slow development of initial flame; variations of the intermittent combustion process can occur when initial conditions at the ignition site are not repeatable from cycle to cycle. The instabilities in the initial flame can lead to significant variations in combustion parameters especially when the lean mixture limit is approached.