The occurrence of combustion oscillations has recently raised a serious concern in the development of scramjet engines. This phenomenon results from the mutual coupling between the unsteady heat release and local flow fluctuations in the flame zone, and has been commonly observed in other types of airbreathing systems such as ramjet and gas-turbine engines. In a scramjet engine, acoustic waves may arise in an unsteady combustion process and propagate upstream through various subsonic flow regions (such as boundary layers, recirculation zones in flame-holding areas, and regions behind precombustion shock waves). These waves then modify the local flowfield and create vortical and entropy disturbances convected downstream into the flame zone. The ensuing pressure and velocity fluctuations perturb the heat-release process and generate acoustic waves traveling upstream. A feedback loop is thus established causing large-amplitude flow oscillations in the engine. Recent experiments have demonstrated the existence of flow oscillations in a hydrocarbon-fueled scramjet engine facility with frequencies of 100-160 Hz for liquid JP-7 fuel and 300-360 Hz for gaseous ethylene fuel. The present work attempts to establish an integrated theoretical/numerical framework to investigate the combustion oscillations in a scramjet combustor equipped with aerodynamic ramp fuel injectors and a cavity flameholder. Various underlying mechanisms responsible for driving instabilities in a combustor are explored systematically.