The processes affecting the nonlinear acoustic stability of a combustor are examined in an overview fashion. Emphasis is placed on liquid-propellant rocket motors but other systems are briefly mentioned and some broadly applied principles and observations are discussed. A nonlinear wave equation is developed for a two-phase mixture and the roles of various terms in the equations are discussed. A review is made of various combustion processes, their associated characteristic times, and the impacts on stability in certain cases. Many relevant scales for length and time are identified. Special issues for supercritical and transcritical combustion are discussed. Bistable operational domains are shown to be present in some systems, making nonlinear triggering of an instability a possibility. Relations between the natural frequency of oscillation for the combustion chamber and the characteristic combustion times are identified with regard to impact on the combustor stability. The amplitude of the limit cycle and the transient time for limit-cycle development are related to the mean-flow Mach number. The role of shock-wave dissipation in amplitude determination is described.