Occurrences of pulsed instabilities in rocket combustion chambers have long posed irritating practical and puzzling theoretical questions. The term "triggering" was applied to the phenomenon in the 1960s to describe observations and computations of the unstable steep-fronted waves generated by sufficiently large pulses injected in linearly stable gas and liquid rockets. All such instabilities are classified as subcritical bifurcations in the theory of dynamical systems. Understanding the physical reasons for the existence of subcritical bifurcations in combustion chambers, and therefore the conditions under which they will occur, has been the subject of many investigations in the last three decades. It has long been recognized that the most likely causes of pulsed instabilities must be associated either with nonlinear gasdynamics or with nonlinear combustion processes. With numerical analysis of longitudinal oscillations, Baum and Levine have convincingly shown that nonlinear combustion is required. By suitable adjustment of parameters in a simple representation of the response of a burning solid, they have shown quite good agreement between computations and many experimental results. The results reported in this article are consistent with those of Baum and Levine, establishing the existence of pulsed instabilities when both nonlinear gasdynamics and nonlinear combustion processes are accounted for.