M practical importance has been attached to the problem of high frequency combustion instability, in particular, the unstable pressure oscillations which may affect the performance of a rocket motor. A thorough mathematical treatment of the linearized aspects of this problem has been given by Crocco and Cheng (1-3). Basing their theory on the sensitive time lag postulate, these authors have derived certain necessary conditions for the unstable operation of a rocket motor. However, the work of Crocco and Cheng does not elucidate the nonlinear dynamics of instability. There is a question of whether or not an acoustical perturbation will grow to become a pressure oscillation of large amplitude and destructive capabilities. An answer to this question is not within the scope of linearized theory. Existing mathematical methods do not permit a complete theoretical analysis of nonlinear combustion instability. Nevertheless, it is possible to understand the qualitative dynamics of finite amplitude pressure oscillations if the combustion field is represented by a relatively simple model. The present paper reports a number of theoretical conclusions which are derived from such a model. Of primary interest is the fact that a mechanism for instability follows from an ordinary equation for the burning rate, without evoking the postulate of a time lag. The stability of a pressure wave is essentially determined by the frequency of the oscillation and the pressure sensitivity of the burning rate function, in qualitative agreement with the original ideas advanced by Crocco (4).