A new analytical technique for the solution of nonlinear longitudinal combustion instability problems in rocket combustors is developed. Using relatively little computation time, this technique is capable of predicting the transient and limit cycle behavior of the combustion instability oscillations as well as the disturbance amplitude required to trigger an instability in a linearly stable motor. The limit cycle waveforms are found to exhibit shock wave characteristics for most unstable engine operating conditions. It is shown that the characteristics of the resulting instability are independent of the nature of the initial disturbance and they depend solely upon the engine operating conditions and the characteristics of the unsteady combustion process. Calculated results indicate that a second-order analysis can adequately describe the behavior of combustion instability oscillations over a broad range of engine operating conditions; however, higher order effects must be included in order to investigate engine triggering. A method for determining the combustion parametersnand τ from experimental data is proposed.