High frequency combustion instability continues to be a major problem in the development and operation of rocket engines. Most mathematical models simulating this phenomena involve the derivation and solution of complex non- linear differential equations. In an effort to overcome the mathematical difficulties associated with the solution of the nonlinear combustion instability problems, two methods of analysis were developed. In investigating the problems of combustion instability in an annular combustion chamber, a modified Galerkin method was used to produce a set of modal amplitude equations from the general non-linear partial differential acoustic wave equation. From these modal amplitude equations, the two-variable perturbation method was used to develop a set of approximate equations of a given order of magnitude. These equations were modeled to show the effects of velocity sensitve combustion instabilities by evaluating the effects of certain parameters in the given set of equations. From evaluating these effects, one can ascertain which parameters cause instabilities to occur in the combustion chamber. In this analysis, it is assumed that in the annular combustion chamber, the liquid propellants are injected uniformly across the injector face, the combustion processes are distributed throughout the combustion chamber and that no time delay occurs in the combustion processes.