The applicability of the Method of Averaging (MOA) in the analysis of nonlinear axial combustion instabilities in solid propellant rocket motors is investigated. An approximate technique utilizing the Galerkin Method was first developed in order to reduce the computer time and core storage required to perform the stability calculations, which involve solving the conservation equations describing the two-phase unsteady flow of gases and particles in solid rocket combustors. At the expense of additional approximations, further reductions in computation time were obtained by using the MOA to solve the Galerkin equations. Solutions obtained with both the Galerkin Method and the MOA are compared with the “exact” numerical calculations for the simple case of the linear attenuation of small amplitude waves in a gas-particle mixture in a closed-ended chamber. For this simple problem, a one-mode approximation was used in the Galerkin and MOA analyses, and heat transfer between the gas phase and the particles was neglected in both “exact” and approximate analyses. Comparison of the decay rates calculated with the Galerkin method and the MOA with those obtained with the “exact” analysis indicates that the MOA may yield erroneous results in certain cases. The inclusion of gas/particle heat transfer and nonlinear mode coupling in these analyses is not expected to eliminate these discrepancies, therefore caution should be exercised in the use of the MOA in solid rocket stability analysis.