Abstract : This report is the final report of a three-year program with a 9-month NCE comprising both theoretical and experimental work on problems arising with unsteady combustion of gases intended for use in propulsion systems. The experimental work comprises two main efforts: (I) measurements providing the basis for inferring the local response function of a reacting mixture: and, (2) accurate determination of the behavior of a Rijke tube. Part (1) is based on greatly extended equipment purchased before this program began, with a DURIP grant from AFOSR. The basic part of the facility is apparatus for PLIF (planar laser induced fluorescence) measurements of a combustion system exposed to a sinusoidally varying pressure field, p' with q , the local fluctuation of heat release, appropriate measurements allow inference of q'/p', proportional to the response function and q'p', the integral over volume is proportional to the Rayleigh factor. In principal, knowledge of these two quantities permits deduction of all important dynamical properties of a dynamical system in the second part of this program, a particularly simple combustion system, the Rijke tube, has been investigated. We believe that we have produced the most accurate data ever obtained to confirm quantitatively much of basic behavior of the device. This result does much to solidify the basis for theoretically and practically treating the dynamics of time-dependent combustion systems.