Research has been undertaken to achieve an improved understanding of physical phenomena present when a supersonic flow undergoes chemical reaction. A detailed understanding of supersonic reacting flows is necessary to successfully develop advanced propulsion systems now planned for use late in this century and beyond. In order to explore such flows, a study was begun to create appropriate physical models for describing supersonic combustion, and to develop accurate and efficient numerical techniques for solving the governing equations that result from these models. From this work, two computer programs were written to study reacting flows. Both programs were constructed to consider the multicomponent diffusion and convection of important chemical species, the finite rate reaction of these species, and the resulting interaction of the fluid mechanics and the chemistry. The first program employed a finite difference scheme for integrating the governing equations, whereas the second used a hybrid Chebyshev pseudospectral technique for improved accuracy. Drummond, J. Philip Langley Research Center BOUNDARY LAYERS; CHEMICAL REACTIONS; FLUID MECHANICS; MIXING; MIXING LAYERS (FLUIDS); NUMERICAL ANALYSIS; SIMULATION; SUPERSONIC FLOW; CHEBYSHEV APPROXIMATION; COMPUTER PROGRAMS; FINITE DIFFERENCE THEORY; HYPERSONIC AIRCRAFT; SUPERSONIC COMBUSTION RAMJET ENGINES...