An investigation of supersonic combustion as related to propulsive systems for high Mach number, high altitude flight is described. A method of laboratory simulation is employed which is considered to be suitable for fundamental studies of diffusional-controlled supersonic combustion under conditions approaching those of actual flight. A numerical analysis of the mixing and combustion processes for an axisymmetric hydrogen-air ducted flow system was carried out, using a computer code based upon boundary layer concepts and including the effects of finite-rate chemistry. A limited parametric study of the combustor flow field was made for a Mach number range of 1.5 to 2.5 for the injected air stream. Hydrogen injection is central and parallel to the air stream and is assumed to occur sonically. A matched pressure condition between the fuel and air streams is assumed to exist at the combustor inlet. Inlet static pressures in the range of 0.1 to 0.2 atmospheres were considered. Results of the parametric study indicated the inlet conditions required to achieve auto-ignition within a reasonable combustor length. Based on the numerical data obtained, a mixing and combustion chamber was designed and fabricated for the performance of experimental tests under conditions closely matching those of the numerical study. Experimental data from a number of laboratory tests in which supersonic combustion was obtained are presented and discussed. (Author).