An investigation of supersonic combustion simulating conditions anticipated in propulsive systems for high altitude, high Mach number flight is described. A unique test facility in operation at the Aerospace Research Laboratories has the capability of simulating supersonic combustion conditions for flight Mach numbers near 12. The facility is considered unique because of its capability of providing conditions under which supersonic combustion can occur at low desities (1-4 psia) with diffusive mixing and with combustion resulting from auto-ignition. Experiments have been conducted with injector/combustor configurations to evaluate the ignition mechanism for axisymmetric streams of hydrogen and air and to evolve a combustion chamber design suitable for experimental study of sustained supersonic combustion. In a parallel theoretical phase, a numberical analysis of the combustion chamber flow field has been made by high speed computer; a parametric study of supersonic combustion in the diffusive hydrogen-air flow field over an air-jet Mach number range of 1.5 to 2.5 and a static pressure range of 1 to 3 psia was accomplished. Experimental data to-date have conclusively established the occurrence of sustained supersonic combustion in the diffusive hydrogen-air flow field at combustor entrance static pressures near 2.5 psia. (Author).