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In the lecture there are considered basic schemes of fuel-air mixture detonative combustion in supersonic direct flow chambers. The main goal of the work is the formation of stable detonation combustion of the fuel-air mixture coming into Laval nozzle with a high supersonic velocity. It is numerically shown reality of stationary detonative combustion of hydrogen-air mixtures coming with high supersonic velocity in axisymmetric convergent-divergent nozzle at altitudes up to 16 km in addition an efficiency of this combustion rises with the altitude. Obtained stationary regimes of detonative combustion proved to be resistant to high-frequency short-wave perturbations of the mixture composition with not high amplitude. Central co-axial body can be an effective tool for initiation and stabilization of detonative combustion of fuel-air mixtures. The problem of a start up of axisymmetric convergent-divergent nozzle in high speed supersonic flow is solved numerically and experimentally. Fortunate start up was realized by throwing of the nozzle into preliminary formed supersonic stream.