**Abstract**

Using elements of the theory of classical detonation and previously obtained relations for spherical waves, the author tried to establish the range of admissible values of temperature, Mach numbers, and specific hydrogen content in the gas mixture of the possible existence of normal spherical detonation. The work took into account the critical values of the parameters associated with the kinetics of the chemical reaction at the front of the blast wave and the parameters that determine the intensity of the shock transition (minimum and maximum Mach number) for a given reacting medium. Using the example of the interaction of hydrogen and oxygen in a hydrogen-oxygen mixture, it was possible to graphically determine the range of values of the main physical quantities and parameters - the critical temperature, the detonation temperature of the quiescent medium, and the specific hydrogen content in the mixture required for spherical detonation. Mathematical modeling of the process was carried out at a fixed value of the pressure of the gaseous medium.

**Keywords:** detonation wave, critical temperature, range of permissible values, process modeling
