<p>A simulation of the continuously rotating transverse detonation waves in a plane-radial annular combustion chamber has been carried out, and the peculiarities of the initial (linear) stage of their development were determined. The problem on the linear mode stability, arising in this case, of the cylindrical front of Chapman–Jouguet deflagration combustion of a gas mixture in a radially diverging subsonic flow of the mixture with a small Mach number was solved taking into account the diffusion-thermal processes in the combustion front with the use of the Markstein model. The unstable modes of oscillations and waves with increasing amplitudes in such a flow were revealed. The quasi-eigenfrequencies and three-dimensional modes of the oscillations and waves of disturbance of the combustion front were determined. Results of investigation of the stability of the modes of oscillations in a flow of a combustible mixture, depending on the Markstein constant and the diffusion-thermal process in the combustion front, are presented.</p>