The development of inviscid and viscous two-dimensional subsonic disturbances in a supersonic boundary layer of a vibrationally excited gas on a flat plate was studied on the basis of the linear stability theory. A system of two-temperature gas dynamics including the Landau - Teller relaxation equation used as initial model. The unperturbed flow was described by a selfsimilar boundary layer solution for a perfect gas. In the linearized system of equations the temperature disturbances of the transport coefficients were taken into account. It is shown that vibrational excitation has practically no effect on the wavenumbers of inviscid modes. At the same time, the maximum growth rates of the most unstable second inviscid mode are reduced by approximately twelve percent compared to the ideal gas. The neutral stability curves for the first and second most unstable modes are calculated for the finite Reynolds numbers. It is shown that for both modes the critical Reynolds numbers at maximum excitation exceed by approximately thirteen percent the corresponding values for a perfect gas.
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