The linear stability of viscous two-dimensional perturbations in the supersonic plane Couette flow of perfect and vibrationally excited gases is investigated. In both cases an alternative is considered so that the transport coefficients were taken either constant or dependent on the static flow temperature. The Sutherland model is used to take the temperature dependence of the shear viscosity into account. It is shown that “viscous” stratification increases considerably the flow stability as compared with the case of constant viscosity. At the same time, the simple constant viscosity model conserves all characteristic features of the development of viscous perturbations in the Sutherland model. The dissipation effect of excitation of the vibrational mode is conserved in taking the temperature dependence of the transport coefficients into account. For both models the corresponding increase in the critical Reynolds number is of approximately 12%.