Stability of three-dimensional swept-wing boundary layers has been investigated in the framework of the linear theory. The most results were obtained for the local self-similar basic flow which was performed within Falkner-Scan-Cooke solution generalized for compressible flows. It has been established that computed subsonic swept-wing boundary-layer stability characteristics correlate well with the experiment. For the supersonic Mach number M=2 boundary layer computations agree with

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... for spanwise scales of the unstable cross-flow disturbances. However theoretical growth rates differ considerably from measured. This difference is explained by high intensity of the initial perturbations excited in the experiment that does not allow to apply linear theory. However the evolution of the natural disturbances of moderate amplitude is predicted well by the theory. It is shown that influence of the compressibility on cross-flow instability modes is insignificant. Also in paper the linear instability of three-dimensional swept-wing boundary layer was studied for a basic flow satisfied to full boundary layer equation. The results difference obtained for self-similar flows and flows satisfied to full boundary layer equation was not more than 15%. Conclusion is made that approximation of local similarity ensures sufficient accuracy and can be applied for simulation of stability experiments at supersonic speeds.