The stability of a supersonic near-wall flow above a finely corrugated plate in the incident flow inside an aerodynamic tube with a Mach number of 6 has been studied experimentally. We obtained the perturbation growth coefficients that show that a wavy wall stabilizes the flow in the boundary layer with respect to the perturbations of the second mode, but it destabilizes the perturbations of the first mode. A bispectral analysis of perturbations is carried out. It is shown that with decreasing pulsation amplitudes of the second mode, nonlinear processes in the boundary layer behind the wavy surface become strongly suppressed: there is no harmonic resonance of the second mode, and nonlinear processes in the low-frequency region of the spectrum have an interaction amplitude that is an order of magnitude smaller and a much more limited frequency range. Due to the stabilizing effect of a wavy surface on perturbations of the second mode, the onset of a laminar-turbulent transition is generally delayed.