The three‐dimensional (3‐D) time‐dependent compressible Navier–Stokes equations are numerically solved by a Fourier–Chebyshev collocation method to study the stability of supersonic flows over a flat plate. Several direct simulations carried out in this study suggest the existence of a secondary instability that might provide a route to transition. The interaction of the modes involved in the secondary instability is possibly amenable to a Floquet‐type analysis. Pertinent differences between this instability and the analogous incompressible K‐type secondary instability are pointed out. Some preliminary results of a 2‐D direct simulation of the nonlinear evolution of a second mode perturbation wave are also discussed.