For high-speed flows during re-entry conditions, the chemical reactions in the flow heavily influence the stability properties of boundary-layer flows. The possible presence of shock-induced nonequilibrium in the flow makes it necessary not only to look at equilibrium flows. Instabilities that eventually lead to laminarturbulent transition in a hypersonic flat-plate boundary layer are investigated by direct numerical simulation of the full unsteady three-dimensional Navier-Stokes equations with appropriate additions for the chemical source terms and the thermodynamical properties. As examples, the flat-plate boundary-layer flow at M=20 at an altitude of H=50Km is examined as well as the wake flow of a boundary-layer sized object in a M=6.8 boundary-layer.