The instability of hypersonic boundary-layer flows over flat plates is considered. The viscosity of the fluid is taken to be governed by Sutherland's law, which gives a much more accurate representation of the temperature dependence of fluid viscosity at hypersonic speeds than Chapmans's approximate linear law; although at lower speeds the temperature variation of the mean state is less pronounced so that the Chapman law can be used with some confidence. Attention is focussed on the so-called vorticity mode of instability of the viscous hypersonic boundary layer. The instability of the hypersonic boundary layer is non-interactive. The vorticity mode of instability of this flow operates on a significantly different lengthscale than that obtained if a Chapman viscosity law is assumed. The growth rate predicted by a linear viscosity law overestimates the size of the growth rate by O (M-sq). Next, the development of the vorticity mode as the wavenumber decreases is described, and it is shown that acoustic modes emerge when the wavenumber has decreased from it's O(1) initial value to O (M to the -3/2 power). (jhd).