Past work on the influence of Mach number on the viscous and inviscid instability of flat-plate boundary layers is reviewed, and new spatial calculations are presented. These calculations support the previous view that viscosity is only stabilizing for both two- and three-dimensional first-mode waves above M1=3.0, and for second-mode waves at all Mach numbers. It is concluded that the calculations of Wazzan, Taghavi, and Keltner that show viscous instability at M1=6.0 for first-mode 50° waves, and at M1=3.0 for two-dimensional second-mode waves, are not correct.