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 aboveM1=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 atM1=6.0 for first‐mode 50° waves, and atM1=3.0 for two‐dimensional second‐mode waves, are not correct.