By applying an approach similar to that used in the Miles-Howard theor
y [1], [2] we derive simple constraints on the phase speed c(r) of th
e neutral three-dimensional (3-D) monochromatic disturbances in an inv
iscid compressible parallel two-dimensional (2-D) shear flow. It is sh
own that for a boundary layer flow [a0(y*)]2 - [U0*(y*) - c(r)*]2 mus
t have a zero in [y1, y2*) for the neutral 2-D modes whose phase spee
d c(r) does not belong to the range of U0*(y*). For the unstable wave
s the argument of Chimonas [3] applies leading to the Howard semi-circ
le theorem. Here U0(y*) and a0*(y*) are the dimensional base velocity
and local sonic speed respectively. It is suggested that hypersonic f
lows possess vertically highly undulated unstable normal modes.