The linear stability of axial parallel Poiseuille-Couette flow in an a
nnulus between concentric circular cylinders is considered. Using a lo
ng-wave version of the axisymmetric Orr-Sommerfeld equation the stabil
ity chart of this flow in the velocity ratio-radius ratio plane is der
ived. It is shown that pure sliding Couette flow can become unstable i
f the radius ratio is below a specific threshold value. Finally, apply
ing the results to other flow geometries, it is shown that the boundar
y layer along a slender cylinder can become unstable in a confined reg
ion downstream the leading edge only.