  The stability of a two-dimensional viscous flow between two rotating porous
cylinders is studied. The basic steady flow is the most general
rotationally-invariant solution of the Navier-Stokes equations in which the
velocity has both radial and azimuthal components, and the azimuthal velocity
profile depends on the Reynolds number. It is shown that for a wide range of
the parameters of the problem, the basic flow is unstable to small
two-dimensional perturbations. Neutral curves in the space of parameters of the
problem are computed. Calculations show that the stability properties of this
flow are determined by the azimuthal velocity at the inner cylinder when the
direction of the radial flow is from the inner cylinder to the outer one and by
the azimuthal velocity at the outer cylinder when the direction of the radial
flow is reversed. This work is a continuation of our previous study of an
inviscid instability in flows between rotating porous cylinders (see
\cite{IM2013}).
