  We study the stability of the Couette-Taylor flow between porous cylinders
with radial throughflow. It had been shown earlier that this flow can be
unstable with respect to non-axisymmetric (azimuthal or helical) waves provided
that the radial Reynolds number, $R$ (constructed using the radial velocity at
the inner cylinder and its radius), is high. In this paper, we present a very
detailed and, in many respects, novel chart of critical curves in a region of
moderate values of $R$, and we show that, starting from values of $R$, as low
as $10$, the critical modes inherited from the inviscid instability gradually
substitute the classical Taylor vortices. Also, we have looked more closely at
the effect of a weak radial flow (relatively low $R$) on the Taylor instability
and found that a radial flow directed from the inner cylinder to the outer one
is capable of stabilizing the Couette-Taylor flow provided that the gap between
the cylinders is wide enough. This observation is in a sharp contrast with the
case of relatively narrow gaps for which the opposite effect is well-known.
