The convective instability boundary of a circular Couette flow in the annular region bounded by two co- or counter-rotating coaxial cylinders with angular velocities&ohgr;1and&ohgr;2, respectively, is studied in the presence of an axial flow due to a constant axial pressure gradient and a radial flow through the permeable walls of the cylinders. A linear stability analysis is carried out for positive and negative radial Reynolds numbers corresponding to outward and inward radial flows, respectively. Axisymmetric and non-axisymmetric disturbances are considered. In the particular case of no axial flow, the Couette flow is stabilized by an inward, or a strong outward, radial flow, but destabilized by a weak outward radial flow. Non-axisymmetric disturbances lead to instability for some negative values of&mgr;=&ohgr;2/&ohgr;1. Bifurcation diagrams for combined radial and axial flows are more complicated. For particular values of the parameters of the problem, the Couette flow has regions of stabilization and destabilization in the parameter space. Computational results are compared with experimental data. ©1997 American Institute of Physics.