This contribution presents new phenomena regarding the stability of pressure driven flows within annular pipes. The fluid is advected downstream due to an axial pressure gradient but also subjected to centrifugal mechanisms due to the independent rotation of the coaxial cylinders that contain it. Coexistence of upstream and downstream spiral secondary flows is observed in the co-rotating regime for a medium gap configuration η =0 . 5a nd the boundary bicritical curve is provided for a wide range of angular speeds of the cylinders and axial velocities. A particular computation of the linear stability of the basic flow is carried out for a small gap case with η =0 .77 in order to detect the unstable modes and recover the also termed as Double Secondary Spiral Flows observed experimentally in the past by other authors. The provided linear stability results for this case are, within their limitations, qualitatively consistent with the experimental observations.