An examination is made of waves moving under centrifugal force and surface tension along the core in a swirling liquid. The waves may be of varicose form in which the cross-section of the core remains circular, or they may be helical, giving the core the shape of a multi-threaded screw. The relation is obtained between the lengths of the waves and their axial and angular velocities; at a critical length the waves possess a minimum velocity. The group velocities are determined, and are shown to be negative under certain conditions. It is found that waves can exist which move so slowly that they should be readily visible although the core may be revolving at high speed.