The flow driven by a rotating end wall in a cylindrical container with aspect ratio H/R = 2.5 is time dependent for Reynolds numbers Re = ΩR2/ν>2700. For Reynolds numbers up to 4000 three solution branches have been identified, and we examine a solution on each one. At Re = 3000, the flow is axisymmetric and time periodic. At Re = 3500, the flow is quasiperiodic with a low-frequency modulation and supports a modulated rotating wave with azimuthal wave number k = 5. At Re = 4000, the flow is time periodic with a qualitatively different mode of oscillation to that at Re = 3500. It also supports a modulated rotating wave, with k = 6. The peak kinetic energy of the nonaxisymmetric modes is associated with the jet-like azimuthal flow in the interior. (C) 2000 American Institute of Physics.