The transition to three-dimensionality in the near wake of a circular cylinder involves two successive transitions, each of which corresponds with a discontinuity in the Strouhal-Reynolds number relationship. The first discontinuity BETWEEN Reynolds numbers (Re) of 170 to 180 is associated with the inception of vortex loops, and it is hysteretic. The second discontinuity (between Re=230 to 260) corresponds with a change to a finer-scale streamwise vortex structure. At this discontinuity there is no hysteresis, and it is suggested that two modes of vortex shedding alternate in time.