We study time-modulated Taylor–Couette flow for the simple case in which the inner cylinder's angular velocity oscillates around zero mean at given amplitude and frequency and the outer cylinder is at rest. We find that, provided the amplitude of modulation is large enough, two classes of Taylor vortex flows are possible – reversing and non-reversing. In the latter, which takes place at relatively high frequency, the direction of the Taylor vortices does not change every half-cycle.