For the same Froude number and depth of submergence beneath a free surface, the wake of a cylinder exhibits two admissible states. The first state involves a jet-like flow generally attached to the free surface; it gives rise to a large-amplitude, quasistationary wave. In the second state, the jet is detached from the free-surface, which exhibits only mild distortion. The critical feature of the transformation between these two states involves the formation of a separated vorticity layer from the free-surface and its interaction with the vorticity layer from the surface of the cylinder. This transformation can occur spontaneously over a time scale much longer than the Kármán period.