There have been a number of papers published that concern the design and operation of electromagnetic, eddy-current dampers for controlling lateral vibration of rotating machinery. Many of these papers have included analysis approaches and all have been generally effective for low-speed operations. There have been a few reports concerning high-speed (supercritical) operations and many of these have indicated instability problems, but none of these have provided a valid analysis to account for instability. That is, all of the analytical approaches have ignored the disk rotation, relative to the magnetic field, and no obvious sources of instability have been found. In this paper, we will present our work in which we have rederived the analyses of this system in which we have not made the common assumption of no rotation between the disk and the magnetic field. In this case, the potential of instability for supercritical speed operation is clear and, in fact, the equivalent negative damping contribution of the eddy-current damper, under these conditions, has a negative effect on the system even if not fully unstable. We have carefully performed a series of experimental tests which corroborate this analytical approach. Finally, we briefly discuss alternative eddy-current damper design approaches that could be considered to provide effective damping at all speeds and avoid these instability problems.