Seismological observations suggest the inner core has been rotating faster than the mantle during the past 30--50 years. Differential rotation can produce large gravitational torques on the mantle which, if not balanced by other torques, would be detectable as changes in the rotation rate of the mantle (Length of Day or LOD). We compare seismological estimates of inner core rotation with estimates derived by inverting LOD observations using models of gravitational coupling. Model predictions depend on several parameters, but for the expected range of parameter values, the seismological estimates of relative rotation are at least an order of magnitude larger than those predicted by the LOD data. Furthermore, the LOD data predict oscillation in the angular alignment of the inner core and mantle during the past 30--50 years, while the seismological data seem to require a component of steady rotation. We show that steady rotation of the inner core implies a steady torque on the mantle. This torque is not accelerating the rotation rate of the mantle, so it must be opposed by another torque. The required torque is consistent with a frictional electromagnetic stress on the base of the mantle due to a westward flow at the top of the core. ¿ 1999 American Geophysical Union