Strong gravitational coupling between the solid inner core and the mantle provides a means of exchanging angular momentum between the fluid outer core and the mantle. The proposed mechanism involves oscillations in the fluid core which exert a large electromagnetic torque on the inner core by virtue of its high electrical conductivity. The inner core does not freely respond to this torque because it is constrained by gravitational forces to remain nearly aligned with the mantle. Angular momentum is transferred to the mantle by the gravitational torques that result from small misalignments with the inner core. A calculation of the normal modes of this coupled system predicts observable fluctuations of the mantle with periods of several decades. Damping of the oscillations due to ohmic losses produces a quality factor Q of about 20. An excitation mechanism to sustain the oscillations is proposed on the basis of recent dynamo calculations. ¿ American Geophysical Union 1996