The effects of gravitational coupling between the inner core and the mantle are incorporated into numerical simulations of the geodynamo. Differential rotation between the inner core and the mantle is permitted by allowing the inner core to viscously deform. Calculations with a deformation time scale of 1 yr, corresponding to an average viscosity of 5¿1016 Pa s, predict eastward rotation of the inner core with a mean rate of 0.02 deg/yr relative to the mantle. Fluctuations about this mean rate of rotation occur with a typical period of 75 yr and have sufficient amplitude to explain observed changes in length of day at decadal periods. When gravitational coupling is removed, or viscous coupling is added by imposing no-slip boundary conditions, the mean inner core rotation rate is almost an order of magnitude greater. ¿ 2000 American Geophysical Union