Core-mantle interaction is now recognized as having a major influence over core dynamics and geomagnetic behavior. We argue that nonlinear effects will dominate longer-term phenomena and be relatively independent of the type of mechanism: whether it be thermal, electromagnetic, or topographic. A detailed study of thermal interaction for non-magnetic rotating convection exhibits locking of the convection to the boundary and resonance between the convective modes and the boundary condition. We speculate that core convection and the geomagnetic field will lock to boundary anomalies giving configurations that are stable for long periods of time, possibly interspersed by intervals of rapid change as the natural time variation of rotating convection asserts itself. The instabilities that arise in the thermal case are rather general and are illustrated here mathematically by a simple analogue equation and physically by a pendulum with variable gravitational force. This generality suggests the same nonlinear behavior may arise in topographic and electromagnetic coupling. ¿American Geophysical Union 1993