A general theory is presented which describes the damping in dynamic force microscopy due to the proximity of the surface, consistently with resonant frequency shift effects. Orders of magnitude for the experimentally measured "dissipation" and image corrugation are reproduced. It is suggested that the damping does not mainly result from energy dissipation, but arises because not all solutions of the microlever equation of motion are accessible. The damping is related to the multivalued nature of the analytical resonance curve, which appears at some critical tip-surface separation.