Calculations are presented for the electromagnetic interactions between a thin conducting layer at the base of the mantle and a magnetic field that is parallel to the core-mantle boundary, the so-called toroidal field. The effect of such interactions on the nutations of Earth is investigated. The analysis shows that a conducting layer in the mantle can significantly increase the amplitude of the toroidal field near the core-mantle boundary. The nutations are affected by the resulting magnetic stresses at the core-mantle boundary, which can arise in one of two ways. One coupling mechanism involves an interaction between the toroidal and radial components of Earth's main field; a perturbation in the radial field caused by the nutations will produce a magnetic stress on the mantle in the presence of a toroidal field. The largest torque results when the dipole field is perturbed in the presence of a quadrupolar toroidal field. The amplitude of this torque, however, is expected to be too small to produce observable changes in the amplitudes of the nutations, which are currently determined with a standard error of 0.04 milliarcseconds (Herring et al., 1991). The other coupling mechanism proves to be more important, but it depends on the presence of nonhydrostatic undulations in the core-mantle boundary. The toroidal field is perturbed by a steady flow in the core over the undulations in the boundaries. The perturbed field diffuses across the boundary, which gives rise to magnetic stresses when the core flow associated with the nutations is superimposed on the steady flow. Calculations based on an earlier study of Moffatt and Dillon (1976) suggest that a 40 G toroidal field could produce observable changes in the nutations if there is a thin layer at the base of the mantle with a conductivity of 5¿105 S m-1. ¿American Geophysical Union 1993