[en] The linear stability of a rotating Boussinesq fluid contained in a spherical shell to three-dimensional distrubances is studied in the presence of a general toroidal magnetic field. The local stability analysis used indicated that the stability of the system is not very different from that already known for the Malkus field (i.e. a field that varies directly as the distance from the rotation axis). The main influence of the general field is the introduction of a zonal flow which Doppler shifts the frequency of the waves. Consequently, the unstable waves in the geophysically relevant case of small q (=kappa/anti eta, where kappa, anti eta are, respectively, the thermal and magnetic diffusivities) drift eastward deep into the core and westward near the core-mantle boundary. For the astrophysically relevant situation q>>1 the presence of the zonal flow also blows the waves eastward in most of the core so that westward propagation is possible only in the top part of the core. (author)