The propagation properties and stability of wave motions in a spherical fluid shell, rotating uniformly in a co-rotating zonal magnetic field, are studied. Various profils of magnetic field and temperature gradient are examined. The fluid is viscous and electrically and thermally conducting. The analysis is applicable when the rotation rate is very high and the Elsasser number Λ ≪ 1. (Λ measures the ratio of Lorentz to Coriolis forces). The wave motions occur in the form of annular cylindrical cells whose thickness is determined by the rotation rate and magnetic field amplitude (Eltayeb and Kumar, 1977).