The problem of onset of convection in spherical fluid shells is considered in the limit of high rotation rates. Solutions are obtained as a function of the distance s from the axis, the Prandtl number, and the radius ratio η of the spherical boundaries. Analytical results are derived in the thin shell limit η → 1. The main result of the paper is the qualitative difference of convection modes inside and outside the cylindrical surface touching the inner spherical boundary at the equator. This feature was used earlier (Busse, 1976) to explain the difference in cloud formations at low and high latitudes of the Jovian atmosphere.