A two-layer model is used to study the effect of divergence on the inertial (barotropic) stability of zonal jets on a rotating sphere. Both the β effect and divergence stabilize eastward jets, but both these effects can destabilize westward jets. The following are principal results concerning the stability of zonal currents in the tropical oceans. Instabilities of the Equatorial Undercurrent are unlikely in the Indian and Atlantic oceans but may occur in the central Pacific in March and April. (The undercurrent has been found to be at its most intense in this location at this time.) The unstable waves, which will cause the undercurrent to meander about the equator, have a wavelength of about 900 km, a period of approximately 40 days, and an e folding time of more than 2 weeks. Such an instability could explain measurements in the Pacific by Taft et al. (1974). Meanders of the undercurrent may also be caused by instabilities of the surface current: the westward South Equatorial Current and the adjacent eastward North Equatorial Countercurrent. The westward propagating amplifying waves have a zonal wavelength in excess of 2000 km and a period and e folding time of 2--3 weeks. These results are in reasonable agreement with measurements in the Atlantic. Currents with a given vertical shear and stability that are baroclinically unstable in mid-latitudes are shown to be stabilized as they are moved equatorward. The only zonal equatorial current that could be baroclinically unstable is westward North Equatorial Current between 10¿N and 20¿N.