AbstractA study is made of the horizontal variations of eddy momentum and heat fluxes induced by long planetary waves in a linear two‐layer quasi‐geostrophic spherical model. A wide range of basic flows, consisting of upper‐layer, pure baroclinic or pure barotropic long waves together with solid‐body rotation or either of two zonal jet profiles, characteristic of the troposphere, are considered. The superposition of long planetary waves on otherwise zonal flow profiles has an effect on the eddy fluxes which is profound but is highly variable, depending on the basic flow. It is found, however, that for all profiles involving basic upper‐layer or baroclinic waves, the horizontal structure of both momentum and heat fluxes may be understood in terms of a generalization of Phillips's criterion for incipient instability. For these profiles, the regions of preferential development of baroclinic eddies are also found to be related to the general stability criterion. When barotropic planetary waves are present in the basic flows, the structure of the eddy fluxes is more complicated, reflecting the strong zonal wavenumber coupling in the disturbance stream