The nonlinear stability properties of stationary exact nonzonal solutions for inviscid ilow over topography are examined within a barotropic model in spherical geometry. For stationary solutions, such that the potential vorticity is proportional to the streamfunction,necessary and sufficientconditions for nonlinear stability are established. For a truncated system with rhomboidal truncation wave numberJthese are that the solid body rotation component of the zonal winduibe negative, corresponding to westward flow, asJ→ ∞. These results are established by using the methods of statistical mechanics. The sufficient condition for stability is also established by applying Arnol'd's method.