The secular stability of a gravitating stellar ring

The problem of secular stability of a homogeneous and cold differentially r otating gravitating stellar ring in an external gravitational field is cons idered. For the analysis of stability we use the method of variation of the system energy in the frames of the local hydrodynamical approximation. We show that the considered stellar system is always characterized by secular instability for all non-zero values of the density. This conclusion is vali d also in the case of solid-body rotation of the ring.