A Note on General Covariant Stability Theory

In the present work we suggest a general covariant theory which can be used to study the stability of any physical system treated geometrically. Stability conditions are connected to the magnitude of the deviation vector. This theory is a modification of an earlier joint work, by the same authors, concerning stability. A comparison between the present work and the earlier one is given. The suggested theory can be used to study the stability of planetary orbits, astrophysical configurations and cosmological models.