  The conditions for stability of the elements of linear groups over the
associative rings with identity and their connection with the stability of
rings are analyzed in the article. The stability of rings which are
commutative, satisfy the conditions of stability of rank $\geq 2$, von Neumann
regular, integer-algebraic, nearly local rings introduced by the author, is
examined. The most important classical results of H. Bass, L. Vaserstein, S.H.
Khlebutin, A.A. Suslin, J.S. Wilson, I.Z.Golubchik, are considered from the
unified standpoint.
