  A commutative ring R is locally stable provided that for any $a,b\in R$ such
that $aR+bR=R$, there exist some $y\in R$ such that $R/(a+by)R$ has stable
range 1.For a Bezout ring $R$, we prove that $R$ is an elementary divisor ring
if and only if $R$ is locally stable if and only if $R$ has neat range 1.
