  If $R\subseteq S$ is a ring extension of commutative unital rings, the poset
$[R,S]$ of $R$-subalgebras of $S$ is called catenarian if it verifies the
Jordan-H\"older property. This property has already been studied by Dobbs and
Shapiro for finite extensions of fields. We investigate this property for
arbitrary ring extensions, showing that many type of extensions are catenarian.
We reduce the characterization of catenarian extensions to the case of field
extensions, an unsolved question at that time.
