  In section 1, we show that if $X$ is a Stein normal complex space of
dimension n and $D\subset \subset X$ an open subset which is the union of an
increasing sequence $D_{1}\subset D_{2}\subset ...\subset D_{n}\subset >...$ of
domains of holomorphy in $X$. Then $D$ is a domain of holomorphy.
  In section 2, we prove that a domain of holomorphy $D$ which is relatively
compact in a 2-dimensional normal Stein space $X$ itself is Stein.
  In section 3, we show that if $X$ is a Stein space of dimension n and
$D\subset X$ an open subspace which is the union of an increasing sequence
$D_{1}\subset D_{2}\subset ...\subset D_{n}\subset ...$ of open Stein subsets
of $X$. then $D$ itself is Stein, if $X$ has isolated singularities.
