In section 1, we show that if X is a Stein normal complex space of dimension n and D <FONT FACE=Symbol>ÌÌ</FONT> X an open subset which is the union of an increasing sequence D1 <FONT FACE=Symbol>Ì</FONT> D2 <FONT FACE=Symbol>Ì</FONT> ... <FONT FACE=Symbol>Ì</FONT> Dn <FONT FACE=Symbol>Ì</FONT> <FONT FACE=Symbol>Ì</FONT> ... 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 <FONT FACE=Symbol>Ì</FONT> X an open subspace which is the union of an increasing sequence D1 <FONT FACE=Symbol>Ì</FONT> D2 <FONT FACE=Symbol>Ì</FONT> ... <FONT FACE=Symbol>Ì</FONT> Dn <FONT FACE=Symbol>Ì</FONT> ... of open Stein subsets of X, then D itself is Stein, if X has isolated singularities