In a groupoid (resp. ordered groupoid) $G$, the non-empty

intersection of the elements of a chain of prime ideals, is a

prime ideal of  $G$.  As a consequence, each prime ideal of a

groupoid (resp. ordered groupoid) $G$  containing a non-empty

subset $K$ of $G$, contains a prime ideal  $P^*$  of  $S$ having

the property: If  $T$  is a prime ideal of  $G$  such that

$K\subseteq T\subseteq P^\ast$, then $T = P^\ast$. As a result,

in a groupoid (resp. ordered groupoid) $G$ with zero, each prime

ideal of $G$ contains a minimal prime ideal of $G$. Some further

results on prime ideals of groupoids (resp. ordered groupoids)

are also given.