The right (resp. left) simple and the simple ordered 

semigroups play an important role in the structure of 

ordered semigroups. In this note we prove that there is no 

essential difference between the right (resp. left) simple 

and the right (resp. left)  0-simple ordered semigroups. 

In this respect, we prove that an ordered groupoid $S$  

without zero is right (resp. left) simple if and only if 

the ordered groupoid  $S^0$  arising from  $S$  by the 

adjunction of a zero is right (resp. left)  0-simple. 

Moreover, an ordered semigroup  $S$  with a zero element  

0  is right (resp. left)  0-simple if and only if the set    

$S\setminus \{0\}$  is a right (resp. left) simple subsemigroup 

of  $S$.  The sufficient condition holds in ordered 

groupoids, in general. That is, if  $S$  is an ordered 

groupoid with zero and if the set  $S\setminus \{0\}$  is a right 

(resp. left) simple subgroupoid of  $S$,  then  $S$  is 

right (resp. left)  0-simple.