  A class of graphs $\mathcal{C}$ is closed under powers if for every graph
$G\in\mathcal{C}$ and every $k\in\mathbb{N}$, $G^k\in\mathcal{C}$. Also
$\mathcal{C}$ is strongly closed under powers if for every $k\in\mathbb{N}$, if
$G^k\in\mathcal{C}$, then $G^{k+1}\in\mathcal{C}$. It is known that circular
arc graphs and proper circular arc graphs are closed under powers. But it is
open whether these classes of graphs are also strongly closed under powers. In
this paper we have settled these problems.
