  Let $S(\mathbb{D})$ be the collection of all holomorphic self-maps on
$\mathbb{D}$ of the complex plane $\mathbb{C}$, and $C_{\varphi}$ the
composition operator induced by $\varphi\in S(\mathbb{D})$. We obtain that
there are no hypercyclic composition operators on the little Bloch space
$\mathcal{B}_0$ and the Besov space $B_p$.
