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

Hypercyclic Composition Operators]{Hypercyclic composition operators on the little Bloch space $\mathcal{B}_0$ and the Besov spaces $B_p