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We study a new notion of cyclic avoidance of abelian powers. A finite word$w$ avoids abelian $N$-powers cyclically if for each abelian $N$-power ofperiod $m$ occurring in the infinite word $w^\omega$, we have $m \geq |w|$. Let$\mathcal{A}(k)$ be the least integer $N$ such that for all $n$ there exists aword of length $n$ over a $k$-letter alphabet that avoids abelian $N$-powerscyclically. Let $\mathcal{A}_\infty(k)$ be the least integer $N$ such thatthere exist arbitrarily long words over a $k$-letter alphabet that avoidabelian $N$-powers cyclically.  We prove that $5 \leq \mathcal{A}(2) \leq 8$, $3 \leq \mathcal{A}(3) \leq 4$,$2 \leq \mathcal{A}(4) \leq 3$, and $\mathcal{A}(k) = 2$ for $k \geq 5$.Moreover, we show that $\mathcal{A}_\infty(2) = 4$, $\mathcal{A}_\infty(3) =3$, and $\mathcal{A}_\infty(4) = 2$.

Avoiding abelian powers cyclically