  Let $k$ be an algebraically closed field of characteristic zero, and $k[[z]]$
the ring of formal power series over $k$. We provide several characterizations
of right amenable finitely generated subsemigroups of $z^2k[[z]]$ with the
semigroup operation $\circ $ being composition. In particular, we show that a
subsemigroup $S=\langle Q_1,Q_2,\dots, Q_k\rangle$ of $z^2k[[z]]$ is right
amenable if and only if there exists an invertible element $\beta$ of $zk[[z]]$
such that $\beta^{-1}\circ Q_i \circ \beta =\omega_i z^{d_i},$ $1\leq i \leq
k,$ for some integers $d_i$, $1\leq i \leq k,$ and roots of unity $\omega_i,$
$1\leq i \leq k.$
