Let $f$ be a transcendental meromorphic function and let $U$ be a wandering domain of $f$. Under some conditions, we prove that a finite limit function of $\{f^{n}\}$ on $U$ is in the derived set of the forward orbit of the set sing $(f^{-1})$ of singularities of the inverse function of $f$. The existence of $\{n_{k}\}$ such that
$f^{n_k}}|_{U}$ tends to $\infty$ is also considered when $f$ is entire. If sing$(f^{-l})$ is bounded, however, we show that $\{f^{n}(z)\}_{n=o}^\infty$ in $F(f)$ does not tend to $\infty$.