  In the present work we study solutions of the problem $-(-\Delta)^{\alpha/2}u
= f(x,u)$ in $D_0\setminus \overline{D}_1$, with exterior conditions $u = 0$ in
$R^N \setminus D_0$ and $u = 1$ in $\overline{D}_1$, where $D_1, D_0 \subset
R^N$ are open sets such that $\overline{D}_1 \subset D_0$, $\alpha \in (0,2)$,
and $f$ is a nonlinearity. Under different assumptions on $f$ we prove that, if
$D_0$ and $D_1$ are starshaped with respect to the same point $\bar{x} \in
\overline{D}_1$, then the same occurs for every superlevel set of $u$.
