  Let $L_0$ and $L_1$ be two distinct rays emanating from the origin and let
${\mathcal F}$ be the family of all functions holomorphic in the unit disk
${\mathbb D}$ for which all zeros lie on $L_0$ while all $1$-points lie on
$L_1$. It is shown that ${\mathcal F}$ is normal in ${\mathbb
D}\backslash\{0\}$. The case where $L_0$ is the positive real axis and $L_1$ is
the negative real axis is studied in more detail.
