  Let $\langle G_r,G_b \rangle$ be a pair of plane $st$-graphs with the same
vertex set $V$. A simultaneous visibility representation with L-shapes of
$\langle G_r,G_b \rangle$ is a pair of bar visibility representations
$\langle\Gamma_r,\Gamma_b\rangle$ such that, for every vertex $v \in V$,
$\Gamma_r(v)$ and $\Gamma_b(v)$ are a horizontal and a vertical segment, which
share an end-point. In other words, every vertex is drawn as an $L$-shape,
every edge of $G_r$ is a vertical visibility segment, and every edge of $G_b$
is a horizontal visibility segment. Also, no two L-shapes intersect each other.
An L-shape has four possible rotations, and we assume that each vertex is given
a rotation for its L-shape as part of the input. Our main results are: (i) a
characterization of those pairs of plane $st$-graphs admitting such a
representation, (ii) a cubic time algorithm to recognize them, and (iii) a
linear time drawing algorithm if the test is positive.
