  Given $k$ pairs of vertices $(s_i,t_i)$, $1\le i\le k$, of a digraph $G$, how
can we test whether there exist $k$ vertex-disjoint directed paths from $s_i$
to $t_i$ for $1\le i\le k$? This is NP-complete in general digraphs, even for
$k = 2$, but for $k=2$ there is a polynomial-time algorithm when $G$ is a
tournament (or more generally, a semicomplete digraph), due to Bang-Jensen and
Thomassen. Here we prove that for all fixed $k$ there is a polynomial-time
algorithm to solve the problem when $G$ is semicomplete.
