  Seymour's second neighbourhood conjecture asserts that every oriented graph
has a vertex whose second out-neighbourhood is at least as large as its
out-neighbourhood. In this paper, we prove that the conjecture holds for
quasi-transitive oriented graphs, which is a superclass of tournaments and
transitive acyclic digraphs. A digraph $D$ is called quasi-transitive is for
every pair $xy,yz$ of arcs between distinct vertices $x,y,z$, $xz$ or $zx$
("or" is inclusive here) is in $D$.
