  In this paper, we show that the edge connectivity of a distance-regular
digraph $\Gamma$ with valency $k$ is $k$ and for $k>2$, any minimum edge cut of
$\Gamma$ is the set of all edges going into (or coming out of) a single vertex.
Moreover we show that the same result holds for strongly regular digraphs.
These results extend the same known results for undirected case with quite
different proofs.
