  In a graph, a watchman's walk is a minimum closed dominating walk. Given a
graph $G$ and a single watchman, the length of a watchman's walk in $G$ (the
watchman number) is denoted by $w(G)$ and the typical goals of the watchman's
walk problem is to determine $w(G)$ and find a watchman's walk in $G$. In this
paper, we extend the watchman's walk problem to directed graphs. In a directed
graph, we say that the watchman can only move to and see the vertices that are
adjacent to him relative to outgoing arcs. That is, a watchman's walk is
oriented and domination occurs in the direction of the arcs. The directed
graphs this paper focuses on are families of tournaments and orientations of
complete multipartite graphs. We give bounds on the watchman number and discuss
its relationship to variants of the domination number.
