We consider the problem of searching for a mobile intruder in a circular corridor (a polygon with one polygonal hole) by two searchers, who hold a flashlight. Both searchers move on the outer boundary, directing their flashlights at the inner boundary. The objective is to decide whether there exists a search schedule for the searchers to detect the intruder, no matter how fast he moves. We give a characterization of the class of circular corridors, which are searchable with two flashlights. Based on our characterization, an O(n logn) time algorithm is then presented to determine the searchability of a circular corridor with two flashlights, where n denotes the total number of vertices of the outer and inner boundaries. Moreover, a search schedule can be output in time linear in its size, if it exists. Our result gives the first efficient solution to the polygon search problem for two searchers.