We study the class of rectilinear polygons, called X - Y polygons, with horizontal and vertical edges, which are frequently used as building blocks for very large-scale integrated (VLSI) circuit layout and wiring. In the paper we introduce the notion of convexity within the class of X - Y polygons and present efficient algorithms for computing the X - Y convex hulls of an X - Y polygon and of a set of X - Y polygons under various conditions. Unlike convex hulls in the Euclidean plane, the X - Y convex hull of a set of X - Y polygons may not exist. The condition under which the X - Y convex hull exists is given and an algorithm for testing if the given set of X - Y polygons satisfies the condition is also presented. © 1983 BIT Foundations.