A vague graph is a generalized structure of a fuzzy graph that gives more precision, ‡exibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, we introduce the concept of strong domination numbers of vague graphs. The strong domination numbers of any complete (bipartite) vague graph are determined, and bounds are obtained for the strong numbers of vague graphs. Finally, we present some applications of strong domination numbers.