Summary: As a generalization of directed and undirected graphs, J. Edmonds and E.L. Johnson [Combinat. Struct. Appl., Proc. Calgary internat. Conf. combinat. Struct. Appl., Calgary 1969, 69–87 (1970; Zbl 0268.05019)] introduced bidirected graphs. A bidirected graph is a graph each arc of which has either two positive end-vertices (tails), two negative end-vertices (heads), or one positive end-vertex (tail) and one negative end-vertex (head). We extend the notion of directed paths, distance, diameter and strong connectivity from directed to bidirected graphs and characterize those undirected graphs that allow a strongly connected bidirection. Considering the problem of finding the minimum diameter of all strongly connected bidirections of a given undirected graph, we generalize a result of F. V. Fomin, M. Matamala, E. Prisner and I. Rapaport [in: Szwarcfiter, Jayme (ed.), Proceedings of the Brazilian symposium on graphs, algorithms and combinatorics, Fortaleza, Ceará, Brazil, March 17–19, 2001. Extended abstracts. Amsterdam: Elsevier, Electron. Notes Discrete Math. 7, no pag., electronic only (2001; Zbl 0981.05059)] about directed graphs and obtain an upper bound for the minimum diameter which depends on the minimum size of a dominating set and the number of bridges in the undirected graph.