  Elitzur's theorem stating the impossibility of spontaneous breaking of local
symmetries in a gauge theory is reexamined. The existing proofs of this theorem
rely on gauge invariance as well as positivity of the weight in the Euclidean
partition function. We examine the validity of Elitzur's theorem in gauge
theories for which the Euclidean measure of the partition function is not
positive definite. We find that Elitzur's theorem does not follow from gauge
invariance alone. We formulate a general criterion under which spontaneous
breaking of local symmetries in a gauge theory is excluded. Finally we
illustrate the results in an exactly solvable two dimensional abelian gauge
theory.
