We characterize the automorphisms of a C-algebra A which extend to au
tomorphisms of the crossed product B of A by a compact group dual. The
case where the inclusion A subset-of B is equipped with a group of au
tomorphisms commuting with the dual action is also treated. These resu
lts are applied to the analysis of broken gauge symmetries in Quantum
Field Theory to draw conclusions on the structure of the degenerate va
cua on the field algebra.