  We present a detailed study of the viability of general vector-tensor
theories of gravity in the presence of an arbitrary temporal background vector
field. We find that there are six different classes of theories which are
indistinguishable from General Relativity by means of local gravity
experiments. We study the propagation speeds of scalar, vector and tensor
perturbations and obtain the conditions for classical stability of those
models. We compute the energy density of the different modes and find the
conditions for the absence of ghosts in the quantum theory. We conclude that
the only theories which can pass all the viability conditions for arbitrary
values of the background vector field are not only those of the pure Maxwell
type, but also Maxwell theories supplemented with a (Lorentz type) gauge fixing
term.
