  Cosmological models with vector fields received much attention in recent
years. Unfortunately, most of them are plagued with severe instabilities or
other problems. In particular, it was noted by G. Esposito-Farese, C. Pitrou
and J.-Ph. Uzan in arXiv:0912.0481 that the models with a non-linear function
of the Maxwellian kinetic term do always imply violations of hyperbolicity
somewhere in the phase space. In this work we make this statement more precise
in several respects and show that those violations may not be present around
spatially homogeneous configurations of the vector field.
