  We study the propagation of helicity-1 gravitons in the Fierz--Pauli massive
gravity in nearly Minkowski backgrounds. We show that, generically, there exist
backgrounds consistent with field equations, in which the propagation is
superluminal. The relevant distances are much longer than the ultraviolet
cutoff length inherent in the Fierz--Pauli gravity, so superluminality occurs
within the domain of validity of the effective low energy theory. There remains
a possibility that one may get rid of this property by imposing fine tuning
relations between the coefficients in the non-linear generalization of the
Fierz--Pauli mass term, order by order in non-linearity; however, these
relations are not protected by any obvious symmetry. Thus, among others,
superluminality is a problematic property to worry about when attempting to
construct infrared modifications of General Relativity.
