  We study the poles of the retarded Green's functions of strongly coupled
field theories exhibiting a variety of phase structures from a crossover up to
a first order phase transition. These theories are modeled by a dual
gravitational description. The poles of the holographic Green's functions
appear at the frequencies of the quasinormal modes of the dual black hole
background. We establish that near the transition, in all cases considered, the
applicability of a hydrodynamic description breaks down already at lower
momenta than in the conformal case. We establish the appearance of the spinodal
region in the case of the first order phase transition at temperatures for
which the speed of sound squared is negative. An estimate of the preferential
scale attained by the unstable modes is also given. We additionally observe a
novel diffusive regime for sound modes for a range of wavelengths.
