  We investigate the poles of the retarded Green's functions of strongly
coupled field theories exhibiting a variety of phase structures from a
crossover up to different first order phase transitions. 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 focus on quantifying linearized level dynamical
response of the system in the critical region of phase diagram. Generically
non-hydrodynamic degrees of freedom are important for the low energy physics in
the vicinity of a phase transition. For a model with linear confinement in the
meson spectrum we find degeneracy of hydrodynamic and non-hydrodynamic modes
close to the minimal black hole temperature, and we establish a region of
temperatures with unstable non-hydrodynamic modes in a branch of black hole
solutions.
