  Discrete bright breathers are well known phenomena. They are localized
excitations that consist of a few excited oscillators in a lattice and the rest
of them having very small amplitude or none. In this paper we are interested in
the opposite kind of localization, or discrete dark breathers, where most of
the oscillators are excited and one or a few units of them have very small
amplitude. We investigate using band analysis, Klein--Gordon lattices at
frequencies not close to the linear ones. Dark breathers at low coupling are
shown to be stable for Klein--Gordon chains with soft on--site potentials and
repulsive dispersive interaction, and with hard on--site potentials and
attractive dispersive interactions. At higher coupling dark breathers lose
their stability via subharmonic, harmonic or oscillatory bifurcations,
depending on the model. However, most of these bifurcations are harmless in the
sense that they preserve dark localization. None of these bifurcations
disappear when the system is infinite. Dark breathers in dissipative systems
are found to be stable for both kinds of dispersive interaction.
