  We study the dynamics in phases with vector condensates of gluons (gluonic
phases) in dense two-flavor quark matter. These phases yield an example of
dynamics in which the Higgs mechanism is provided by condensates of gauge (or
gauge plus scalar) fields. Because vacuum expectation values of spatial
components of vector fields break the rotational symmetry, it is naturally to
have a spontaneous breakdown both of external and internal symmetries in this
case. In particular, by using the Ginzburg-Landau approach, we establish the
existence of a gluonic phase with both the rotational symmetry and the
electromagnetic U(1) being spontaneously broken. In other words, this phase
describes an anisotropic medium in which the color and electric
superconductivities coexist. It is shown that this phase corresponds to a
minimum of the Ginzburg-Landau potential and, unlike the two-flavor
superconducting (2SC) phase, it does not suffer from the chromomagnetic
instability. The dual (confinement) description of its dynamics is developed
and it is shown that there are light exotic vector hadrons in the spectrum,
some of which condense. Because most of the initial symmetries in this system
are spontaneously broken, its dynamics is very rich.
