  The SU(N)-symmetric generalization of the model of the electromagnetically
active dynamic aether is formulated. This generalization is based on the
introduction of a Yang-Mills gauge field instead of the Maxwell field, and of a
SU(N)-multiplet of vector fields instead of the standard single vector field.
In the framework of the second order version of the effective field theory this
generalization includes three constitutive tensors, which are the SU(N)
extensions of the tensors appeared in the Einstein-Maxwell-aether theory; we
reconstructed the full-format set of these constitutive tensors. The total
self-consistent system of master equations for the gauge, vector and
gravitational fields is obtained by the variation procedure. The general model
of the SU(N)-symmetric dynamic aether is reduced to the extended
Einstein-Yang-Mills-aether model by the ansatz about spontaneous color
polarization of the vector fields. In fact, this ansatz requires the vector
fields, which form the SU(N) multiplet, to become parallel in the group (color)
space due to a phase transition, and a new selected direction in the group
space to appear, thus converting it into the anisotropic color space.
