  We study the gluonic color-spin locked (GCSL) phase in dense two-flavor quark
matter. In this phase, the color and spatial rotational symmetries are
spontaneously broken down to SO(2)_{diag} with the generator being an
appropriate linear combination of the color and rotational ones. The Meissner
masses of gluons and the mass of the radial mode of the diquark field in the
GCSL phase are calculated and it is shown that this phase is free from the
chromomagnetic and Sarma instabilities in the whole parameter region where it
exists. The GCSL phase describes an anisotropic color and electromagnetic
superconducting medium. Because most of the initial symmetries in this phase
are spontaneously broken, its dynamics is very rich.
