  The fluctuations of the Higgs and pseudo Nambu-Goldstone fields in the 2SC
phase with mismatched pairing are described in the nonlinear realization
framework of the gauged Nambu--Jona-Lasinio model. In the gapless 2SC phase,
not only Nambu-Goldstone currents can be spontaneously generated, but the Higgs
field also exhibits instablity. The Nambu-Goldstone currents generation
indicates the formation of the single plane wave LOFF state and breaks rotation
symmetry, while the Higgs instability favors spatial inhomogeneity and breaks
translation invariance. In this paper, we focus on the Higgs instability which
has not drawn much attention yet. The Higgs instability cannot be removed
without a long range force, thus it persists in the gapless superfluidity and
induces phase separation. In the case of g2SC state, the Higgs instability can
only be partially removed by the electric Coulomb energy. However, it is not
excluded that the Higgs instability might be completely removed in the charge
neutral gCFL phase by the color Coulomb energy.
