  First, we develop the counting rule for Nambu-Goldstone bosons to the system
including two-time derivative terms. In this case, the type-II Nambu-Goldstone
bosons may appear along with the massive Nambu-Goldstone ones. The number of
the bosons is not reduced in contrast to the system without two-time derivative
terms. We also investigate the reduction of the degrees of freedom from the
perspective of the Dirac-Bergmann theory of constraints and reproduce the
counting rule for Nambu-Goldstone bosons without Lorentz invariance. Then, we
construct the generic Higgs model and study a Higgs phenomenon with these
Nambu-Goldstone bosons on the basis of the Dirac-Bergmann theory. We show that
the gauge fields in this system absorb all of the Nambu-Goldstone bosons such
as the type-I, type-II and massive ones.
