  The structure of effective potential surface of the Nambu$-$Jona-Lasinio
(NJL) model with right-left asymmetric Majorana mass terms (corresponds to the
single-flavor type-II seesaw situation of neutrino) is investigated. After the
dynamical generation of Dirac mass, two collective modes appear similar to the
case of ordinary NJL model, and the phase mode (phason), which corresponds to
majoron or pion at vanishing Majorana mass parameter(s), has an excitation
mass. The mechanism of generation of phason as a pseudo Nambu-Goldstone boson
is examined by a mathematical manner, summarized into a theorem
  (claims as the generalized Nambu-Goldstone theorem). The mass of phason is
also evaluated in a supersymmetric version of the NJL-type model, and phason
mass takes the order of that of axion commonly accepted today. An
$SU(2_{c})$-gauge model is constructed for the context of neutrino seesaw
mechanism, and the Schwinger-Dyson equation of dynamical mass functions is
examined. Several physical implications such as decay modes of phason, a
non-linear sigma model for phason are given. It is proposed that the
method/result of this paper can be applied to an understanding on the origin of
the Kobayashi-Maskawa matrix.
