  We compare two QCD-inspired quark models with four-fermion interaction,
without and with the remnant coupling to low-energy gluons, in the regime of
dynamical chiral symmetry breaking (DCSB). The first one, the
Nambu-Jona-Lasinio (NJL) model ensures the factorization of scalar and
pseudoscalar meson poles in correlators, the well-known Nambu relation between
the scalar meson mass and the dynamical quark mass, $m_{\sigma} = 2 m_{dyn}$,
and the residual chiral symmetry in coupling constants characteristic for the
linear $\sigma$-model. The second one, the Gauged NJL model, happens to be
qualitatively different from the NJL model, namely, the Nambu relation is not
valid and the factorization of light meson poles does not entail the residual
chiral symmetry, i.e. it does not result in a linear $\sigma$-model. The more
complicated DCSB pattern in the GNJL model is fully explained in terms of
excited meson states with the same quantum numbers. The asymptotic restrictions
on parameters of scalar and pseudoscalar meson states are derived from the
requirement of chiral symmetry restoration at high energies.
