  We present a nonextensive version of the recently discussed QCD-based Nambu -
Jona-Lasinio (NJL) model of many-body field theory describing behavior of
strongly interacting matter. It is based on the nonextensive generalization of
the Boltzmann-Gibbs (BG) statistical mechanics used in NJL model, which was
taken in the form proposed by Tsallis and characterized by a dimensionless
nonextensivity parameter q (for q -> 1 one recovers the usual BG case). This is
a new phenomenological parameter of the model which accounts summarily for all
possible (so far unspecified) effects leading to departure from the conditions
required by the usual BG approach to be fully applicable. It turns out that
temperature dependencies of chiral symmetry restoration, masses of pion and
sigma meson and characteristic features of spinodal decomposition are sensitive
to the departures from the usual BG case.
