  Nonperturbative studies of the strong running coupling constant in the
infrared region are discussed. Starting from the analyses of the Dyson --
Schwinger equations in the gauge sector of QCD, the conclusion is made on an
incomplete fixing of the perturbation theory summation ambiguity within
"(forced) analytization procedure" (called also a dispersive approach). A
minimal model for $\bar\alpha_s(q^2)$ is proposed so that the perturbative
time-like discontinuity is preserved and nonperturbative terms not only remove
the Landau singularity but also provide the ultraviolet convergence of the
gluon condensate. Within this model, on the one hand, the gluon zero modes are
enhanced (the dual superconductor property of the QCD vacuum) and, on the other
hand, dynamical gluon mass generation is realized, with $m_g$ estimated as $0.6
GeV$. The uncertainty connected with the division into perturbative and
nonperturbative contributions is discussed with the gluon condensate taken as
an example.
