  It is shown that analytic properties of standard QCD perturbation theory
contradict known spectral properties,and contain in particular IR generated
ghost poles and cuts. As an outcome the rigorous background perturbation theory
is developed and its analytic properties are shown to be in agreement with
general requirements. In a limiting case of large Nc, when QCD amplitudes
contain only pole singularities, the strong coupling constant alpha_s(Q) is
shown to be also meromorfic function of external momenta.
  Some simple models and examples are given when nonperturbative beta function
and alpha_s(Q) can be written explicitly.
  General form of amplitudes at large Nc is given in the framework of
background perturbation theory and its correspondence with standard
perturbation theory at large momenta is demonstrated in the example of e^+e^-
annihilation. For time-like momenta the background coupling constant differs
drastically from the standard one but the background series averaged over
energy intervals has the same (AF) asymptotics at large momenta as in the
standard perturbation theory.

High Energy Physics - Phenomenology