  In quantum theory, physical amplitudes are usually presented in the form of
Feynman perturbation series in powers of coupling constant $\al .$ However, it
is known that these amplitudes are not regular functions at $\alpha=0 .$
  For QCD, we propose new sets of expansion parameters ${\bf w}_k(\as)$ that
reflect singularity at $\as=0 $ and should be used instead of powers $\as^k.$
Their explicit form is motivated by the so called Analytic Perturbation Theory.
These parameters reveal saturation in a strong coupling case at the level
$\as^{eff}(\as\gg1)={\bf w}_1(\as\gg 1) \sim 0.5 .$ They can be used for
quanitative analysis of divers low-energy amplitudes.
  We argue that this new picture with non-power sets of perturbation expansion
parameters, as well as the saturation feature, is of a rather general nature.
