  The structure of the QFT expansion is studied in the framework of a new
"Invariant analytic" version of the perturbative QCD. Here, an invariant
(running) coupling $a(Q^2/\Lambda^2)=\beta_1\alpha_s(Q^2)/4\pi$ is transformed
into a "$Q^2$--analytized" invariant coupling $a_{\rm an}(Q^2/\Lambda^2) \equiv
{\cal A}(x)$ which, by constuction, is free of ghost singularities due to
incorporating some nonperturbative structures.
  Meanwhile, the "analytized" perturbation expansion for an observable $F$, in
contrast with the usual case, may contain specific functions ${\cal A}_n(x)=
[a^n(x)]_{\rm an}$, the "n-th power of $a(x)$ analytized as a whole", instead
of $({\cal A}(x))^n$. In other words, the pertubation series for $F(x)$, due to
analyticity imperative, may change its form turning into an {\it asymptotic
expansion \`a la Erd\'elyi over a nonpower set} $\{{\cal A}_n(x)\}$.
  We analyse sets of functions $\{{\cal A}_n(x)\}$ and discuss properties of
non-power expansion arising with their relations to feeble loop and scheme
dependence of observables.
  The issue of ambiguity of the invariant analytization procedure and of
possible inconsistency of some of its versions with the RG structure is also
discussed.
