  A physical characterization of Landau singularities is emphasized, which
should trace the lower boundary N_f^* of the conformal window in QCD and
supersymmetric QCD. A natural way to disentangle ``perturbative'' from
  ``non-perturbative'' contributions below N_f^* is suggested. Assuming an
infrared fixed point is present in the perturbative part of the QCD coupling
even in some range below N_f^* leads to the condition gamma(N_f^*)=1, where
gamma is the critical exponent. This result is incompatible with the existence
of an analogue of Seiberg free dual magnetic phase in QCD. Using the Banks-Zaks
expansion, one gets
  4<N_f^*<6. The low value of N_f^* gives some justification to the infrared
finite coupling approach to power corrections, and suggests a way to compute
their normalization from perturbative input. If the perturbative series are
still asymptotic in the negative coupling region, the presence of a negative
ultraviolet fixed point is required both in QCD and in supersymmetric QCD to
preserve causality within the conformal window. Some evidence for such a fixed
point in QCD is provided through a modified Banks-Zaks expansion. Conformal
window amplitudes, which contain power contributions, are shown to remain
generically finite in the N_f=-\infty one-loop limit in simple models with
infrared finite perturbative coupling.
