  We discuss the model $\bar{\alpha}_{an}(Q^2)$ recently proposed for the QCD
running coupling $\bar{\alpha}_s(Q^2)$ in the Euclidean domain on the basis of
the "asymptotic-freedom" expression and on causality condition in the form of
the $Q^2$-analyticity. The model contains no adjustable parameters and obeys
the important features: (i) Finite ghost-free behavior in the "low $Q^2$"
region and correspondence with the standard RG-summed UV expressions;%\item~ %
(ii) The universal limiting value $\bar{\alpha}_{an}(0)$ expressed only via
group symmetry factors. This value as well as the $\bar{\alpha}_{an}$ behavior
in the whole IR region $Q^2 \leq \Lambda^2$ turns out to be stable with respect
to higher loop corrections; %\item~ (iii) Coherence between observed
$\bar{\alpha}_s(M_{\tau}^2)$ value and integral information on the IR
$\bar{\alpha}_s(Q^2)$ behavior extracted from jet physics.
