  The results of approximate N$^$3LO and detailed NNLO fits to $xF_3$ data of
the CCFR'97 collaboration are presented. We demonstrate that $1/Q^2$
non-perturbative corrections to $xF_3$ modeled by three independent procedures
are shadowed by perturbative QCD effects, starting at the NNLO. Special
attention is paid to revealing the role of the recently calculated NNLO
corrections to the anomalous dimensions and $N^3$LO corrections to the
coefficient functions of odd moments of $xF_3$ with $n\leq 13$. The related
values of $\alpha_s(M_Z)$ are extracted.
