  The results of LO {\it Fixed point} QCD (FP-QCD) analysis of the CCFR data
for the nucleon structure function $~xF_3(x,Q^2)~$ are presented. The
predictions of FP-QCD, in which $~\alpha_{s}(Q^2)~$ tends to a nonzero coupling
constant $\alpha_{0}$ as $~Q^2\to \infty~,$ are in good agreement with the
data. If $~\alpha_{0}~$ is a first order zero of the $~\beta~$ function,
constraints for the possible values of the $~\beta~$ function parameter $~b~$
regulating how fast $~\alpha_ s(Q^2)~$ tends to its asymptotic value
$~\alpha_{0}~$ are found from the data. The corresponding values of
$~\alpha_{0}~$ are also determined. Having in mind the recent QCD fits to the
same data we conclude that in spite of the high precision and the large
$~(x,Q^2)~$ kinematic range of the CCFR data they cannot discriminate between
QCD and FP-QCD predictions for $~xF_3(x,Q^2)~$.
  PACS: 12.38.Qk; 19.90+b; 13.60 Hb
