  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 predic-
tions 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. The description of the data is even better than that in the case of LO
QCD. The FP-QCD parameter $~\alpha_0~$ is determined with a good accuracy:
$~\alpha_0 = 0.198\pm 0.009~$. Having in mind the recent QCD fits to the same
data we conclude that unlike the high precision and large $~(x,Q^2)~$ kinematic
range of the CCFR data they cannot discriminate between QCD and FP - QCD
predictions for $~xF_3(x,Q^2)~$.
