  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 the Callan-Symanzik $~\beta~$ function admits a
{\it second order} ultraviolet zero at $~\alpha = \alpha_0~$ are in good
agreement with the data. Constraints for the possible values of the $~\beta~$
function parameter $~b~$ regulating how fast $~\alpha_ s(Q^2)~$ tends to its
asymptotic value $~\alpha_{0}\ne 0~$ are found from the data. The corresponding
values of $~\alpha_{0}~$ are also determined. Having in mind our recent " First
order fixed point" QCD fit 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 $~xF_3(x,Q^2)~$.
