  The method of truncated Mellin moments in a solving QCD evolution equations
of the nonsinglet structure functions $F_2^{NS}(x,Q^2)$ and $g_1^{NS}(x,Q^2)$
is presented. All calculations are performed within double logarithmic $ln^2x$
approximation. An equation for truncated moments which incorporates $ln^2x$
effects is formulated and solved for the unintegrated structure function
$f^{NS}(x,Q^2)$. The contribution to the Bjorken sum rule coming from the
region of very small $x$ is quantified. Further possible improvement of this
approach is also discussed.
