  We discuss the application of an analytic approach called the analytic
perturbation theory (APT) to the QCD analysis of DIS data. In particular, the
results of the QCD analysis of a set of `fake' data on the polarized nonsinglet
Delta{q3} and the nonsinglet fragmentation function D^{pi+}_{u_v} by using the
Q^2-evolution within the APT are considered. The `fake' data are constructed
based on parametrization of the polarized PDF and nonsinglet combination of the
pion fragmentation functions. We confirm that APT can be successfully applied
to QCD analysis of Delta{q_3}(x,Q^2) and D^{pi+}_{u_v}(z,Q^2) and that the
inequality Lambda_{APT} > Lambda_{PT} obtained previously for the xF3(x)
structure function takes place.
