1. The observed phenomenon of Bjorken scaling in deep inelastic lepton-nucleon scattering has been explained in terms of the asymptotically free gauge theories. n. 2) A consequence of the asymptotic freedom is based on a perturbation expansion in the effective coupling constant (ECC) g 2 (Q2/ A') which decreases as Q' increases. Because the currently available experimental range in Q' is not sufficiently large, the higher order corrections in g 2 are indeed significant to analyze the moments of the structure functions. Further, it is claimed 3l that the full order-g 2 calculations are necessary for us to see the mutual consistency of QCD analyses for different physical processes by comparing the values of scale parameter A determined in each process. Recently, Bardeen and others 4l have presented the higher order corrections in g' to the coefficient functions of the twist two operators in the Wilson expansion of the product of two currents. They combined their results with two-loop calcula tions of the anomalous dimensions of the operators 5) to analyze the flavor non singlet moments of the nucleon structure function F;s.al The results are in favor of QCD. For the singlet moment, however, only the leading order analysis has been done by Duke and Roberts. 7) They insist that the QCD expectation is in consistent with the experimental data on the Nachtmann moments 8) evaluated by themselves using the recent data of SLAC (ep, en) and Fermilab (JLP, !1n) ,9} though their non-singlet combinations of the F 2-moments have no trouble with QCD. Because of the very importance of the problem, we reanalyze the non-singlet and singlet moments of the structure function F, with the full order-g 2 corrections