We discuss the QCD effects of the higher-twist operators in the nucleon spin-dependent structure functions measured by the polarized deep inelastic leptoproduction. We particularly study the renormalization of the twist-3 and twist-4 operators within the framework of operator product expansions and renormalization group methods in perturbative QCD. Emphasis will be placed on the role of the operators proportional to equation of motion which appear in the mixing of the higher-twist operators through renormalization. The logarithmic and power corrections in $Q^2$ due to the lowest spin higher-twist operators are disucussed for the first moment of $g_1$ structure function, Bjorken and Ellis-Jaffe sum rule, as well as the lower moments of $g_2$ structure function.