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It is demonstrated that the infrared renormalon calculus indicates that theQCD theoretical expressions for the Gross-Llewelln Smith sum rules and for theBjorken polarized and unpolarized ones contain an identical negative twist-41/Q^2 correction. This observation is supported by the consideration of theresults of calculations of the corresponding twist-4 matrix elements. Togetherwith the indication of the similarity of perturbative QCD corrections to thesethree sum rules, this observation leads to simple new theoretical relationsbetween the Gross-Llewellyn Smith and Bjorken polarized and unpolarized sumrules in the energy region $Q^2\geq 1 GeV^2$. The validity of this relation ischecked using concrete experimental data for the Gross-Llewellyn Smith andBjorken polarized sum rulesComment: 7 pages, LaTeX, minor misprints corrected, results unchanged, to be  published in JETP Letters, vol 81, issue 1

Infrared Renormalons and the Relations between the Gross–Llewellyn Smith and the Bjorken Polarized and Unpolarized Sum Rules