  New relations between Bjorken polarized, Gross-Llewellyn Smith and Bjorken
unpolarized sum rules are proposed. They are based on the ``universality'' of
the perturbative and non-perturbative $\rm{1/Q^2}$ contributions to these sum
rules. The letter facts can be deduced from the corresponding renormalon
calculations. The similarity of $\rm{1/Q^2}$ corrections are checked by
inspecting the numerical results obtained within several approaches.The
discussed relations are in agreement with existing experimental data.Some
possible new phenomenological applications are mentioned including estimates of
not yet measured Bjorken unpolarized sum rule.
