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We study the large order behaviour in perturbation theory of the Bjorken,Ellis-Jaffe and Gross-Llewellyn-Smith sum rules. In particular, we considertheir first infrared renormalons, for which we obtain their analytic structurewith logarithmic accuracy and also an approximate determination of theirnormalization constant. Estimates of higher order terms of the perturbativeseries are given. The Renormalon subtracted scheme is worked out for theseobservables and compared with experimental data. Overall, good agreement withexperiment is found. This allows us to obtain {\hat a}_0 and some higher-twistnon-perturbative constants from experiment: {\hat a}_0=0.141\pm 0.089;f_{3,RS}(1 GeV)=-0.124^{+0.137}_{-0.142} GeV^2.Comment: 23 pages, 18 figures, one reference added, journal versio

Fit to the Bjorken, Ellis-Jaffe and Gross-Llewellyn-Smith sum rules in a renormalon based approach