This paper deals with the influence of Jupiter's "Great Inequality" (GI) on the orbital evolution of 2:1 resonant asteroids. This perturbation of Jupiter's motion enhances the chaotic diffusion of orbits and the depletion of asteroids in the Hecuba gap. The failure of models that adopt for Jupiter an elliptic motion with only secular perturbations is explained. We also show the dependence of the diffusion rates on the GI period, and the maximum diffusion rates that would take place if the GI period were closer to the libration period. Significant similar effects are absent in the 3:2 asteroidal resonance.