How to test scaling in asymptotically free theories

It is shown how, in asymptotically free gauge theories, one can, given the deep-inelastic structure functions for values of q² in the asymptotic region, calculate explicitly the structure functions for all larger q². The ratio of structure functions for q²=50 and 5 GeV² is estimated. Substantial deviations from scaling are found, as well as a dramatic ω dependence, for values of 1< ω< 4.