  We consider in detail the Q^2 -dependence of the DIS structure functions,
with Q being the virtual photon momentum. Quite often this dependence is
claimed to be originated by the Q^2-dependence of the QCD coupling. This leads
to the small-x asymptotics of the structure functions with Q^2 -dependent
intercepts. We demonstrate that the DGLAP parametrization alpha_s = alpha_s
(Q^2) is an approximation valid in the region of large x (where 2pq can be
approximated by Q^2) only, providing the factorization scale is also large.
Outside this region, the DGLAP parametrization fails, so alpha_s should be
replaced by an effective coupling which is independent of Q^2 at small x. As a
consequence, intercepts of the structure functions are independent of Q^2.
Nevertheless, the small-x asymptotics of the structure functions explicitly
depend on Q^2, even when the coupling does not depend on it. We also consider
the structure functions at small Q^2 and give a comment on power-Q^2
corrections to the structure functions at large and small Q^2
