  We study the twist-4 contribution to the unpolarized nucleon structure
functions, F_L and F_2, in an approach where the vacuum structure of QCD is
described by a dilute medium of instantons ($\bar\rho / \bar R \ll 1$). The
dominant power corrections come from the twist-4 quark-gluon operators and are
of the order $1/(\bar\rho^2 Q^2)$. The contributions from four-quark operators
are suppressed. The approach predicts large 1/Q^2-corrections to F_L, in
agreement with the results of QCD fits to the data.
