  We study the power corrections (infrared renormalon contributions) to the
coefficient functions for non-singlet deep inelastic structure functions due to
gluon vacuum polarization insertions in one-loop graphs. Remarkably, for all
the structure functions $F_1$, $F_2$, $F_3$ and $g_1$, there are only two such
contributions, corresponding to $1/Q^2$ and $1/Q^4$ power corrections. We
compute their dependence on Bjorken $x$. The results could be used to model the
dominant higher-twist contributions.
