  We investigate the power-suppressed corrections to the fragmentation
functions of the current jet in non-singlet deep inelastic lepton-hadron
scattering. The current jet is defined by selecting final-state particles in
the current hemisphere in the Breit frame of reference. Our method is based on
an analysis of one-loop Feynman graphs containing a massive gluon, which is
equivalent to the evaluation of leading infrared renormalon contributions. We
find that the leading corrections are proportional to $1/Q^2$, as in $e^+e^-$
annihilation, but their functional forms are different. We give quantitative
estimates based on the hypothesis of universal low-energy behaviour of the
strong coupling.
