  Power corrections to the Q**2 behaviour of the low-order moments of both the
longitudinal and transverse structure functions of proton and deuteron have
been investigated using available phenomenological fits of existing data in the
Q**2 range between 1 and 20 (GeV/c)**2. The Natchmann definition of the moments
has been adopted for disentangling properly target-mass and dynamical
higher-twist effects in the data. The leading twist has been treated at
next-to-leading order in the strong coupling constant and the effects of higher
orders of the perturbative series have been estimated using a
renormalon-inspired model. The contributions of (target-dependent) multiparton
correlations to both 1/Q**2 and 1/Q**4 power terms have been determined in the
transverse channel, while the longitudinal one appears to be consistent with a
pure infrared renormalon picture in the whole Q**2-range between 1 and 20
(GeV/c)**2. Finally, the extracted twist-2 contribution in the deuteron turns
out to be compatible with the hypothesis of an enhanced d-quark parton
distribution at large x.
