  The off-mass-shell behavior of the nucleon structure function, $F_2^N$, is
studied within an approach motivated by the Sullivan model. Deep inelastic
scattering on the nucleon is considered in the second order in the pion-nucleon
coupling constant, corresponding to the dressing of the bare nucleons by the
mesonic cloud. The inclusive and semi-inclusive deep inelastic processes on the
deuteron involving off-shell nucleons are considered. A deformation of the
mesonic cloud for the off-mass-shell nucleon, compared to the free one,
generates observable effects in deep inelastic scattering. In particular, it
leads to the breakdown of the convolution model, i.e. the deuteron structure
functions are not expressed through the free nucleon structure function.
Analysis of the semi-inclusive deep inelastic scattering on the deuteron, in
the spectator approximation, shows that this reaction opens new possibilities
to study the role of the off-shell effects in determining in detail the nucleon
structure function.
