  The dynamics of a class of zero-range processes exhibiting a condensation
transition in the stationary state is studied. The system evolves in time
starting from a random disordered initial condition. The analytical study of
the large-time behaviour of the system in its mean-field geometry provides a
guide for the numerical study of the one-dimensional version of the model. Most
qualitative features of the mean-field case are still present in the
one-dimensional system, both in the condensed phase and at criticality. In
particular the scaling analysis, valid for the mean-field system at large time
and for large values of the site occupancy, still holds in one dimension. The
dynamical exponent $z$, characteristic of the growth of the condensate, is
changed from its mean-field value 2 to 3. In presence of a bias, the mean-field
value $z=2$ is recovered. The dynamical exponent $z_c$, characteristic of the
growth of critical fluctuations, is changed from its mean-field value 2 to a
larger value, $z_c\simeq 5$. In presence of a bias, $z_c\simeq 3$.
