  We perform a detailed analysis of flavour changing neutral current processes
in the charm sector in the context of 331 models. As pointed out recently, in
the case of $Z^\prime$ contributions in these models there are no new free
parameters beyond those already present in the $B_{d,s}$ and $K$ meson systems
analyzed in the past. As a result, definite ranges for new Physics (NP) effects
in various charm observables could be obtained. While generally NP effects turn
out to be small, in a number of observables they are much larger than the tiny
effects predicted within the Standard Model. In particular we find that the
branching ratio of the mode $D^0 \to \mu^+ \mu^-$, despite remaining tiny, can
be enhanced by 6 orders of magnitude with respect to the SM. We work out
correlations between this mode and rare $B_{d,s}$ and $K$ decays. We also
discuss neutral charm meson oscillations and CP violation in the charm system.
In particular, we point out that 331 models provide new weak phases that are a
necessary condition to have non-vanishing CP asymmetries. In the case of
$\Delta A_{CP}$, the difference between the CP asymmetries in $D^0 \to K^+ K^-$
and $D^0 \to \pi^+ \pi^-$, we find that agreement with experiment can be
obtained provided that two conditions are verified: the phases in the ranges
predicted in 331 models and large hadronic matrix elements.
