  Observational data for type Ia supernovae, shows that the expansion of the
universe is accelerated. This accelerated expansion can be described by a
cosmological constant or by dark energy models like quintessence. An
interesting question may be raised here. Is it possible to describe the
accelerated expansion of universe using varying--$G$ cosmological models? Here
we shall show that the price for having accelerated expansion in
slow--varying--$G$ models (in which the dynamical terms of $G$ are ignored) is
to have highly non--conserved matter and also that it is in contradiction with
other data.
