  We discuss a class of flat FRW cosmological models based on D=4 axion-dilaton
gravity universally coupled to cosmological background fluids. In particular,
we investigate the possibility of recurrent acceleration, which was recently
shown to be generically realized in a wide class of axion-dilaton models, but
in absence of cosmological background fluids. We observe that, once we impose
the existence of radiation -and matter- dominated earlier stages of cosmic
evolution, the axion-dilaton dynamics is altered significantly with respect to
the case of pure axion-dilaton gravity. During the matter dominated epoch the
scalar fields remain either frozen, due to the large expansion rate, or enter a
cosmological scaling regime. In both cases, oscillations of the effective
equation of state around the acceleration boundary value are impossible. Models
which enter an oscillatory stage in the low redshift regime, on the other hand,
are disfavored by observations. We also comment on the viability of the
axion-dilaton system as a candidate for dynamical dark energy. In a certain
subclass of models, an intermediate scaling regime is succeeded by eternal
acceleration. We also briefly discuss the issue of dependence on initial
conditions.
