  This work explores the dynamical stability of cosmological models where dark
matter and dark energy can non-minimally couple to spacetime (scalar)
curvature. Two different scenarios are presented here. In the initial case,
only dark matter sector is coupled to curvature in the presence of a
quintessence scalar field. In the second case both dark matter and the
quintessence field are coupled to curvature. It is shown that one can get an
accelerating expansion phase of the universe in both the cases. The nature of
the fixed points show that there can be stable or unstable phases where the
curvature coupling vanishes and dark energy and dark matter evolve
independently. On the other hand there can be stable accelerating expansion
phases where both the components are coupled to curvature.
