  We consider perturbations in a cosmological model with a small coupling
between dark energy and dark matter. We prove that the stability of the
curvature perturbation depends on the type of coupling between dark sectors.
When the dark energy is of quintessence type, if the coupling is proportional
to the dark matter energy density, it will drive the instability in the
curvature perturbations; however if the coupling is proportional to the energy
density of dark energy, there is room for the stability in the curvature
perturbations. When the dark energy is of phantom type, the perturbations are
always stable, no matter whether the coupling is proportional to the one or the
other energy density.
