  Collective excitations of coupled electron-phonon systems are calculated for
both monolayer and bilayer graphene, taking into account the non-perturbative
Coulomb coupling between electronic excitations in graphene and the substrate
longitudinal optical phonon modes. We find that the plasmon-phonon coupling in
monolayer graphene is strong at all densities, but in bilayer graphene the
coupling is significant only at high densities satisfying the resonant
condition $\omega_{pl} \approx \omega_{ph}$. The difference arises from the
peculiar screening properties associated with chirality of graphene.
Plasmon-phonon coupling explains the measured quasi-linear plasmon dispersion
in the long wavelength limit, thus resolving a puzzle in the experimental
observations.
