  We derive core-level spectra for doped free-standing bilayer graphene.
Numerical results are presented for all nine combinations of the doping
concentrations $10^{12}\rm{cm}^{-2}$, $10^{13}\rm{cm}^{-2}$, and
$10^{14}\rm{cm}^{-2}$ in the two graphene sheets and we compare the results to
the reference spectra for monolayer graphene. We furthermore discuss the
spectrum of single-particle inter-band and intra-band excitations in the
$\omega q$-plane, and show how the dispersion curves of the collective modes
are modified in the bilayer system.
