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.
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