  We present a formalism based on nonequilibrium dynamical mean field theory
(DMFT) which allows to compute the time-resolved X-ray absorption spectrum
(XAS) of photo-excited solids. By applying this formalism to the photo-doped
half-filled and quarter-filled two-orbital Hubbard models in the Mott
insulating regime we clarify how the time-resolved XAS signal reflects the
nonequilibrium population of different local states. Apart from the missing
broadening associated with continuum excitations, the atomic XAS spectrum
computed with the nonthermal state populations provides a good approximation to
the full nonequilibrium DMFT result. This suggest a route to combine the
accurate DMFT description of nonequilibrum states of solids with cluster
calculations of the XAS signal.
