  Closed expressions are derived for resonant multidimensional X-ray
spectroscopy using the quasiparticle nonlinear exciton representation of
optical response. This formalism is applied to predict coherent four wave
mixing signals which probe single and two core-hole states. Nonlinear X-ray
signals are compactly expressed in terms of one- and two- particle Green's
functions which can be obtained from the solution of Hedin-like equations at
the $GW$ level.
