Time-resolved x-ray magnetic circular dichroism was used to investigate epitaxial MgO(100)/Co₂Cr_0.6Fe_0.4Al and MgO(100)/Co₂Cr_0.6Fe_0.4Al/Cr/CoFe films. The precessional motion of the individual sublattice magnetization, excited by continuous microwave excitation in the range 2–10 GHz, was detected by tuning the x-ray photon energy to the L ₃ absorption edges of Cr, Fe and Co. The relative phase angle of the sublattice magnetization's response is smaller than the detection limit of 2°. A weakly antiferromagnetically coupled CoFe layer causes an increase in the ferromagnetic resonance linewidth consisting of a constant offset and a component linearly increasing with frequency that we partly attribute to non-local damping due to spin pumping.