We report on an element-selective study of the fate of charge carriers in photoexcited inorganic CsPbBr3 and CsPb(ClBr)3 perovskite nanocrystals in toluene solutions using time-resolved X-ray absorption spectroscopy with 80 ps time resolution. Probing the Br K-edge, the Pb L3-edge, and the Cs L2-edge, we find that holes in the valence band are localized at Br atoms, forming small polarons, while electrons appear as delocalized in the conduction band. No signature of either electronic or structural changes is observed at the Cs L2-edge. The results at the Br and Pb edges suggest the existence of a weakly localized exciton, while the absence of signatures at the Cs edge indicates that the Cs+ cation plays no role in the charge transport, at least beyond 80 ps. This first, time-resolved element-specific study of perovskites helps understand the rather modest charge carrier mobilities in these materials.