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We analyze rare-earth 3d-core x-ray-absorption spectra (3d XAS) in PrO 2, as well as in CeO 2, using the impurity Anderson model. It is shown that the interplay between the atomic multiplet coupling and the solid-state hybridization between rare-earth 4f and oxygen 2p states is essential in determining the spectral shape. The calculated spectra are in fair agreement with experimental data which supports the theory that there is a strong mixing between 4 f 1 and 4 f 2 v in the ground state of PrO 2, where v denotes a hole in the oxygen 2p valence band. A theoretical prediction of Pr 4d XAS of PrO 2 is also given. Because it contains much structure, experimental determination of this spectrum would be very valuable for the study of mixed-valence compounds.