Chemical shifts (ChSh) of nine emission lines of the uranium L-series in uranium oxides UO_2+x (x = 0-1) with respect to UO₂ were studied by using a precise crystal-diffraction X-ray spectrometer. ChSh of Lα₁, α₂ uranium and thorium lines in solid solutions yUO₂ · (1-y)ThO₂ (y = 0÷1) were measured with respect to UO₂ and ThO₂, respectively. The changes in energy of spin-orbital splitting (SOS) - Δδnl _± of inner nl-orbitals of the uranium atom were calculated from the data of ChSh of spin-doublet lines. For UO_2+x oxides, a linear decrease in Δδnl_± values with increasing degree of uranium oxidation was found. Sign inversion of Δδnl _± for uranium levels was found on passing to solid solutions. No change in the SOS energy of inner thorium levels was detected. The values of Δδnl_± were found to correlate with the experimental values of the effective magnetic moment of uranium in oxides. On the basis of the comparison of experimental Δδnl_± values with Dirac-Hartree-Fock atomic calculations, it was concluded that the observed variations in Δδnl_± values are due to the redistribution of electron and spin density between the 5 f_7/2- and 5 _f5/2-levels of the fine structure of the uranium atom without changes in atomic charge state. On the basis of the hypothesis of intraatomic relativistic U 5 f_7/2 ↔ U 5 f_5/2 transition, a model of paramagnetic moment formation on the uranium atom in uranium dioxide was proposed.