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Radiative lifetimes have been calculated for 15 levels of Xe VII belonging to the configurations 5s5p, 5p2, 5s5d, 5s6s, 5p5d, 4f5p, 5p5d and 5s5f and for 4 levels of the 5p and 5d configurations of Xe VIII. A relativistic Hartree-Fock approach including core-polarization effects, on the one hand, and a purely relativistic multiconfiguration Dirac-Fock method, on the other hand, have been used for the calculations. The accuracy of the present set of results has been assessed through comparisons with radiative lifetime measurements obtained by beam-foil spectroscopy. A good agreement between theory and experiment is observed for most of the levels. A new set of transition probabilities is proposed for 169 transitions of Xe VII and 45 transitions of Xe VIII. [ABSTRACT FROM AUTHOR]