Analysis of the Ag L-series X-ray spectrum has been performed, based on relaxed-orbital relativistic transition-energy calculations. Satellite energies were computed in intermediate coupling. It is found that satellites arising from LN double-hole states generally fall within the natural width of the parent diagram lines. Contrary to previous assumption, the observed high-energy satellites are due to LM double-hole states produced by L1-L3M4,5 Coster-Kronig transitions and by shakeoff. The observed peak structure in the satellite spectrum is due to multiplet splitting of the initial and final double-hole states. Theoretical L1-L3M4,5 transition rates based on the Coster-Kronig energies computed by Chen et al. (1977) are closer to experiment than previous results, but still are too large by a factor of about 2, indicating an as-yet undetected flaw in the theory.