The relation between shifts in Auger energies and shifts in electron binding energies is explored. The prediction of Auger energies in metals from one-hole and two-hole optical energies as well as from electron binding energies in metals is described, with proper accounting for final-state coupling, relaxation, and reference energies. A decrease in values of extra-atomic relaxation energies for 3d metals between Ni and Cu, arising from the loss of d-wave screening at the 3d-shell closure, was derived for the L3M23M23 Auger transition in which the final state is localized. A similar decrease can be derived from the data on the L3M45M45 transition, suggesting that the 3d hole state may be localized. Shifts in either Auger or electron binding energies between solids have no direct significance when taken alone, but the difference between the two is shown to be equal to the difference in the corresponding extra-atomic relaxation energies. Differential shifts are reported for sodium and its salts and for zinc and its salts. The differential shift between sodium metal and NaF is 8.7 eV, while the Zn-to-ZnF2 shift is 5.2 eV, in good agreement with expectations. The Zn(3d)-F(2p) peak in the ZnF2 spectrum gives clear evidence for crystal-field splitting in the final state. © 1974 The American Physical Society.