The effect of relaxation on KLL, LMM, and MNN Auger-electron spectra of Ne, Mg, Ar, Ca, Zn, and Kr has been studied by the Dirac-Fock method. The relaxation is shown to depend universally on the Auger-electron energy aud on the number of peel electrons (N") in subshells above the final-state holes. In the sudden approx-imation limit (large N") the relaxation saturates to 14%%uo reduction of the Auger rates in analogy to the 20'Fo reduction of deep inner-shell Dirac-Fock photoionization cross sections well above threshold. The isotropy of the relaxation is emphasized by its small influence on the angular distribution of Auger electrons. PACS number(s): 32.80.Hd, 32.80.Fb