The deexcitation of the resonantly excited Kr 3${\mathit{d}}_{3/2,5/2}^{\mathrm{\ensuremath{-}}1}$5p states has been studied by recording the electron spectra with very high photon and electron energy resolution and by comparing the results with multiconfiguration Dirac-Fock calculations. The high resolution has enabled us to resolve the fine structures in detail by utilizing the Auger resonant Raman effect. High-quality experimental results are used to confirm the roles of exchange interaction and of initial- and final-state interactions in distributing the intensity to the fine structures in the spectra. \textcopyright{} 1996 The American Physical Society.