The Auger-photoelectron coincidence spectroscopy (APECS) and Auger Auger-electron coincidence spectroscopy (AAECS) spectral behaviors of Auger cascade decay are discussed by a many-body theory. There is a significant difference in the coincidence intensity distribution in a two-dimensional map according to whether a pair of coincidence electrons are generated, respectively, by creation and annihilation of the same n-hole state (n⩾1). The difference manifests as a line narrowing and a peak KE shift of the coincidence spectrum compared to the singles (noncoincidence) one. We discussed the inherent mechanism of APECS (AAECS), which causes the difference.