The core hole localization, multiplets in the singly core-excited state, and their Auger-like two-electron de-excitation are discussed in some diatomic systems from the viewpoint of the exchange interaction. The exchange repulsion arising.,e from the core-core overlap is proved very small, indicating that the core electron is essentially localized on a specified atom, even in homonuclear systems. Relatively large core-valence exchange interaction between the adjacent atoms results in observable 1ssigma(g)-sigma(u) splittings in N-2 and C2H2. The 1s --> pi* excitation of a doublet radical NO gives three different electronic states. The (2)Sigma(-) state energy relative to the (2)Delta and (2)Sigma(+) states is dependent on the exchange integral between the core and pi* electrons. The two dipole-allowed (2)Pi 1s --> sigma* excited states of NO are characterized by singlet and triplet couplings between two of the three open-shell electrons. In the N 1s excitation, the sigma* and pi* electrons are strongly coupled with the triplet and singlet spins. In the O 1s, the core and pi* electrons are weakly coupled; then, the singlet-coupled is lower in energy and weaker in intensity than the triplet. Triplet radicals O-2, S-2, and Se-2 have two dipole-allowed (3)Sigma(n)(-) 1s --> sigma* excited states with four open shells, which are characterized by doublet and quartet couplings among three of the four electrons. In the S and Se 1s excitations, the sigma* and two pi* electrons are relatively strongly coupled with the quartet and doublet spins. In the O 1s, the core and two pi* electrons are weakly coupled; then, the doublet-coupled is lower in energy and weaker in intensity than the quartet. In the resonant photoionization via the 1s --> pi* and 1s --> sigma* excited states in NO and O-2, the two-electron de-excitation selection and propensity rules are discussed in terms of state symmetry, spin multiplet and S-z value. In the case that the two electrons taking part in the de-excitation have the same spins, additional exchange-type interaction reduces the transition probability. (C) 2002 Elsevier Science B.V. All rights reserved.