Photoelectron partial-yield and constant-initial-state (CIS) spectra of the layered-semiconductor GeS, GeSe, SnS0.9Se0.1, and SnSe single crystals were investigated with use of synchrotron radiation. The cation d core (Ge 3d and Sn 4d) yield spectra show intense and sharp doublets due to cation-derived core excitons. The CIS spectra exhibit strong resonance due to an interference between the direct-recombination process of the core excitons and the direct-excitation process of the valence electrons. The strong resonance is characteristic of core excitons with a long lifetime and a fairly localized nature. The anion p and d core (S 2p and Se 3d) yield spectra are much broader than the cation d core spectra and reflect the density of states (DOS) of the conduction bands. Energies of the experimental DOS peaks compare favorably with conduction-band features derived from interband optical-absorption spectra.