Core-level spectra of individual heteroepitaxial nanocrystals were measured with a spectroscopic photoelectron emission and low-energy electron microscope that allows laterally resolved photoemission spectroscopy. The nanocrystals were obtained by depositing nominally 2 and 4 monolayers of InAs on a Se-terminated GaAs(001) surface. Using the high lateral resolution of our microscope in combination with the well-known chemical sensitivity of synchrotron radiation photoelectron spectroscopy, we were able to obtain spectra from individual nanocrystals and to deduce their elemental composition. Consequently, during the growth of InAs, interdiffusion and segregation take place. Furthermore, the differences in work function and valence band edge energy between nanocrystals and the substrate were observed, which indicates that Se diffusion onto the InAs nanocrystals during nanocrystal growth leads to the formation of a Se termination of the InAs.