We describe the development of an equipment which can be employed for examining various surface phenomena in real-time by performing time-resolved core-level photoelectron spectroscopy. We demonstrate this unique capability by examining the desorption of Sb atoms occurring from GaSb(001) as well as Sb/GaAs(001) in the temperature range of 440^oC∼580^oC, which is the usual growth temperature. The time dependence of core-level photoelectron spectra revealed that the activation energy for Sb desorption varies from 0.7 eV to 2.5 eV due to the difference in local bonding structures. In addition, experiments on alternating growth of GaAs suggest that there are two Ga adsorption sites, the occupation of which is dependent on the Ga coverages. This finding is in agreement with theoretical studies. These results demonstrate the potential of the technique to elucidate the surface process by real-time analysis.