The alternating growth of GaAs on a (001) surface was analyzed by time-resolved core-level photoelectron spectroscopy (CLPES) and measuring reflection high-energy electron diffraction (RHEED) specular beam intensity. When looking at a Ga supply period, a saturation of Ga coverage was found from the time-dependence of Ga CLPES intensity. The RHEED specular beam intensity decreased even after the saturation coverage of Ga. These results indicate that Ga droplets begin to grow after Ga has been grown laterally. The inflection points of photoelectron intensity change were found at about half a monolayer of Ga supply at a substrate temperature of 560 degrees C. The spectrum analysis of the time-resolved CLPES clarifies that the Ga adsorption site changes at about half a monolayer of Ga supply. These results show the potential of using time-resolved CLPES for the real-time analysis of the growth process.