A theory of coherent excitation of a localized state on an adatom by two-photon photoemission spectroscopy(TR-2PPE) is presented within a microscopic model and the time-dependent formalism. Coherent oscillation and incoherent population decay of the excitation are obtained, and are shown to attain well-defined lifetime constants only in the long-delay limit. In addition, we have found a competing excitation channel via electron transfer. The theory is applied to Cs/Cu (111), which reproduces a few qualitative features observed in recent experiments. The effect of atomic motion on the 2PPE spectra, which manifests dominantly as a redshift in the spectrum, has been analysed.