We investigate the effects of photoexcited-hole decay on time-resolved two-photon photoemission spectra of metal surfaces by non-equilibrium Green function method. We show that it is necessary for calculating the photoelectron intensity to introduce a Green function depending on the observation time of the photoelectron. The photoexcited-hole decay causes the loss of coherence of the system and hence accounts for acceleration of the decay of the photoexcited-electron density. Then the effective lifetimes estimated from the photoelectron intensity as a function of the pump-probe delay time can be the lifetimes of the photoexcited '(non-excitonic) electron-hole pairs' even when direct interactions between photoexcited electrons and holes are negligible while it is usually considered that the effective lifetimes correspond to the electron lifetimes. (C) 2003 Elsevier Science B.V. All rights reserved.