The dynamics of electrons in image-potential resonances on the Ag(111) surface, i.e., image-potential states that are resonant with bulk bands, have been studied by time-resolved two-photon photoemission in combination with quantum-beat spectroscopy. Energies and lifetimes of these resonances were determined up to a quantum number n = 7. Both quantities show a hydrogen-like scaling with quantum number n. The measured decay time of the first image-potential state (n = 1), which is still located in the projected band gap, is 31.5(1.5) fs. The decay time decreases to 23(2) fs for the resonance n = 2 and then increases up to 1 ps for n = 7. It is concluded that the elastic decay of the resonances due to elastic electron transfer into the bulk is nearly one order of magnitude faster than the inelastic electron-hole pair decay. Nevertheless, the elastic decay is found to be slower than theoretically predicted. The pure dephasing times of the resonances n = 3-7 are longer than the decay times. This suggests that electron-phonon scattering is weak despite a large bulk penetration of the resonance wave functions.