Dispersion relations of the s-p derived surface state on (111) surfaces of silver and copper have been measured using low-temperature scanning tunneling microscopy and spectroscopy. For silver as well as for copper we find a significant deviation from a parabolic dispersion characteristic of free-electron-like systems. A simple tight-binding model accounts for the trends in the measured dispersions. (C) 2000 Elsevier Science B.V. All rights reserved.