The two-dimensional (2D) Fermi surfaces formed by a surface resonance band on three ordered structures of In/Cu(0 0 1) were studied. All structures are in charge-density-wave (CDW) ground states at room temperature. The Fermi surfaces have circular shapes, indicating that the surface resonance band has a 2D nearly-free-electron-like character. While the area of the Fermi surfaces increases slightly with increasing coverage, their shape is almost invariant. This indicates that the electron-phonon (e-ph) coupling plays a dominant role in the CDW phase transitions. (C) 2004 Elsevier B.V. All rights reserved.