Discrete image-potential states (ISs) are revealed at double-walled carbon nanotubes by means of scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) in the distance-voltage z(V) spectroscopy mode. The nanotubes are supported by flat Au(111) substrates. Due to the high sensitivity of the hot IS electrons to local variations of the surface potential, they can be considered as a sensitive probe to investigate interactions with the supporting substrate and impurities or defects at the nanotube surface. ISs provide information on the local electronic structure as well as on the electron dynamics at supported nanotubes.