The spectrum and the collisionless damping of surface electromagnetic
waves in a conducting medium bordering a dielectric (or a metal) are o
btained for a case of an arbitrary spatial dispersion. The both, quant
um and classical, approximations are considered. It is shown that the
spatial dispersion of the dielectric plasma constant changes the spect
rum, collisionless damping and penetration depth of the surface wave.
As the conduction electrons are scattered by the wave potential, in ad
dition to the Landau damping, the nonresonant collionsionless damping
takes place that associated with the charged particles moving along no
rmal to boundary. This damping may be of the same order of magnitude o
r more than the Landau damping.