  We study the response of a semi-bounded one-component fully degenerate
electron plasma to an initial perturbation in the electrostatic limit. We show
that the part of the electric potential corresponding to surface waves in such
plasma can be represented, at large times, as the sum of two terms, one term
corresponding to "conventional" (Langmuir) surface waves and the other term
representing a new type of surface waves resulting from specific analytic
properties of degenerate plasma's dielectric response function. These two terms
are characterized by different oscillation frequencies (for a given wave
number), and, while the "conventional" term's amplitude decays exponentially
with time, the new term is characterized by a slower, power-law decay of the
oscillation amplitude and is therefore dominant at large times.
