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 plasmas dielectric response function. These two terms are characterized by different oscillation frequencies (for a given wave number), and, while the conventional terms 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.
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