The small-scale motions of a liquid surface due to thermally excited capillary waves are dominated by overdamped local modes of oscillation, which for a water surface at 300 K occupy the range of wave vectors between the critically damped k(c) = 1709 cm(-1) and k(max) approximate to 10(-8) cm(-1). Values of k below k(c) correspond to under-damped, normal modes of oscillation. For values of k near k(max), the peak displacement produced by a given increment of surface energy, at constant surface tension, increases sharply with increasing k, an effect which probably contributes to the reported apparent decrease in surface tension at high k. The radial dependence of a local mode is of the form exp(-kr)J(0)(kr), where J(0)(kr) is a Bessel function and the exponential factor arises from the finite rate at which the displacement spreads out from the site of the initial disturbance. The time dependence of a local mode consists of a rapid initial displacement of the surface followed by a very slow recovery. Any element of the surface spends most of its time in the recovery phase, and the rate of recovery is independent of k when k much greater than k(c). The recovery process transfers molecules out of the surface layer; hence the first-order rate constant fur transfer of a surface molecule into the bulk liquid is found to be k(B)T/2h sigma (2) s(-1), where eta is the viscosity and sigma is the molecular size.