  Recent measurements of the short-wavelength (~ 1--100 nm) fluctuations in
stacks of lipid membranes have revealed two distinct relaxations: a fast one
(decay rate of ~ 0.1 ns^{-1}), which fits the known baroclinic mode of bulk
lamellar phases, and a slower one (~ 1--10 \mu s^{-1}) of unknown origin. We
show that the latter is accounted for by an overdamped capillary mode,
depending on the surface tension of the stack and its anisotropic viscosity. We
thereby demonstrate how the dynamic surface tension of membrane stacks could be
extracted from such measurements.
