  We study the capillary wave dynamics of a single viscoelastic supported film
and of a double layer of immiscible viscoelastic supported films. Using both
simple scaling arguments and a continuum hydrodynamic theory, we investigate
the effects of viscoelasticity and interfacial slip on the relaxation dynamics
of these capillary waves. Our results account for the recent observation of a
wavelength-independent decay rate for capillary waves in a supported
polystyrene/brominated polystyrene double layer [X. Hu {\em et al.}, Phys. Rev.
E {\bf 74}, 010602 (R) (2006)].
