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We study the capillary wave dynamics of a single viscoelastic supported filmand of a double layer of immiscible viscoelastic supported films. Using bothsimple scaling arguments and a continuum hydrodynamic theory, we investigatethe effects of viscoelasticity and interfacial slip on the relaxation dynamicsof these capillary waves. Our results account for the recent observation of awavelength-independent decay rate for capillary waves in a supportedpolystyrene/brominated polystyrene double layer [X. Hu {\em et al.}, Phys. Rev.E {\bf 74}, 010602 (R) (2006)].Comment: 14 pages, 9 figure

Erratum: Capillary wave dynamics on supported viscoelastic films: Single and double layers [Phys. Rev. E.75, 021604 (2007)]