The boundary value problem for velocity of propagation and attenuation of capillary ripples over viscoelastic surface films is set up and solved from the viewpoint of continuum hydrodynamics. Both soluble and insoluble films are treated. Successive approximation methods are used to derive explicit formulas for velocity of propagation and amplitude attenuation; formulas for these quantities, accurate to second order, are given for slightly viscoelastic and highly viscoelastic films, and formulas, accurate to first order, are given for films of intermediate viscoelasticity.