A new theory is presented explaining why not only short surface ripples, but also longer ocean surface waves are damped by oil films floating on the sea surface. The wave attenuation by viscoelastic surface films is attributed to the Marangoni effect, which causes a strong resonance-type wave damping in the short-gravity-wave region, and to nonlinear wave-wave interaction, by means of which wave energy is transferred from the longer waves to the energy sink in the Marangoni resonance region. A viscoelastic surface film changes the free surface boundary layer. As a consequence, wave energy is dissipated by enhanced viscous damping in the short-gravity-wave region due to large velocity gradients induced by in the viscous damping in the short-gravity-wave region due to large velocity gradients induced in the viscous boundary layer. Estimates of the influence of surface films on nonlinear transfer rates are given. Data on wave damping obtained in laboratory and field experiments by previous investigators are discussed in the light of the proposed theory. It is found that this theory is capable of explaining the observed strong wave damping by viscoelastic surface films. The theory predicts that in the equilibrium range of the spectrum, but outside the Marangoni resonance region, wave damping increases with wave number k as k3/2 and increases quadratically with wind speed (up to the limit where the film is ''washed down''). The higher the elasticity of the surface film, the stronger is the wave damping. ¿ American Geophysical Union 1989