The observation of ship Kelvin wakes by the Seasat synthetic aperture raises a question concerning the persistence of patterns of surface gravity waves. Time scales vary with wavelength and environmental conditions. The range extends from fractions of a second at the shortest wavelengths to many days for ocean swell. Several mechanisms for destroying a wave pattern are investigated here. These are viscous dissipation, direct wind-wave interation, and nonlinear hydrodynamic interaction with ambient surface waves. The nonlinear hydrodynamic interactions appear to be the most significant.