The damping of horizontal waves on a deep fluid has been measured and compared with published theoretical predictions for the following systems: (1) clean water (frequency range: 50 to 920 c/s): (2) solutions of soluble surface-active agents (frequency range 14 to 800 c/s); (3) aqueous solutions on which has been spread a monolayer of an insoluble surfaceactive agent (frequency 150 c/s). The results for clean water agree closely with the appropriate theoretical equations. Data on the damping as a function of frequency and concentration for a soluble surface-active agent (sodium lauryl sulphate) show a relaxational effect, due to desorption and adsorption of the film during the passage of each wave. Three other surface-active agents of different chain lengths have been studied to determine the effect of the rate of desorption on the damping at different frequencies. The results are consistent with theory. Soluble and insoluble films possessing different surface compressibilities and shear viscosities have been studied to find how these factors affect the damping at various surface pressures. Results are in excellent accord with the mathematical theory of Dorrestein (1951): the surface compressional modulus is of prime importance in damping capillary waves, and quite low values of this modulus can cause wave damping which considerably exceeds that at a completely immobile surface.