Uranus' magnetosphere has a well-developed, thick ((4.6--14)¿103km) magnetopause that was fully traversed twice by Voyager 2 once inbound to the planet and once outbound. This boundary appears to resemble Earth's magnetopause in approximate shape and even to the extent of supporting surface waves which were observed on the inbound pass at a distance of 18.3 RU (RU=25,600 km). There were apparently eight partial transitions from the magnetosheath into the current sheet of the magnetopause at this time, followed by a final complete transition to the magnetosphere. Six of the estimated normal vectors to the local boundary show clear evidence of oscillations in the slope with typical angular excursions, from one partial transition to the next, of ≂90¿. The vectors oscillated approximately in a plane that was severely tilted by ≂49¿ with respect to Uranus' orbital plane. Analysis of these waves shows that on average the ''tailward'' wave speed was (76¿3.0) km/s, the amplitude was (4.5¿3.0)¿103 km, the wavelength was (34¿20)¿103 km, and the period was (6.9¿3.0) min. The wave properties are compared to those at Earth and Saturn, where similar surface waves have been observed. ¿ American Geophysical Union 1987