The Voyager photopolarimeter experiment detected the Neptunian rings 1989N1R and possibly 1989N2R. These rings were also photographed by the Voyager imaging cameras in August 1989. Our firm detection of 1989N1R has an equivalent depth (the product of the radial width and mean normal optical depth) of 0.77¿0.13 km, while a less certain deteciton of 1989N2R has an equivalent depth of 0.7 km ¿0.2 km. Several statistical techniques were used to search for additional material in the Neptune ring system and none was identified at a high confidence level. ¿The American Geophysical Union 1990