As a result of its remarkably high salinity and despite its small volume input, remnants of Red Sea Water (RSW) have been identified in the Agulhas Current, over 6000 km distant of their source. This provided the motivation to investigate the long-term mean spreading of RSW throughout the Indian Ocean, using a comprehensive set of observations, taken from the National Oceanographic Data Center archives and from the World Ocean Circulation Experiment Hydrographic Program for the Indian Ocean. After emerging from the Gulf of Aden into the Arabian Sea, RSW spreads predominantly southwestward along the African continental slope, as indicated by strongly inclined isohalines across the Arabian Sea. There is some monsoon variability, so that during the winter monsoon there is more RSW present in the Gulf of Aden and an intensification of southward spreading along the western boundary, between 12° and 5°N. Elsewhere the intermediate depth salinity field of the Indian Ocean appears relatively stationary. Between 5° and 10°S, in the region of the South Equatorial Current, isohalines of the RSW layer become quasi-zonal across the width of the Indian Ocean, only dipping southward toward the western boundary west of 50°E. South of here, there is a strong tongue of RSW spreading southward through the Mozambique Channel and into the Agulhas Current. These conclusions concur with previous localized investigations of intermediate water properties. Using a simple mixing model, the percentage of RSW throughout the Indian Ocean was quantified. It was found that the flux of salt into the Gulf of Aden from the Red Sea is similar to that estimated to cross 32°S in the Agulhas Current. This result implies that all the RSW which is mixed into the interior of the Indian Ocean may eventually be exported at the western boundary. Furthermore, it implies that RSW is the dominant component of the salt budget for the intermediate layer and that input from the Indonesian Seas and via diapycnic processes are small.