One hundred and fifty three Geos 3 altimetry profiles have been obtained in the Indian Ocean around the Kerguelen Islands, during a limited campaign which took place from February to June 1976. A detailed geoid has been computed in this area with a resolution of 0.5¿, based on accurate orbits provided by the Defense Mapping Agency (DMA). On this occasion, several algorithms have been developed and compared, which all give the same predicted values (within 1 m) at the no des of a regular grid. Strong correlations with the sea bottom topography are already visible, especially with Crozet, Kerguelen, and Heard Islands and with the newly discovered seamounts Ob, Lena, and Marion Dufresne, Geophysical interpretation of these correlations are under way.