Altimeter profiles of the ERS-1 and Topex-Poseidon satellites have been used to compute a geoid surface from which we have extracted medium-wavelength geoid anomalies over the central Pacific. In this region, the geoid shows prominent elongated anomalies of 20--40 cm in amplitude, with a spacing of ~1000 km and oriented N60 ¿W. In the south central Pacific, the Polynesian hotspot swells seem to be located on the linear geoid highs. However, the latter extend much farther eastward, preceeding the active hotspots. To the north, other geoid lines are visible but they do not coincide with known tectonic features. The wavelet transform applied to raw geoid data clearly detects a strong signal at the 1000--1200 km wavelength. The amplitude of the lineations increases with age, by a factor of 3 between 10 and 50 my. Analysis of seafloor topography corrected for age and sediments reveals topography anomalies correlated with the geoid lineations. Admittance and coherence calculations give high coherence (0.9) in the 1000--1200 km waveband and admittance values of 1.5 m/km at 10 my and 3 m/km at 60 my. The mechanism producing the lineations is unclear. Their characteristics however are not incompatible with a convective origin. ¿ American Geophysical Union 1995