The preprocessing and the crossover adjustment of Geosat altimeter data are carried out in order to obtain a precise approximation of the sea surface heights in the Mediterranean Sea. Altimeter data from the U.S. National Oceanographic Data Center (NODC) have been used covering a time period of about 1 year. With the rejection of outliers and subsatellite points whose root-mean-square (rms) error exceeds 0.09 m, the rms corssover discrepancy was 3.5 m. When a crossover adjustment was performed, the RMS crossover discrepancy decreased to 0.14 m. After the fit and crossover adjustment model applied, about the same rms crossover discrepancy was found (0.16 m). The latter solution was applied successfully in the test area as indicated by the results obtained from the comparisons of Geosat sea surface heights with OSU81 geoidal heights as well as with locally computed gravimetric geoidal heights by the fast Fourier transform (FFT) method. These comparisons showed a very good agreement at the level of 0.70 m. ¿ American Geophysical Union 1990