The sea-state bias in Geosat altimeter range measurements expressed as a percentage of significant wave height (SWH) is examined as a function of SWH. The bias is shown to be approximately a fixed -3.5% of SWH for SWH smaller than about 4 m. For larger SWH, the bias decreases in magnitude approximately linearly to a value of about -1.5% of SWH for 6 m SWH. Because of this ''saturation effect'' associated with lage SWH, estimates of the Geosat sea-sate bias which have been based on the assumption of a fixed percentage of SWH are too small by up to 1.5% of SWH. The saturation effect is so large at high latitudes in the southern hemisphere (where about 1/4 of the SWH values exceed 4 m) that it apparently overwhelms any wind speed dependence in the sea-state bias suggested by several recent studies. The apparent SWH dependence found in this study appears to be the result of attitude and sea-state errors in the Geosat altimeter on-board tracking algorithm. ¿American Geophysical Union 1991