TOPEX (Ku band) and POSEIDON altimeter measurements at crossover points are used to estimate the sea state bias (SSB) of these two instruments. Different SSB models are tested, ranging from a constant fraction of the significant wave height (SWH) to more elaborate models involving up to four adjustable parameters. For TOPEX, the data show a decrease in the magnitude of the relative bias (SSB/SWH) with SWH. This behavior is well reproduced using a simple empirical model with two adjustable parameters. The three-parameter SSB model used in the NASA geophysical data records does well in explaining the wind-induced variations of the bias. A model including four adjustable parameters is needed to account for both the wind- and SWH-related variability of the SSB. POSEIDON data analysis reveals a significantly larger SSB than for TOPEX. This bias seems to consist of a skewness plus tracker bias of -2 to -3% of SWH superimposed on a natural EM bias whose wind- and SWH-related variations are similar to those of TOPEX.