Since 1990, the NOAA National Environmental Satellite Data and Information Service (NESDIS) has provided satellite-derived sea surface temperature (SST) measurements based on nonlinear SST algorithms, using advanced very high resolution radiometer (AVHRR) multiple-infrared window channel data. This paper develops linear and nonlinear SST algorithms from the radiative transfer equation. It is shown that the nonlinear algorithms are more accurate than linear algorithms but that the functional dependence of the nonlinearity is data dependent. This theoretical discussion (sections 2--4) is followed with a discussion in section 5 of the accuracy over a 9-year period of the satellite-derived SST measurements provided by NOAA NESDIS when compared with coincident drifting buoys. Between 1989 and 1998 the global scatter of the daytime satellite SST against drifting buoy measurements has decreased from ~0.8¿ to 0.5 ¿C, while the nighttime scatter has remained fairly constant at 0.5 ¿C. An exception to these accuracy measurements occurred after the eruption of Mount Pinatubo in June 1991. ¿ 1998 American Geophysical Union