This is a study of the surface longwave radiation characteristics over the Weddell Sea during winter, based on measurements performed from a ship and ice floe camps during the Antarctic Zone Flux Experiment (ANZFLUX), which occurred in July and August 1994. Net longwave radiation is the dominant term in the regional surface energy balance. The net longwave radiational cooling of the surface is 62 W m-2 greater during clear skies than during overcast skies. The downwelling longwave radiation during clear skies is 17% less, and during overcast skies, it is 3% less than for reported Arctic cases with the same surface temperature. Previously published formulas of downwelling longwave radiation based on surface variables have a total rms error of 10--43 W m-2 for the clear-sky cases and 10--20 W m-2 for overcast cases when applied to the ANZFLUX data. There is no correlation of downward longwave radiation with any standard surface meteorological parameters, except air temperature and observed cloud cover, with the possible exception of wind speed, which has a slight negative correlation during clear skies. Predictions from newly derived formulas using only air temperature have an rms error of 5.8 W m-2 for overcast skies and 7.2 W m-2 for clear skies. When information on cloud bottom temperature and cloud thickness is available, downwelling radiation is predicted to within 3.9 W m-2. These rms errors are based on parameterizations that are tuned to the ANZFLUX data set and are better than the accuracies to be expected when applying the parameterizations to other situations, including other Weddell Sea wintertime cases.