Using Gauss's divergence theorem, we examine the role of the net radiative cooling and of the entrainment of potentially warm air from the free atmosphere into the surface layer in determining the intensity of the cold-air outflow at the rim of the Antarctic continent. The result shows that a large amount of cold air, significant at even a global climatological scale, is exported through this process from high- to low-latitude regions. The theory gives also the average intensity of the wind at the coast. In the coastal regions of Antarctica the wind exhibits a complex behavior. Observations show that katabatic winds in the near-coastal region can be periodic or continuous, or can stay a long time in a quiescent near-critical state, then burst in short and strong gusts. We examine some aspects of these katabatic winds in terms of the mesoscale energy theory developed by Dalu and Green (1983). This complex behavior is described by a nonlinear system, where the relevant parameter is the Froude number of the inflow at a Rossby radius distance from the coast. The analytical theory developed agrees well with qualitative features observed. ¿ American Geophysical Union 1992