Due to the nonlinear equation of state of sea water it is possible for the mixture of two Parcels of sea water with the same density but different temperatures and salinities to have a density greater than that of the constituent parcels. This phenomenon is sometimes called cabbeling. In the deep parts of the Weddell Sea the surface water is usually colder and less saline than the underlying deep water. In winter the salinity of the surface water can increase due to sea ice formation, and then mixtures of surface water and deep water may become denser than the underlying deep water. An instability can develop which may transport the heavier mixed water through the deep water and contribute to the formation of Antarctic Bottom Water. A time-dependent, finite-amplitude, theoretical analysis of this instability has been made. Assuming turbulent mixing, expressions for the preferred horizontal spacing and velocities of the resulting convection currents have been derived for conditions that may be typical of the Weddell Sea. It is concluded that the cabbeling instability may he important to the formation of Antarctic Bottom Water.