The basic features of the flow of meltwater under ice shelves can be described by a set of simple relations and length scales. The flow may be divided into two regions, with different basic processes dominating in each. In the first region, melting of the underside of the ice shelf is important and the temperature and salinity of the current tend toward ''equlibrium'' values, such that the change due to melting of the ice shelf are balanced by changes due to entrainment of ambient seawater. The equilibrium values change with depth owing to the effect of the change in pressure on the freezing point. As the current increases in thickness, it is no longer able to adjust sufficiently rapidly to the chaning equilibrium values, and the flow moves into the second region. The extent of the first region is governed by the location of the ''ambient freezing point.'' In the second region, melting is less important and the current behaves as an entraining drag-limited gravity current in a stratified ambient fluid, leaving the shelf once the current has the same density as the ambient seawater. The heights of the two regions depend mainly on the ambient conditions and only indirectly on parameters such as slope angle, entrainment constant, drag coefficient, and turbulent transfer coefficients. ¿American Geophysical Union 1995