Abstract-The hydromagnetic Kelvin-Helmholtz stability problem is studied for an infinite plane interface between compressible infinitely conducting fluids. The critical value of the relative streaming velocity for stability is studied by use of the equations for marginal stability without making the simplifying physical assumptions used by previous authors. In application to the magnetosphere boundary we find we can make some predictions without too precise a knowledge of all the parameters involved. At middle and low latitudes the first growing modes propagate across the Earth's field with a very low phase velocity and wave fronts closely aligned to meridian planes. The modes tend to exhibit circular polarisation in a plane almost perpendicular to the Earth's field. This behaviour should also occur at high latitudes when the magnetosheath field is closely aligned to he Earth's field
