The Kelvin-Helmholtz instability takes place on the interface between two horizontally stratified fluid layers which are in a state of relative shear flow with respect to each other. The problem was solved for the ideal case of inviscid and incompressible fluids in 1871 by Lord Kelvin. The first case of superfluid shear flow has been discovered in uniformly rotating superfluid He-3, when the phase boundary between the A and B phases is maintained at a stable location with a magnetic barrier field. At sufficiently high rotation the AB interface undergoes an instability, in which the interface becomes corrugated in a standing-wave pattern. The critical velocity of this process displays the temperature and magnetic field dependences which fit the characteristics of the Kelvin-Helmholtz instability. (C) 2003 Elsevier Science B.V. All rights reserved.