The problem described by the title is investigated when the magnetic field is uniform and parallel to the velocity on the two sides of a surface of discontinuity of velocity in an electrically conducting inviscid fluid. The secular equation depends on two parameters β and N, where β is the ratio of magnetic Reynolds number to dimensionless wave number and N is the ratio of the magnetic to the kinetic energy of the fluid. It is found that the flow is unstable for all values of β and N. © 1963, Cambridge University Press. All rights reserved.