In previous papers [1, 2] the author has considered the stability of a current-vortex sheet in a non-diffusing incompressible fluid, the magnetic field being parallel to the plane of discontinuity. In [1] a criterion was given for a parallel magnetic field to stabilise a vortex sheet, and in [2] the energy balance of this system was considered and it was shown how the magnetic energy level is increased at the expense of mechanical kinetic energy when the system becomes unstable. In this paper the oscillations on a plane interface are considered when the magnetic field is not parallel to the interface.