The stability of a multicomponent flow of cold inhomogeneous plasma with respect to conservative electromagnetic oscillations is investigated in two-fluid hydrodynamics. It is shown that, when there is a strong external axial magnetic field parallel to the plasma flux, the inhomogeneous plasma may be unstable with respect to short-wave oscillations described by the methods of geometrical optics. When there is no external magnetic field only long-wave oscillations, for whose description geometrical optics cannot be employed, are unstable; short-wave oscillations are unstable even when there is a magnetic field. The instabilities considered can develop when there is no beam instability in the plasma, and longwave instability is possible even in a currentless plasma (plasma jet). The long-wave instability is by its nature analogous to the Rayleigh flow instability of an ideal fluid with an inhomogeneous velocity profile.