This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly conducting and inviscid fluid of very high compressibility. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible cliscontinuities in their values across the jet surface. In the limit of infinite compressibifity, the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic field is sufficiently small. For these disturbances the infinitely compressible jet behaves like an incompressible one when the wavenumber of disturbances is small. The effect of (infinite) compressibility becomes more evident as the wavenumber of disturbances increases and the jet becomes stable when the wavelength tends to vanish.