The gravitational influence of our Galaxy on a hypothetical Local Group plasma, which was calculated in a previous paper by one of us (R.H.), is here shown to give rise to a flux of soft X-rays which may already have been detected. The required parameters of the plasma are n∼2-5×10-4cm-3and n∼2-30×105 K. The predicted soft X-ray flux would vary systematically with the angle between the line of sight and the direction to the galactic centre by a factor depending onT, but of order 4 in typical cases. The fraction of the radiation coming from distances closer than the Magellanic Clouds depends onT, and is calculated to exceed 75 per cent for T © Royal Astronomical Society.