A ≡7-hr observation of the central part of the Coma cluster of galaxies has been performed with the EXOSAT LE telescopes and CMA detectors. Five serendipitous sources are detected within the inner 35 arcmin radius of the field. Optical spectroscopy shows that four of these are background AGN not associated with the cluster. At the sensitivity level of the EXOSAT exposure, the authors would have expected to detect only 0.01 background sources on the basis of the Einstein Medium Sensitivity Survey. They discuss ways of interpreting this result and in particular the possibility that the AGN detected in the EXOSAT field have a much softer average X-ray spectrum than that usually considered to be 'canonical'.