Globular clusters, the most ancient stellar groups in our galaxy, are known to contain bright X-ray sources, faint X-ray sources and millisecond pulsars, The bright X-ray sources are neutron stars accreting matter from a companion star(1), and the millisecond pulsars are believed to be descendants of these sources(2). But the origin of the faint X-ray sources remains unclear Here we report satellite-based X-ray observations of the globular cluster M28 which reveal two faint X-ray sources; an extended source slightly offset from the centre of the duster, and a point source. The point source pulsates with the same period as a well-known(3,4) 3-millisecond pulsar in M28. The nature of the extended source is more puzzling, however, and its spatial and spectral properties permit a range of plausible models. We argue that this source is either a collection of low-luminosity accreting neutron-star binaries or a synchrotron nebula powered by a recent outburst of energy from an unknown source. Sensitive optical and X-ray observations should be able to distinguish between these two possibilities.