  It is thought that neutron stars in low-mass binary systems can accrete
matter and angular momentum from the companion star and be spun-up to
millisecond rotational periods. During the accretion stage, the system is
called a low-mass X-ray binary, and bright X-ray emission is observed. When the
rate of mass transfer decreases in the later evolutionary stages, these
binaries host a radio millisecond pulsar whose emission is powered by the
neutron star's rotating magnetic field. This evolutionary model is supported by
the detection of millisecond X-ray pulsations from several accreting neutron
stars and also by the evidence for a past accretion disc in a rotation-powered
millisecond pulsar. It has been proposed that a rotation-powered pulsar may
temporarily switch on during periods of low mass inflow in some such systems.
Only indirect evidence for this transition has hitherto been observed. Here we
report observations of accretion-powered, millisecond X-ray pulsations from a
neutron star previously seen as a rotation-powered radio pulsar. Within a few
days after a month-long X-ray outburst, radio pulses were again detected. This
not only shows the evolutionary link between accretion and rotation-powered
millisecond pulsars, but also that some systems can swing between the two
states on very short timescales.
