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It is thought that neutron stars in low-mass binary systems can accretematter and angular momentum from the companion star and be spun-up tomillisecond rotational periods. During the accretion stage, the system iscalled a low-mass X-ray binary, and bright X-ray emission is observed. When therate of mass transfer decreases in the later evolutionary stages, thesebinaries host a radio millisecond pulsar whose emission is powered by theneutron star's rotating magnetic field. This evolutionary model is supported bythe detection of millisecond X-ray pulsations from several accreting neutronstars and also by the evidence for a past accretion disc in a rotation-poweredmillisecond pulsar. It has been proposed that a rotation-powered pulsar maytemporarily switch on during periods of low mass inflow in some such systems.Only indirect evidence for this transition has hitherto been observed. Here wereport observations of accretion-powered, millisecond X-ray pulsations from aneutron star previously seen as a rotation-powered radio pulsar. Within a fewdays after a month-long X-ray outburst, radio pulses were again detected. Thisnot only shows the evolutionary link between accretion and rotation-poweredmillisecond pulsars, but also that some systems can swing between the twostates on very short timescales.

Swings between rotation and accretion power in a millisecond binary pulsar