We investigate the conditions by which neutron star retention in globular c
lusters is favoured. We find that neutron stars formed in massive binaries
are far more likely to be retained. Such binaries are likely to then evolve
into contact before encountering other stars, possibly producing a single
neutron star after a common envelope phase. A large fraction of the single
neutron stars in globular clusters are then likely to exchange into binarie
s containing moderate-mass main-sequence stars, replacing the lower-mass co
mponents of the original systems. These binaries will become intermediate-m
ass X-ray binaries (IMXBs), once the moderate-mass star evolves off the mai
n sequence, as mass is transferred on to the neutron star, possibly spinnin
g it up in the process. Such systems may be responsible for the population
of millisecond pulsars (MSPs) that has been observed in globular clusters.
Additionally, the period of mass-transfer (and thus X-ray visibility) in th
e vast majority of such systems will have occurred 5-10 Gyr ago, thus expla
ining the observed relative paucity of X-ray binaries today, given the MSP
population.