THE birth-rate of radio pulsars in globular clusters (GCs) is thought to be a factor of 10 to 100 times greater than that of their candidate progenitors, low-mass X-ray binaries (LMXBs) of canonical lifetime 108 to 109 yr. This apparent discrepancy1,2 would be removed either if there were more rapid accretion of mass onto the primary in the late stages of LMXB evolution (as suggested by the self-excited wind model3), or if there occurred accretion-induced collapse of white dwarfs in binaries with wide orbits4,5. But the available data (Table 1) indicate that GC pulsars cannot be formed by either of these mechanisms alone. Here we suggest that both processes may be necessary to some extent, the corollary of which is that GC pulsars may have at least two distinct classes of progenitors. Many solitary and binary pulsars with short orbital periods may have descended from rapidly evolving LMXBs, whereas others, especially those with long periods, may have formed from binaries that undergo nuclear evolution of the secondary and eventual accretion-induced collapse of the white-dwarf primary.