The discovery of planets around PSR~1257+12 suggests that planetary systems may be detected around the recycled pulsars found in globular clusters. Planetary systems in dense clusters have lifetimes to disruption due to perturbations by passing stars comparable to or shorter than the pulsar lifetime, and observations of planets in the cores of clusters may reveal planetary systems formally dynamically unstable on time scales short compared to the characteristic age, $\tau _c$, of the system. Planets formed around cluster pulsars will most likely be restricted to semi--major axis of $\sim 0.1-1.0\, AU$, while ``scavenged'' planets may be observed in wider orbits, with no stable systems expected in the densest clusters. Observation is most probable in the rich high--density pre--core collapse clusters such as 47Tuc.
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