  We model the potentially observable populations of normal and millisecond
radio pulsars in the Large and Small Magellanic Clouds (LMC and SMC) where the
known population currently stands at 19 normal radio pulsars. Taking into
account the detection thresholds of previous surveys, and assuming optimal
period and luminosity distributions based on studies of Galactic pulsars, we
estimate there are (1.79 +/- 0.20) x 10^4 and (1.09 +/- 0.16) x 10^4 normal
pulsars in the LMC and SMC respectively. When we attempt to correct for beaming
effects, and the fraction of high-velocity pulsars which escape the clouds, we
estimate birth rates in both the LMC and SMC to be comparable and in the range
0.5--1 pulsar per century. Although higher than estimates for the rate of
core-collapse supernovae in the clouds, these pulsar birth rates are consistent
with historical supernova observations in the past 300 yr. A substantial
population of active radio pulsars (of order a few hundred thousand) have
escaped the LMC and SMC and populate the local intergalactic medium. For the
millisecond pulsar (MSP) population, the lack of any detections from current
surveys leads to respective upper limits (at the 95% confidence level) of
15,000 for the LMC and 23,000 for the SMC. Several MSPs could be detected by a
currently ongoing survey of the SMC with improved time and frequency resolution
using the Parkes multibeam system. Giant-pulse emitting neutron stars could
also be seen by this survey.
