  We have investigated the formation of the binary radio pulsars PSR B2303+46
and PSR J1141-6545 via Monte Carlo simulations of a large number of interacting
stars in binary systems. PSR B2303+46 has recently been shown (van Kerkwijk &
Kulkarni 1999) to be the first neutron star - white dwarf binary system
observed, in which the neutron star was born after the formation of the white
dwarf. We discuss the formation process for such a system and are able to put
constraints on the parameters of the initial ZAMS binary. We present
statistical evidence in favor of a white dwarf companion to the binary pulsar
PSR J1141-6545, just recently discovered in the Parkes Multibeam Survey. If
this is confirmed by observations this system will be the second one known in
which the neutron star was born after its white dwarf companion. We also
predict a minimum space velocity of 150 km/s for PSR J1141-6545, and show it
must have experienced an asymmetric SN in order to explain its low
eccentricity. Finally, we estimate the birthrate of these systems relative to
other binary pulsar systems and present the expected distribution of their
orbital periods, eccentricities and velocities.
