  We present a possible evolutionary pathway to form planetary nebulae (PNe)
with close neutron star (NS)-white dwarf (WD) binary central stars. By
employing a comprehensive binary population synthesis technique we find that
the evolution involves two common envelope evolution (CEE) phases and a core
collapse supernova explosion between them that forms the NS. Later the lower
mass star engulfs the NS as it becomes a red giant, a process that leads to the
second CEE phase and to the ejection of the envelope. This leaves a hot
horizontal branch star that evolves to become a helium WD and an expanding
nebula. Both the WD and the NS power the nebula. The NS in addition might power
a pulsar wind nebula inside the expanding PN. From our simulations we find that
the Galactic formation rate of NS-WD PNe is $1.8 \times 10^{-5} {\rm yr}^{-1}$
while the Galactic formation rate of all PNe is $0.42 {\rm yr}^{-1}$. There is
a possibility that one of the observed Galactic PNe might be a NS-WD PN, and a
few NS-WD PNe might exist in the Galaxy. The central binary systems might be
sources for future gravitational wave detectors like LISA, and possibly of
electromagnetic telescopes.
