  We discuss the stochastic background of gravitational waves from ultra
compact neutron star-white dwarf (NS-WD) binaries at cosmological distances.
Under the assumption that accreting neutron stars and donor white dwarf stars
form most of the low mass X-ray binaries (LMXBs), our calculation makes use of
recent results related to the luminosity function determined from X-ray
observations. Even after accounting for detached NS-WD binaries not captured in
X-ray data, the NS-WD background is at least an order of magnitude below that
due to extragalactic white dwarf-white dwarf binaries and below the
detectability level of the Laser Interferometer Space Antenna (LISA) at
frequencies between 10^-5 Hz and 10^-1 Hz. While the extragalactic background
is unlikely to be detected, we suggest that around one to ten galactic NS-WD
binaries may be resolved with LISA such that their positions are determined to
an accuracy of several degrees on the sky.
