  We investigate the effects of mass transfer and gravitational wave (GW)
radiation on the orbital evolution of contact neutron-star-white-dwarf (NS-WD)
binaries, and the detectability of these binaries by space GW detectors (e.g.,
Laser Interferometer Space Antenna, LISA; Taiji; Tianqin). A NS-WD binary
becomes contact when the WD component fills its Roche lobe, at which the GW
frequency ranges from ~0.0023 to 0.72 Hz for WD with masses ~0.05-1.4 Msun. We
find that some high-mass NS-WD binaries may undergo direct coalescence after
unstable mass transfer. However, the majority of NS-WD binaries can avoid
direct coalescence because mass transfer after contact can lead to a reversal
of the orbital evolution. Our model can well interpret the orbital evolution of
the ultra-compact X-ray source 4U 1820--30. For a 4-year observation of 4U
1820--30, the expected signal-to-noise-ratio (SNR) in GW characteristic strain
is ~11.0/10.4/2.2 (LISA/Taiji/Tianqin). The evolution of GW frequencies of
NS-WD binaries depends on the WD masses. NS-WD binaries with masses larger than
4U 1820--30 are expected to be detected with significantly larger SNRs. For a
(1.4+0.5) Msun NS-WD binary close to contact, the expected SNR for a one week
observation is ~27/40/28 (LISA/Taiji/Tianqin). For NS-WD binaries with masses
of (1.4+>~1.1) Msun, the significant change of GW frequencies and amplitudes
can be measured, and thus it is possible to determine the binary evolution
stage. At distances up to the edge of the Galaxy (~100 kpc), high-mass NS-WD
binaries will be still detectable with SNR>~1.
