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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 binarybecomes contact when the WD component fills its Roche lobe, at which the GWfrequency ranges from ~0.0023 to 0.72 Hz for WD with masses ~0.05-1.4 Msun. Wefind that some high-mass NS-WD binaries may undergo direct coalescence afterunstable mass transfer. However, the majority of NS-WD binaries can avoiddirect coalescence because mass transfer after contact can lead to a reversalof the orbital evolution. Our model can well interpret the orbital evolution ofthe ultra-compact X-ray source 4U 1820--30. For a 4-year observation of 4U1820--30, the expected signal-to-noise-ratio (SNR) in GW characteristic strainis ~11.0/10.4/2.2 (LISA/Taiji/Tianqin). The evolution of GW frequencies ofNS-WD binaries depends on the WD masses. NS-WD binaries with masses larger than4U 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 weekobservation is ~27/40/28 (LISA/Taiji/Tianqin). For NS-WD binaries with massesof (1.4+>~1.1) Msun, the significant change of GW frequencies and amplitudescan be measured, and thus it is possible to determine the binary evolutionstage. At distances up to the edge of the Galaxy (~100 kpc), high-mass NS-WDbinaries will be still detectable with SNR>~1.

Orbital Evolution of Neutron-Star -- White-Dwarf Binaries by Roche-Lobe Overflow and Gravitational Wave Radiation