  We study theoretical X-ray light curves and polarization properties of
accretion-powered millisecond pulsars. We assume that the radiation is produced
in two antipodal spots at the neutron star surface which are associated with
the magnetic poles. We compute the angle-dependent intensity and polarization
produced in an electron-scattering dominated plane-parallel accretion shock in
the frame of the shock. The observed flux, polarization degree and polarization
angle are calculated accounting for special and general relativistic effects.
The calculations also extended to the case of nuclear-powered millisecond
pulsars -- X-ray bursts. In this case, we consider one spot and the radiation
is assumed to be produced in the atmosphere of the infinite Thomson optical
depth. The light curves and polarization profiles show a large diversity
depending on the model parameters. Presented results can be used as a first
step to understand the observed pulse profiles of accretion- and
nuclear-powered millisecond pulsars. Future observations of the X-ray
polarization will provide a valuable tool to test the geometry of the emission
region and its physical characteristics.
