  Spectra of the spreading layers on the neutron star surface are calculated on
the basis of the Inogamov-Sunyaev model taking into account general relativity
correction to the surface gravity and considering various chemical composition
of the accreting matter. Local (at a given latitude) spectra are similar to the
X-ray burst spectra and are described by a diluted black body. Total spreading
layer spectra are integrated accounting for the light bending, gravitational
redshift, and the relativistic Doppler effect and aberration. They depend
slightly on the inclination angle and on the luminosity. These spectra also can
be fitted by a diluted black body with the color temperature depending mainly
on a neutron star compactness. Owing to the fact that the flux from the
spreading layer is close to the critical Eddington, we can put constraints on a
neutron star radius without the need to know precisely the emitting region area
or the distance to the source. The boundary layer spectra observed in the
luminous low-mass X-ray binaries, and described by a black body of color
temperature Tc=2.4+-0.1 keV, restrict the neutron star radii to R=14.8+- 1.5 km
(for a 1.4-Msun star and solar composition of the accreting matter), which
corresponds to the hard equation of state.
