  The spectral properties of X--ray radiation produced in a static atmosphere
around a neutron star accreting at very low rates are investigated. Previous
results by Alme \& Wilson (1973) are extended to the range $10^{-7}\leq
L/L_{Edd}\leq 10^{-3}$ to include the typical luminosities, $L\sim
10^{31}-10^{32} \ {\rm ergs\, s^{-1}}$, expected from isolated neutron stars
accreting the interstellar medium. The emergent spectra show an overall
hardening with respect to the blackbody at the neutron star effective
temperature in addition to a significant excess over the Wien tail. The
relevance of present results in connection with the observability of
low--luminosity X--ray sources is briefly discussed.
