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The spectral properties of X--ray radiation produced in a static atmospherearound a neutron star accreting at very low rates are investigated. Previousresults by Alme \& Wilson (1973) are extended to the range $10^{-7}\leqL/L_{Edd}\leq 10^{-3}$ to include the typical luminosities, $L\sim10^{31}-10^{32} \ {\rm ergs\, s^{-1}}$, expected from isolated neutron starsaccreting the interstellar medium. The emergent spectra show an overallhardening with respect to the blackbody at the neutron star effectivetemperature in addition to a significant excess over the Wien tail. Therelevance of present results in connection with the observability oflow--luminosity X--ray sources is briefly discussed.Comment: 14 pages (3 postscript figures available on request), PlainTex,  submitted to Ap

X-ray spectra from neutron stars accreting at low rates