  The contribution of weakly--magnetized ($B\sim 10^9$ G) neutron stars
accreting the interstellar medium to the diffuse X--ray emission observed in
the Galactic Center is investigated. It is shown that, under rather
conservative assumptions about the neutron stars and gas distributions, the
accretion luminosity can account for a sizable fraction, possibly most, of the
detected X--ray flux in the 2.5--7 keV band. In particular, model results are
compared with {\it Granat\/} data and show a general agreement in both the flux
energy and radial distributions.
