  In this paper we semianalyticaly evaluate influence of the exponential decay
of magnetic field on the fate of isolated neutron stars. The fact of ROSAT
observations of several X-ray sources, which can be accreting old isolated
neutron stars gives us an opportunity to put some limits on the parameters of
the exponential decay.
  We argue, that, if most part of neutron stars have approximately the same
decay and initial parameters, then the combinations of the bottom magnetic
momentum, $\mu_b$, in the range $\sim 10^{28}-10^{29.5} {\rm G} {\rm cm}^3$ and
characteristic time scale, $t_d$, in the range $\sim 10^7-10^8 {\rm yrs}$ for
standard initial magnetic momentum, $\mu_0=10^{30} {\rm G} {\rm cm}^3$, can be
excluded, because for that sets of parameters neutron stars never come to the
stage when accretion of the interstellar medium on their surfaces is possible
even for low velocity of neutron stars and relatively high density of the
interstellar medium. The region of excluded parameters increases with $\mu_0$
decreasing.
