  Old neutron stars (ONSs) which have radiated away their internal and
rotational energy may still shine if accreting the interstellar medium. Rather
stringent limits from the analysis of ROSAT surveys indicate that most
optimistic predictions on ONSs observability are in excess of a factor as large
as $\sim 100$. Here we explore two possible evolutionary scenarios that may
account for the paucity of ONSs. In the first it is assumed that the ONS
population is not too fast ($V<100 km s^{-1}$) and that magnetic field decay
guides the evolution. In the second, NSs move with high speed ($V>100$ km
s$^{-1}$) and preserve their magnetic field at birth. We find that according to
the former scenario most ONSs are now in the propeller phase, while in the
latter nearly all ONSs are silent, dead pulsars.
