  The paucity of old isolated accreting neutron stars in ROSAT observations is
used to derive a lower limit on the mean velocity of neutron stars at birth.
The secular evolution of the population is simulated following the paths of a
statistical sample of stars for different values of the initial kick velocity,
drawn from an isotropic Gaussian distribution with mean velocity $0\leq <
V>\leq 550$ ${\rm km s^{-1}}$. The spin-down, induced by dipole losses and the
interaction with the ambient medium, is tracked together with the dynamical
evolution in the Galactic potential, allowing for the determination of the
fraction of stars which are, at present, in each of the four possible stages:
Ejector, Propeller, Accretor, and Georotator. Taking from the ROSAT All Sky
Survey an upper limit of $\sim 10$ accreting neutron stars within $\sim 140$ pc
from the Sun, we infer a lower bound for the mean kick velocity, $ < V>\ga
200-300$ ${\rm km s^{-1}}$. The same conclusion is reached for both a constant
($B\sim 10^{12}$ G) and a magnetic field decaying exponentially with a
timescale $\sim 10^9$ yr. Present results, moreover, constrain the fraction of
low velocity stars, which could have escaped pulsar statistics, to $\la 1%$.
