  As it is well known for stiff equations of state an existence of neutron
stars with masses $\ga 2 M_{\sun}$ is possible. Especially interesting
possibility is opened if the equation of state based on the Skyrme theory is
realized in nature. This equation of state was proposed recently by Ouyed and
Butler. We discuss different channels of formation of massive rapidly rotating
neutron stars. We use a population synthesis code to estimate numbers of
massive neutron stars on different evolutionary stages. A neutron star
increases its mass by accretion from a secondary companion.
  Significant growth of a neutron star mass due to accretion is possible only
for certain values of initial parameters of the binary. In this paper we show
that significant part of massive neutron stars with $M\ga 2 M_{\sun}$ can be
observed as millisecond radio pulsars, as X-ray sources in pair with white
dwarfs, and as accreting neutron stars with very low magnetic fields.
