  The oscillation of neutrons $n$ into mirror neutrons $n'$, their mass
degenerate partners from dark mirror sector, can have interesting implications
for neutron stars: an ordinary neutron star could gradually transform into a
mixed star consisting in part of mirror dark matter. Mixed stars can be
detectable as twin partners of ordinary neutron stars: namely, there can exist
compact stars with the same masses but having different radii. For a given
equation of state (identical between the ordinary and mirror components), the
mass and radius of a mixed star depend on the proportion between the ordinary
and mirror components in its interior which in turn depends on its age. If $50
\% - 50\%$ proportion between two fractions can be reached asymptotically in
time, then the maximum mass of such "maximally mixed stars" should be $\sqrt2$
times smaller than that of ordinary neutron star while the stars exceeding a
critical mass value $M^{\rm max}_{NS}/\sqrt2$ should collapse in black holes
after certain time. We evaluate the evolution time and discuss the implications
of $n-n'$ transition for the pulsar observations as well as for the
gravitational waves from the neutron star mergers and associated
electromagnetic signals.
