  We investigate the effects of rapid and slow conversions on the
fundamental-mode eigenfrequencies of hybrid neutron stars having highly
discontinuous transitions between hadronic and quark matter, the so-called twin
stars. We analyze some characteristic cases in the available parameter space of
the equations of state for the hadronic and quark phases. Furthermore, we also
consider the possibility that these stellar configurations are electrically
charged. Our results indicate that for neutral configurations under rapid
conversions the stability window coincides with the usual stability criterion,
i.e. $\partial M/\partial p_c > 0$ and that the two branches are disconnected.
This discontinuity remains when electric charge is considered, but the usual
criterion is not sufficient to determine the star's stability. On the other
hand, slow conversions connect initially disconnected branches and increase the
stability window of the hybrid configurations. For both conversion speeds, the
presence of electric charge diminishes the magnitude of the eigenfrequencies
and its stability window.
