  We investigate the parity nonconservation effect in the elastic scattering of
polarized electrons on heavy He-like ions, being initially in the ground state.
The enhancement of the parity violation is achieved by tuning the energy of the
incident electron in resonance with quasidegenerate doubly-excited states of
the corresponding Li-like ion. We consider two possible scenarios. In the first
one we assume that the polarization of the scattered electron is measured,
while in the second one it is not detected.
