  The paper discusses the two-loop (NNLO) electroweak radiative corrections to
the parity violating electron-electron scattering asymmetry induced by squaring
one-loop diagrams. The calculations are relevant for the ultra-precise 11 GeV
MOLLER experiment planned at Jefferson Laboratory and experiments at
high-energy future electron colliders. The imaginary parts of the amplitudes
are taken into consideration consistently in both the infrared-finite and
divergent terms. The size of the obtained partial correction is significant,
which indicates a need for a complete study of the two-loop electroweak
radiative corrections in order to meet the precision goals of future
experiments.
