  Several parity violating left-right asymmetries in M\o ller electron-electron
and muon-muon scattering are considered in the context of the electroweak
standard model at tree level in fixed target and collider experiences. We show
that in colliders the asymmetry with only one of the beam polarized is large
enough to compensate the smaller cross section at high energies. We also show
that these asymmetries are very sensitive to a doubly charged vector bilepton
resonance but they are insensitive to scalar ones.
