  By considering left-right (L-R) asymmetries we study the capabilities of
lepton colliders in searching for new exotic vector bosons. Specifically we
study the effect of a doubly charged bilepton boson and an extra neutral vector
boson appearing in a 3-3-1 model on the L-R asymmetries for the processes
$e^-e^-\to e^-e^-$, $\mu^-\mu^-\to\mu^-\mu^-$ and $e^-\mu^-\to e^-\mu^-$ and
show that these asymmetries are very sensitive to these new contributions and
that they are in fact powerful tools for discovery this sort of vector bosons.
