By considering left-right (L-R) asymmetries we study the capabilities of le
pton colliders in searching for new exotic vector bosons. Specifically we s
tudy the effect of a doubly charged bilepton boson and an extra neutral vec
tor boson appearing in a 3-3-1 model on the L-R asymmetries for the process
es e(-)e(-) --> e(-)e(-), mu (-)mu (-) --> mu (-)mu (-) and e(-)mu (-) -->
e(-)mu (-) and show that these asymmetries are very sensitive to these new
contributions and that they are in fact powerful tools for discovery of thi
s sort of vector bosons.