  Gauged extensions [$SU(2)_L\otimes U(1)_Y\otimes U(1)_X$] of the standard
$SU(2)_L\otimes U(1)_Y$ model obtained without extending the fermion content of
the model are studied. Models that are possible when $U(1)_X$ is identified
with some combination of the family lepton numbers are systematically
classified. Most of these contain flavor violations in the leptonic sector.
These flavor violations are correlated to the mixing of the $U(1)_X$ gauge
boson $Z'$ with the ordinary $Z$ in the models considered here. Detailed
phenomenological implications of a typical model are discussed. Constraints on
the $Z'$ mass and the $Z$-$Z'$ mixing following from ({\em i}) the observations
at LEP, ({\em ii}) rare processes like $Z\rightarrow e\tau$ and ({\em iii})
flavor violating $\tau$ decays are presented. It is found that the constraints
coming from the LEP allows the rare processes like $\tau \rightarrow eee $ at
the level of the present limits on its branching ratio. Thus the future search
could either improve on the existing LEP limits or would find such flavor
violating decays.
