  The preliminary LEP data on the e^+e^- -> l^+l^- scattering are analysed to
establish a model-independent search for the signals of virtual states of the
Abelian Z' boson. The recently introduced observables give a possibility to
pick up uniquely the Abelian Z' signals in these processes. The mean values of
the observables are in accordance with the Z' existence. However, the accuracy
of the experimental data is deficient to detect the signal at more than the
1\sigma confidence level. The results of other model-independent fits and
further prospects are discussed.
