Signals of the Abelian Z' boson within the analysis of the LEP2 data

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.