  The preliminary LEP data set on the total cross sections and the
forward-backward asymmetries of the $e^+e^-\to\bar{f}f$ processes are analysed
to establish a model-independent search for the signals of the virtual Abelian
Z' boson. The recently introduced observables giving possibility to pick up
uniquely the Z' signals in these processes are used. The mean values of the
observables are in accordance with the Z' detection at the $1\sigma$ accuracy.
The results of other model-independent fits and further prospects are
discussed.
