  The many-parametric fit of the LEP2 data on e^+e^-\to e^+e^-, \mu^+\mu^-,
\tau^+\tau^- processes is performed to estimate signals of the Abelian Z'-boson
beyond the standard model. The model-independent relations between the Z'
couplings to the standard model particles allow to describe the Z' effects in
lepton processes by 4 independent parameters. No signal is found by the
complete LEP2 data set, and the 1.3\sigma signal is detected by the fit of the
backward bins. The Z' couplings to the vector and axial-vector lepton currents
are constrained. The comparisons with the one-parameter fits and with the LEP1
experiments are performed.
