  The paper deals with an approach to the model-independent searching for the
Z' gauge boson as a virtual state in scattering processes. The relations
between the Z' couplings to fermions covering a wide class of models beyond the
standard model are found and used. They reduce in an essential way the number
of parameters to be fitted in experiments. Special observables which uniquely
pick out the Z' at energies of LEP and ILC colliders in different leptonic
processes are introduced and the data of LEP experiments are analyzed. The Z'
couplings to leptons and quarks are estimated at 95% confidence level. At this
level, the LEP data are compatible with the existence of the Z' with the mass
of order 1-1.2 TeV. These estimates may serve as a guide for experiments at the
Tevatron and/or LHC. A comparison with other approaches and results is given.
