  An approach to the model-independent searching for the Z' gauge boson as a
virtual state in scattering processes is developed. It accounts for as a basic
requirement the renormalizability of underlying unspecified in other respects
model. This results in a set of relations between low energy couplings of Z' to
fermions that reduces in an essential way the number of parameters to be fitted
in experiments. On this ground the observables which uniquely pick out the Z'
boson in leptonic processes are introduced and the data of LEP experiments
analyzed. The Z' couplings to leptons and quarks are estimated at 95%
confidence level. These estimates may serve as a guide for experiments at the
Tevatron and/or LHC. A comparison with other approaches and results is given.
