  The integral observables for model-independent detections of Abelian Z' gauge
boson in e^+ e^- -> mu^+ mu^- (tau^+ \tau^-) process with unpolarized beams at
the ILC energies are proposed. They are based on the differential cross-section
of deviations from the standard model predictions calculated with a low energy
effective Lagrangian and taking into consideration the relations between the Z'
couplings to the fermions derived already. Due to these relations, the
cross-section exhibits angular distribution giving a possibility for
introducing one- or two parameter observables which effectively fit the mass
m_Z', the axial-vector (a_Z)'^2 and the product of vector couplings v_e v_mu
(v_e v_tau). Comparison with other results and approaches is given.
