  Heavy neutral gauge bosons, Z's, are predicted by many theoretical schemes of
physics beyond the Standard Model, and intensive searches for their signatures
will be performed at present and future high energy colliders. It is quite
possible that Z's are heavy enough to lie beyond the discovery reach expected
at the CERN Large Hadron Collider LHC, in which case only indirect signatures
of Z' exchanges may occur at future colliders, through deviations of the
measured cross sections from the Standard Model predictions. We here discuss in
this context the foreseeable sensitivity to Z's of fermion-pair production
cross sections at an e^+e^- linear collider, especially as regards the
potential of distinguishing different Z' models once such deviations are
observed. Specifically, we assess the discovery and identification reaches on
Z' gauge bosons pertinent to the E_6, LR, ALR and SSM classes of models, that
should be attained at the planned International Linear Collider (ILC). With the
high experimental accuracies expected at the ILC, the discovery and the
identification reaches on the Z' models under consideration could be increased
substantially. In particular, the identification among the different models
could be achieved for values of Z' masses in the discovery (but beyond the
identification) reach of the LHC. An important role in enhancing such reaches
is played by the electron (and possibly the positron) longitudinally polarized
beams. Also, although the purely leptonic processes are experimentally cleaner,
the measurements of c- and b-quark pair production cross sections are found to
carry important, and complementary, information on these searches.
