Search Limits for Extra Neutral Gauge Bosons at High Energy Lepton Colliders

We study and compare the discovery potential for heavy neutral gauge bosons (Z') at the various $e^+e^-$ and $\mu^+\mu^-$ colliders that have been proposed. Typical search limits for the e^+e^- colliders are 2-10 times sqrt{s} with the large variation reflecting the model dependence of the limits. The search limits for the mu^+ mu^- colliders are slightly lower. Polarization and flavour tagging are important in realizing the highest discovery limits possible. Because the search limits are based on indirect inferences of deviations from standard model predictions, they are sensitive to systematic errors.