Z' bosons that couple preferentially to the third generation fermions can
arise in models with extended weak (SU(2)xSU(2)) or hypercharge (U(1)xU(1))
gauge groups. We show that existing limits on quark-lepton compositeness set by
the LEP and Tevatron experiments translate into lower bounds of order a few
hundred GeV on the masses of these Z' bosons. Resonances of this mass can be
directly produced at the Tevatron. Accordingly, we explore in detail the limits
that can be set at Run II using the process p pbar -> Z' -> tau tau -> e mu. We
also comment on the possibility of using hadronically-decaying taus to improve
the limits.Comment: LaTeX2e, 24 pages (including title page), 13 figures; version 2:
corrected typographical errors and bad figure placement; version 3: added
references and updated introduction; version 4: changes to compensate for old
latex version on arXiv server; version 5: additional references, and embedded
fonts in eps files for PRD; version 6: corrected some minor typos to address
PRD referee's comment
