  The model-independent constraints on the Abelian Z' couplings from the LEP
data are applied to estimate the Z' production in experiments at the Tevatron
and LHC. The Z' total and partial decay widths are analyzed. The results are
compared with model-dependent predictions and present experimental data from
the Tevatron. If we assume the 1-2sigma hints from the LEP data to be a signal
of the Abelian Z' boson, then the Tevatron data constrain the Z' mass between
400 GeV and 1.2 TeV.
