  The CDF and D0 experiments have reported on the measurement of the
forward-backward asymmetry of top quark pair production at the Tevatron and the
result is that it is more than 2 standard deviations above the predicted value
in the Standard Model. This has to be added to the longstanding anomaly in the
forward-backward asymmetry for bottom quark production at LEP which is 3
standard deviations different from the Standard Model value. The discrepancy in
the bottom asymmetry can be accounted for by the contributions of Kaluza-Klein
excitations of electroweak gauge bosons at LEP in warped extra dimensional
models in which the fermions are localized differently along the extra
dimension so that the gauge interactions of heavy third generation fermions are
naturally different from that of light fermions. In this paper, we show that it
is more difficult to elaborate a model generating a significant top asymmetry
in a similar way -- through exchanges of Kaluza-Klein gluons at the Tevatron --
due to the indirect constraints originating from precision electroweak data.
