We study the effects of dimension-six operators contributing to the gt(t) o
ver bar vertex in top quark pair production at the Fermilab Tevatron collid
er. We derive both the limits from run 1 data and the potential bounds from
future runs (runs 2 and 3). Although the current constraints are not very
strong, the future runs are quite effective in probing these operators. We
investigate the possibility of disentangling different operators with the t
t invariant mass distribution and the top quark polarization asymmetry. We
also study the effects of a different set of operators contributing to sing
le top quark production via the Wt(b) over bar coupling. We derive the curr
ent and potential future bounds on these anomalous operators and find that
the upgraded FermiIab Tevatron collider can improve the existing constraint
s from R-b for one of the operators. [S0556-2821(98)07121-5].