  We investigate the prospects to observe effects of transverse polarization of
top quarks in $pp,p\bar{p}\to t\bar{t}X$. QCD absorptive parts generate a
polarization of top quarks and antiquarks transverse to the production plane in
the partonic processes $q\bar{q}\to t\bar{t}$ and $gg\to t\bar{t}$, which
reaches values of a few percent. These perturbative QCD effects are decreased
at the hadronic level. A measurement through momentum correlations among the
$t$ and $\bar{t}$ decay products will be difficult both at an upgraded Tevatron
and at the LHC.
