  Top quark-antiquark ($t\bar t$) pairs will be produced copiously at the
Tevatron collider and in huge numbers at the LHC. This will make possible
detailed investigations of the properties and interactions of this quark
flavor. The analysis and interpretation of future data requires precise
predictions of the hadronic production of $t\bar t$ pairs and of their
subsequent decays. In this talk the reactions $p {\bar p}, p p \to t{\bar t} +
X \to l^+ l'^- + X$ are considered and results are presented of our calculation
of the dilepton angular distribution at next-to-leading order QCD, keeping the
full dependence on the spins of the intermediate $t\bar{t}$ state. The angular
distribution is determined for different choices of reference axes that can be
identified with the $t$ and $\bar t$ spin axes. While the QCD corrections to
the leading-order distribution turn out to be small in the case of the LHC, we
find them to be sizeable in the case of the Tevatron and find, moreover, the
angular distribution to be sensitive to the parton content of the proton.
