The production of top-antitop-quark pairs at hadron colliders is interesting both in its own right as signal process, but also as background to many searches for new physics. The corresponding predictions aim at the precision level of few per cent, rendering not only the inclusion of radiative corrections of the strong and electroweak interactions relevant, but also of off-shell and finitewidth effects originating from the top-quark decays t → bW → b + l + ν l /qq ′ . We report on a calculation

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... for the full process pp → W + W − bb → ν e e + µ −ν µ bb at next-to-leading order QCD and discuss the effects of the finite widths of the top quarks and of the W bosons for selected observables. Generically it turns out that finite-top-width effects are at the per-cent level whenever the top-quark resonances dominate, but those effects can reach tens of per cent in off-shell tails. Finite-W-width effects, on the other hand, are suppressed to less than 0.5% whenever the top quarks can become resonant and only become sizeable in exceptional cases. One such case, however, is the invariant mass of a bottom quark and the corresponding charged lepton, which result from the same top-quark decay-an observable that is relevant for precision measurements of the top-quark mass.