  I present a calculation of next-to-next-to-next-to-leading-order (NNNLO)
soft-gluon corrections for top-antitop pair production in hadronic collisions.
Approximate NNNLO (aNNNLO) results are obtained by adding the NNNLO soft-gluon
corrections to the complete next-to-next-to-leading-order (NNLO) cross section.
Theoretical predictions are shown for the total aNNNLO $t{\bar t}$ cross
section at LHC and Tevatron energies. The aNNNLO cross sections are larger but
have smaller theoretical uncertainties than at NNLO.
