  We calculate the leading O(alpha_s^4) contributions to the invariant mass
distribution of top-quark pairs produced at the Tevatron and LHC, in the limit
where the invariant mass of the t-tbar pair approaches the partonic
center-of-mass energy. Our results determine at NNLO in alpha_s the
coefficients of all singular plus distributions and scale-dependent logarithms
in the differential partonic cross sections for q-qbar, gg -> t-tbar + X. A
numerical analysis showing the effects of the NNLO corrections on the central
values and scale dependence of the invariant mass distribution is performed.
The NNLO corrections are found to significantly enhance the cross section and
reduce the perturbative uncertainties compared to the NLO calculation.
