  We determine the next-to-leading logarithmic (NLL) QCD corrections to the
cross section sigma(e+e- to t bar t H) for center-of-mass energies up to 500
GeV. The dynamics is dominated by nonrelativistic effects, and the summation of
terms singular in the relative t bar t velocity is mandatory to all orders in
the strong coupling constant alpha_s using an effective theory. The summations
lead to an enhancement of the tree level predictions by about a factor of two
and are important for the determination of the top Yukawa coupling. We also
study the impact of polarization of the electron-positron beams and provide a
fast approximation formula for the known O(alpha_s) QCD fixed-order prediction.
