  We investigate the inclusive production of a Higgs boson with a pair of heavy
quarks (t-tbar b-bbar), in e^+e^- collisions at high energies, sqrt(s)=500 GeV
and sqrt(s)=1 TeV. We consider both the Standard Model and the supersymmetric
case. In both cases O(alpha_s) QCD corrections are included. The associated
production of a Higgs boson with a t-tbar pair is extremely sensitive to the
top-Higgs Yukawa coupling and may allow the precision measurement of this
coupling. In some regions of the supersymmetric parameter space the associated
production of a Higgs boson with a b-bbar pair receives large resonant
contributions and can have a significant rate.
