  Higgs bosons can be searched for in the channels $p\bar p/pp\to t\bar tH+X$
at the Tevatron and the LHC. We have calculated the QCD corrections to these
processes in the Standard Model at next-to-leading order. The higher-order
corrections reduce the renormalization and factorization scale dependence
considerably and stabilize the theoretical predictions for the cross sections.
At the central scale $\mu=(2m_t+M_H)/2$ the properly defined $K$ factors are
slightly below unity for the Tevatron ($K \sim 0.8$) and slightly above unity
for the LHC ($K \sim 1.2$).
