Higgs radiation off top quarks at the Tevatron and the LHC

Higgs bosons can be searched for in the channels pp macro/pp-->tt macro H + X at the Fermilab Tevatron and the Cern Large Hadron Collider (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 approximately 0.8) and slightly above unity for the LHC (K approximately 1.2).