We consider QCD corrections to Higgs boson production through gluon-gluon f
usion in hadron collisions. Using the recently evaluated [14] two-loop ampl
itude for this process and the corresponding factorization formulae [15]-[1
8] describing soft-gluon bremsstrahlung at O(alpha (2)(S)), we compute the
soft and virtual contributions to the next-to-next-to-leading order cross s
ection. We also discuss soft-gluon resummation at next-to-next-to-leading l
ogarithmic accuracy. Numerical results for Higgs boson production at the LH
C are presented.