The loop-induced processes gg -> h,H,A provide the dominant Higgs
boson production mechanisms at the Tevatron and LHC in a large range
of the minimal supersymmetric extension of the Standard Model. For
squark masses below \sim 400 GeV squark loop contributions become
important in addition to the top and bottom quark loops. We have
therefore determined the next-to-leading order QCD corrections to the
squark contributions of these processes including the full squark and
Higgs mass dependences. They turn out to be large and thus important
for the LHC experiments. Squark mass effects of the K factors can be
of O(20%). In addition we have derived the QCD corrections to the
squark contributions of the Higgs couplings to photons, which play a
role for the Higgs searches in the photonic decay mode at the LHC and
in the gamma gamma collider option of the ILC.