Neutral Higgs-boson-pair production provides the possibility of studying th
e trilinear Higgs couplings at future high-energy colliders. We present the
QCD corrections to the gluon-initiated processes in the limit of a heavy t
op quark in the loops and the Drell-Yan-like pair production of scalar and
pseudoscalar Higgs particles. The pp cross sections are discussed for CERN
LHC energies within the standard model and its minimal supersymmetric exten
sion. The QCD corrections are large, enhancing the total cross sections sig
nificantly. [S0556-2821(98)03719-9].