  We present detailed results of a diagrammatic calculation of the leading
two-loop QCD corrections to the masses of the neutral CP-even Higgs bosons in
the Minimal Supersymmetric Standard Model (MSSM). The two-loop corrections are
incorporated into the full diagrammatic one-loop result and supplemented with
refinement terms that take into account leading electroweak two-loop and
higher-order QCD contributions. The dependence of the results for the
Higgs-boson masses on the various MSSM parameters is analyzed in detail, with a
particular focus on the part of the parameter space accessible at LEP2 and the
upgraded Tevatron. For the mass of the lightest Higgs boson, m_h, a parameter
scan has been performed, yielding an upper limit on m_h which depends only on
tan(beta). The results for the Higgs-boson masses are compared with results
obtained by renormalization group methods. Good agreement is found in the case
of vanishing mixing in the scalar quark sector, while sizable deviations occur
if squark mixing is taken into account.
