  We calculate the cross sections for the neutral Higgs-boson production at
e+e- colliders in the Minimal Supersymmetric Standard Model (MSSM) using the
Feynman-diagrammatic approach and the on-shell renormalization scheme. We
incorporate the Higgs-boson propagator corrections, evaluated up to two-loop
order, into the prediction of the cross sections for the Higgs-boson production
mechanism e+e- -> hZ, hA. The propagator corrections consist of the full
one-loop contribution, including the effects of non-vanishing external
momentum, and at the two-loop level of the dominant corrections of O(alpha
alpha_s) and further sub-dominant contributions. The results are supplemented
with the complete set of one-loop vertex and box corrections. The effects of
the two-loop propagator corrections are investigated in detail. We briefly
discuss also the effect of the box contributions for high $\sqrt{s}$. We
compare our results with the case where only the corrections to the effective
mixing angle, evaluated within the renormalization-group-improved one-loop
Effective Potential approach, are taken into account. We find agreement better
than 10% for LEP2 energies and deviations larger than 20% for $\sqrt{s}$ = 500
GeV.
