[en] 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(αα_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 √(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 √(s)=500 GeV. (orig.)