We present the first complete 1-loop diagrammatic calculation of the cross sections for the neutral Higgs production processes $e^+e^-ra Z^0h^0$ and $e^+e^-ra A^0h^0$ in the minimal supersymmetric standard model. We compare the results from the diagrammatic calculation with the corresponding ones of the simpler and compact effective potential approximation and discuss the typical size of the differences.
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