  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.
