  We analyse the loop induced production of Higgs boson pairs at future
high--energy $e^+e^-$ colliders, both in the Standard Model and in its minimal
supersymmetric extension. The cross sections for Standard Model Higgs pair
production through $W/Z$ boson loops, $\ee \ra H^0 H^0$, are rather small but
the process could be visible for high enough luminosities, especially if
longitudinal polarization is made available. In the Minimal Supersymmetric
Standard Model, the corresponding processes of CP--even or CP--odd Higgs boson
pair production, $\ee \ra hh, HH, Hh$ and $\ee \ra AA$ have smaller cross
sections, in general. The additional contributions from chargino/neutralino and
slepton loops are at the level of a few percent in most of the supersymmetric
parameter space.
