  The cross sections for the multiple production of the lightest neutral Higgs
boson at high--energy $e^+ e^-$ colliders are presented in the framework of the
Minimal Supersymmetric extension of the Standard Model (MSSM). We consider
production through Higgs--strahlung, associated production of the scalar and
the pseudoscalar bosons, and the fusion mechanisms for which we will use the
effective longitudinal vector--boson approximation. These cross sections allow
one to determine trilinear Higgs couplings $\lambda_{Hhh}$ and $\lambda_{hhh}$,
which are theoretically predicted by the Higgs potential.
