  In order to verify the Higgs mechanism experimentally, the Higgs
self-couplings have to be probed. These couplings allow the reconstruction of
the characteristic Higgs potential responsible for the electroweak symmetry
breaking. The couplings are accessible in a variety of multiple Higgs
production processes. The theoretical analysis including the most relevant
channels for the production of neutral Higgs boson pairs at high-energy and
high-luminosity $e^+e^-$ linear colliders will be presented in this note.
