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An important task at future colliders is the investigation of the Higgs-bosonsector. Here the measurement of the triple Higgs coupling(s) plays a specialrole. Based on previous analyses, within the framework of Two Higgs DoubletModels (2HDM) type~I and~II, we define and analyze several two-dimensionalbenchmark planes, that are over large parts in agreement with all theoreticaland experimental constraints. For these planes we evaluate di-Higgs productioncross sections at future high-energy $e^+e^-$ colliders, such as ILC or CLIC.We consider two different channels for the neutral di-Higgs pairs $h_ih_j=hh,hH,HH,AA$: $e^+e^- \to h_i h_j Z$ and $e^+e^- \to h_i h_j \nu \bar \nu$.In both channels the various triple Higgs-boson couplings contributesubstantially. We find regions with a strong enhancement of the productionchannel of two SM-like light Higgs bosons and/or with very large productioncross sections involving one light and one heavy or two heavy 2HDM Higgsbosons, offering interesting prospects for the ILC or CLIC. The mechanismsleading to these enhanced production cross sections are analyzed in detail. Wepropose the use of cross section distributions with the invariant mass of thetwo final Higgs bosons where the contributions from intermediate resonant andnon-resonant BSM Higgs bosons play a crucial role. We outline which process atwhich center-of-mass energy would be best suited to probe the correspondingtriple Higgs-boson couplings.

Sensitivity to Triple Higgs Couplings via Di-Higgs Production in the 2HDM at e+e- Colliders