  In the framework of the $\mathcal{CP}$ conserving Two Higgs Doublet Model
(2HDM), type I and II, we study the triple Higgs couplings with at least one
light $h$ Higgs boson that is identified by the 125 GeV Higgs boson. We define
benchmark planes that exhibit large values of triple Higgs couplings, while
being in agreement with all experimental and theoretical constraints. Finally,
we analyze the impact of the triple Higgs couplings on the production cross
section of two neutral Higgs bosons in two channels, $\sigma(e^+e^-\to h_i h_j
Z)$ and $\sigma(e^+e^- \to h_i h_j \nu\bar{\nu})$ with $h_i h_j = hh, hH, HH,
AA$. We show that the triple Higgs couplings have an important impact on these
$e^+e^-$ production cross sections.
