  We study the triple Higgs self-coupling at future $e^{+}e^{-}$ colliders
energies, with the reactions $e^{+}e^{-}\to b \bar b HH$ and $e^{+}e^{-}\to t
\bar t HH$. We evaluate the total cross section of $b\bar bHH$, $t\bar tHH$ and
calculate the total number of events considering the complete set of Feynman
diagrams at tree-level. The sensitivity of the triple Higgs coupling is
considered in the Higgs mass range 110-190 $GeV$, for the energy which is
expected to be available at a possible Next Linear $e^{+}e^{-}$ Collider with a
center-of-mass energy $800, 1000, 1500$ $GeV$ and luminosity 1000 $fb^{-1}$.
