We study the Higgs pair-production in the Standard Model of the strong and electroweak interactions at future $e^{+}e^{-}$ collider energies, with the reaction $e^{+}e^{-}to t bar t HH$. We evaluated the total cross section of $tbar tHH$ and calculate the number total of events considering the complete set of Feynman diagrams at tree-level. The numerical computation is done for the energy which is expected to be available at a possible Next Linear $e^{+}e^{-}$ Collider: with center-of-mass energy $800, 1600$ $GeV$ and luminosity 1000 $fb^{-1}$.
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