We analyzed the double production and the triple self-coupling of the standard model Higgs boson at future γγ collider energies, with the reactions γγ → ttHH. We evaluated the total cross section for ttHH and calculated the total number of events considering the complete set of Feynman diagrams at tree-level and for different values of the triple coupling κλHHH . The numerical computation was done for the energy which is expected to be available at a possible Future Linear γγ Collider with a

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... ter-of-mass energy 500−3000 GeV and luminosities of 1000 and 5000 f b −1 . We found that the number of events for the process γγ → ttHH, taking into account the decay products of both t and H, is enough to obtain relevant information about the triple Higgs boson self-coupling.