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In this paper, we study the almost sure scattering for the Klein-Gordonequations with Sobolev critical power. We obtain the almost sure scatteringwith random initial data in $H^s \times H^{s-1}$; $11/12 < s < 1$ for $d = 4$,$15/16 < s < 1$ for $d = 5$. We use the induction on scales and bushes argumentin [9] where the model equation is wave equation. For d = 5, we use the massterm of the Klein-Gordon equation to obtain the control of the increment ofenergy in the process of induction on scales.

Almost sure scattering for the nonlinear Klein-Gordon equations with Sobolev critical power