  We consider the evolution of the correlations between the Fourier coeficients
of a solution of the Kamdostev-Petviavshvili II equation when these
coefficients are initially independent random variables. We use the structure
of normal forms of the equation to prove that those correlations remain small
until times of order $\varepsilon^{-5/3}$ or $\varepsilon^{-2}$ depending on
the quantity considered.
