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The aim of this article is to prove a Thom-Sebastiani theorem for theasymptotics of the fiber-integrals. This means that we describe the asymptoticsof the fiber-integrals of the function $f \oplus g : (x,y) \to f(x) + g(y)$ \on $(\mathbb{C}^p\times \mathbb{C}^q, (0,0))$ in term of the asymptotics of thefiber-integrals of the holomorphic germs $f : (\mathbb{C}^p,0) \to(\mathbb{C},0)$ and $g : (\mathbb{C}^q,0) \to (\mathbb{C},0)$. This reduces tocompute the asymptotics of a convolution $\Phi_*\Psi$ from the asymptotics of$\Phi$ and $\Psi$ modulo smooth terms. To obtain a precise theorem, giving thenon vanishing of expected singular terms in the asymptotic expansion of$f\oplus g$, we have to compute the constants coming from the convolutionprocess. We show that they are given by rational fractions of Gamma factors.This enable us to show that these constants do not vanish.

Un th\'eor\`eme \`a la "Thom-Sebastiani" pour les int\'egrales-fibres