  We study asymptotic expansion as $\nu\to0$ for integrals over ${ \mathbb{R}
}^{2d}=\{(x,y)\}$ of quotients $F(x,y) \big/ \big( (x\cdot y)^2+(\nu
\Gamma(x,y))^2\big)^{-1}$, where $\Gamma$ is strictly positive and $F$ decays
at infinity sufficiently fast. Integrals of this kind appear in description of
the four--waves interactions.
