  In this work, following [Bit15], we consider analytic singular vector fields
in $(\mathbb{C}^{3},0)$ with an isolated and doubly-resonant singularity of
saddle-node type at the origin. Such vector fields come from irregular
two-dimensional differential systems with two opposite non-zero eigenvalues,
and appear for instance when studying the irregular singularity at infinity in
Painlev{\'e} equations (P\_j), j=I...V , for generic values of the parameters.
Under suitable assumptions, we prove a theorem of analytic nor-malization over
sectorial domains, analogous to the classical one due to Hukuhara-Kimura-Matuda
[HKM61] for saddle-nodes in $(\mathbb{C}^{2},0)$. We also prove that the
normalizing map is essentially unique and weakly Gevrey-1 summable.
