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In this work, we consider germs of analytic singular vector elds in (C^3,0)with an isolated and doubly-resonant singularity of saddle-node type at theorigin. Such vector elds come from irregular two-dimensional dierential systemswith two opposite non-zero eigenvalues, and appear for instance when studyingthe irregular singularity at innity in Painlev{\'e} equations (P j) j=I,...,Vfor generic values of the parameters. Under suitable assumptions, we prove atheorem of analytic normalization over sectorial domains, analogous to theclassical one due to Hukuhara-Kimura-Matuda for saddle-nodes in (C^2,0). Wealso prove that these maps are in fact the Gevrey-1 sums of the formalnormalizing map, the existence of which has been proved in a previous paper.Finally we provide an analytic classication under the action of bereddieomorphisms, based on the study of the so-called Stokes dieomorphismsobtained by comparing consecutive sectorial normalizing maps {\`a} laMartinet-Ramis / Stolovitch for 1-resonant vector fields.

Doubly-resonant saddle-nodes in (C^3,0) and the fixed singularity at infinity in Painlev{\'e} equations: analytic classification