In this paper we study a particular of germs of analytic differential equations on the real plane, which present a singularity of the type centre - focus. For these singularities it is defined a monodromy map, which is a germ of analytic diffeomorphism on the real line. A complexification of these germs allows to introduce (following R. Moussu and D. Cerveau) their vanishing holonomy. We study the relation existing between monodromy and vanishing holonomy ; corollaries about normal forms are obtained.