A result coming from Dulac, and proved independently by Écalle and Ilyashenko in the 80's, asserts that an analytic vector field in the real plane cannot have a sequence of limit cycles accumulating to a singular point. In this talk, we deal with this problem for analytic vector fields in dimension three, in a non-trivial but not too degenerated situation. Namely, the linear part at the singularity has two non-zero imaginary eigenvalues. We describe completely the distribution of all possible local cycles around the singularity, showing that there are no isolated ones in some neighborhood, which proves Dulac's property. Joint work with Nuria Corral and María Martín.