  We consider germs of holomorphic vector fields at a fixed point having a
nilpotent linear part at that point, in dimension $n \geq 3$. Based on
Belitskii's work, we know that such a vector field is formally conjugate to a
(formal) normal form. We give a condition on that normal form which ensure that
the normalizing transformation is holomorphic at the fixed point. We shall show
that this sufficient condition is a nilpotent version of Bruno's condition (A).
In dimension 2, no condition is required since, according to Str{\'o}zyna-
Zoladek, each such germ is holomorphically conjugate to a Takens normal form.
Our proof is based on Newton's method and $\frak{sl}\_2(\Bbb
C)$-representations.
