  We study germs of smooth vector fields in a neighborhood of a fixed point
having an hyperbolic linear part at this point. It is well known that the
"small divisors" are invisible either for the smooth linearization or normal
form problem. We prove that this is completely different in the smooth Gevrey
category. We prove that a germ of smooth $\al$-Gevrey vector field with an
hyperbolic linear part admits a smooth $\be$-Gevrey transformation to a smooth
$\be$-Gevrey normal form. The Gevrey order $\be$ depends on the rate of
accumulation to $0$ of the small divisors. We show that a formally linearizable
Gevrey smooth germ with the linear part satisfies Brjuno's small divisors
condition can be linearized in the same Gevrey class.
