I will talk about local classification of germs of holomorphic vector fields vanishing at zero. It is always possible to transform, by a formal change of coordinates, a vector field into a simpler model, called a normal form. Such a transformation is usually a divergent formal power series at the origin. I will show how the problem of convergence is related to a small divisors condition. If the convergence cannot be obtained, I’ll show that the conjugacy can be Gevrey smooth or holomophic in a sectorial domain which contains zero in the boundary in some cases.