abstract: We are interested in the local dynamics of a fibered holomorphic transformation $(\theta,z)\to (\theta+\alpha, f\theta(z))$ around an invariant curve. We found generalisations of some well known results in the constant case, showing that the curve plays the role of a center for the dynamics, which is gouverned by a fibered rotation number. We are interested then on the existence of invariant curves. We found that this last problem is closely related to arithmetical properties of the fibered rotation number. Under a Brjuno like arithmetical condition we show the persistence of an invariant curve.