  We introduce the study of the local dynamics around a parabolic indifferent
invariant curve for fibred holomorphic maps. As in the classical non-fibred
case, we show that petals are the main ingredient. Nevertheless, one expects
the properties of the base rotation number should play an important role in the
arrangement of the petals. We exhibit examples where the existence and the
number of petals depend not just on the complex coordinate of the map, but on
the base rotation number. Furthermore, under additional hypothesis on the
arithmetics and smoothness of the map, we present a theorem that allows to
characterize the local dynamics around a parabolic invariant curve.
