  The functional autoregressive model is a Markov model taylored for data of
functional nature. It revealed fruitful when attempting to model samples of
dependent random curves and has been widely studied along the past few years.
This article aims at completing the theoretical study of the model by adressing
the crucial issue of weak convergence for estimates from the model. The main
difficulties stem from an underlying inverse problem as well as from dependence
between the data. Traditional facts about weak convergence in non parametric
models appear : the normalizing sequence is an o($sqrt{n}$), a bias terms
appears. Several original features of the functional framework are pointed out.
