Facial analysis in videos, including head pose estimation and facial landmark localization, is key for many applications such as facial animation capture, human activity recognition, and human-computer interaction. In this paper, we propose to use a recurrent neural network (RNN) for joint estimation and tracking of facial features in videos. We are inspired by the fact that the computation performed in an RNN bears resemblance to Bayesian filters, which have been used for tracking in many previous methods for facial analysis from videos.