We have described a series of predictive models which have been developed for capturing some kind of dependency inside non stationary sequences. Although the precise motivations and the inspiration sources for these different models have been multi-fold, they are aimed at the same goal. Other attempts have been developed which we have not described here. An important class of models which uses parametric trajectories is that of Segment Models, a review and a comparison with HMMs may be found in [37]. Up to now, predictive models have not led to better results than classical multi-gaussian HMMs. Most of the time, the experiments reported by the different authors are performed on small sized or limited complexity problems. However, some authors also report excellent performances of some predictive models on different tasks. In the second part of the paper, we have described a non linear predictive HMM, which is based on regressive neural networks. We have presented experiments on two relatively large tasks where the model reaches state of the art performances.