This thesis is devoted to the analysis and modelling of time series and it is concentrated on models and techniques which are of practical value. In particular we developed a wide class of non-linear dynamic models which are useful in the handling of real life problems. Initially we review the basic principles of Bayesian forecasting and the design of Dynamic Linear Models. The main body of the thesis attacks the problem of Normal non-linear estimation and forecasting. Some applications to the seasonal multiplicative model are exhaustively discussed. Following this we present the results of an application of Bayesian transfer response in Market Research. This application worked as the very first stimulus to extend the non-linear models to the exponential family. Finally we discuss the concepts of stochastic transfer response modelling and associated sequential estimation, and we report some applications of the method and models for long term forecasting.