This thesis considers the Bayesian analysis of general multivariate DLM's (Dynamic Linear Models) for vector time series forecasting where the observational variance matrices are unknown. This extends considerably some previous work based on conjugate analysis for a special sub—class of vector DLM's where all marginal univariate models follow the same structure. The new methods developed in this thesis, are shown to have a better performance than other competing approaches to vector DLM analysis, as for instance, the one based on the Student t filter. Practical aspects of implementation of the new methods, as well as some theoretical properties are discussed, further model extensions are considered, including non—linear models and some applications with real and simulated data are provided.