Summary: We suggest the use of simulation techniques to extend the applicability of the usual Gaussian state space filtering and smoothing techniques to a class of non-Gaussian times series models. This allows a fully Bayesian or maximum likelihood analysis of some interesting models, including outlier models, discrete Markov chain components, multiplicative models and stochastic variance models. Finally we discuss at some length the use of a non-Gaussian model to seasonally adjust the published money supply figures.