In this paper, we address the problem of sequential Bayesian model selection. This problem does not usually admit any closed-form analytical solution. We propose here an original sequential simulation-based method to solve the associated Bayesian computational problems. This method combines sequential importance sampling, a resampling procedure and reversible jump MCMC moves. We describe a generic algorithm and then apply it to the problem of sequential Bayesian model order estimation of autoregressive (AR) time series observed in additive noise. 1 Introduction Model selection is a fundamental data analysis task. It has many applications in various fields of science and engineering. Over the past two decades many of these problems have been addressed using information criteria such as AIC or MDL. The widespread use of these criteria is mainly due to their intrinsic simplicity. AIC and MDL are applied by evaluating two terms: a data term which requires the maximization of the likeliho...