Abstract. In this paper, we propose a fully Bayesian approach to the special class of nonlinear time-series models called the logistic smooth transition autoregressive (LSTAR) model. Initially, a Gibbs sampler is proposed for the LSTAR where the lag length, k, is kept fixed. Then, uncertainty about k is taken into account and a novel reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is proposed. We compared our RJMCMC algorithm with well-known information criteria, such as the Akaikes̀ information criteria, the Bayesian information criteria (BIC) and the deviance information criteria. Our methodology is extensively studied against simulated and real-time series.