Summary This article considers a Bayesian approach to the multistate extension of the Jolly–Seber model commonly used to estimate population abundance in capture–recapture studies. It extends the work of George and Robert (1992, Biometrika79, 677–683), which dealt with the Bayesian estimation of a closed population with only a single state for all animals. A super-population is introduced to model new entrants in the population. Bayesian estimates of abundance are obtained by implementing a Gibbs sampling algorithm based on data augmentation of the missing data in the capture histories when the state of the animal is unknown. Moreover, a partitioning of the missing data is adopted to ensure the convergence of the Gibbs sampling algorithm even in the presence of impossible transitions between some states. Lastly, we apply our methodology to a population of fish to estimate abundance and movement.