ABSTRACTCircular time series have received relatively little attention in statistics, and modeling complex circular time series using the state space approach is nonexistent in the literature. In this article we introduce a flexible Bayesian nonparametric approach to state-space modeling of observed circular time series where even the latent states are circular random variables. Crucially, we assume that the forms of the observational and evolutionary functions, both of which are circular in nature, are unknown and time-varying. We model these unknown circular functions by appropriate wrapped Gaussian processes having desirable properties. We develop an effective Markov-chain Monte Carlo strategy for implementing our Bayesian model by judiciously combining Gibbs sampling and Metropolis–Hastings methods. Validation of our ideas with a simulation study and two real bivariate circular time-series data sets, where we assume one of the variables to be unobserved, revealed very encouraging performance of our mo...