A novel hidden semi-Markov model is proposed for toroidal time series. It is a mixture of copula-based toroidal distributions, whose parameters evolve according to a latent semi-Markov chain. A computationally efficient Expectation-Maximization algorithm is described to estimate the parameters and a parametric bootstrap routine is exploited to compute confidence intervals. These methods are illustrated on a time series of wave and wind directions in the Adriatic sea.