We present a class of stochastic regime-switching models.The time-series models may have periodic transition probabilities andthe drifts may be seasonal. In the latter case, the model exhibitsseasonal dummy variation that may change with the regime. Theprocesses entail nontrivial interactions between so-called businessand seasonal cycles. We discuss the stochastic properties as well astheir relationship with periodic ARMA processes. Estimation andtesting are also discussed in detail.