We examine local stability under learning of stationary Markov sunspot equilibria (SSEs) in a simply dynamic nonlinear model. Necessary and sufficient conditions for local convergence of a recursive learning algorithm to SSEs are shown to be given (generically) by expectational stability (E-stability) conditions. We distinguish between weak and strong E-stability, where the latter requires stability also with respect to overparameterizations of the sunspot solution. Weak and strong E-stability of the corresponding deterministic solutions. The E-stability of SSEs near a single deterministic steadt state is also analyzed. Three economic applications are given: the standard OLG (overlapping generations) model, the OLG model with government expenditures finances by seignorage, and the OLG model with increasing social returns in production.