We study abstract macroeconomic systems in which expectations play an important role. Consistent with the recent literature on recursive learning and expectations, we replace the agents in the economy with econometricians. Unlike the recursive learning literature, however, the econometricians in the analysis here are Bayesian learners. We are interested in the extent to which expectational stability remains the key concept in the Bayesian environment. We isolate conditions under which versions of expectational stability conditions govern the stability of these systems just as in the standard case of recursive learning. We conclude that Bayesian learning schemes, while they are more sophisticated, do not alter the essential expectational stability findings in the literature.