Dynamic models in which agents' behavior depends on expectations of future prices or other endogenous variables can have steady states that are stationary equilibria for a wide variety of expectations rules, including rational expectations. When there are multiple steady states, stability is a criterion for selecting among them as predictions of long-run outcomes. The purpose of this paper is to study how sensitive stability is to certain details of the expectations rules, in a simple OLG model with constant government debt that is financed through seigniorage. We compare simple recursive learning rules, learning rules with vanishing gain, and OLS learning, and also relate these to expectational stability. One finding is that two adaptive expectation rules that differ only in whether they use current information can have opposite stability properties.