Kalai and Lehrer (93a, b) have shown that if players' beliefs about the future evolution of play is absolutely continuous with respect to play induced by optimal strategies then Bayesian updating eventually leads to Nash equilibrium. In this paper, we present the first set of necessary and su±cient conditions that ensure that Bayesian updating eventually leads to Nash equilibrium. More important, we show that absolute continuity does not rule out any observable behavior that is asymptotically consistent with Nash equilibrium.