We analyze the expectational stability (E-stability) of the different solutions of a linear rational expectations model in which the endogenous variable depends on expectations of its current and future values, formed in the past, and also on its own lagged value. It is shown that the continuum of bubble solutions cannot be strongly E-stable. In contrast, for certain parameter values, a particular solution which would normally be identified as a bubble solution can be strongly E-stable. The results are applied to a macroeconomic model with real balance effects.