The empirical literature provides a wide range of estimates for trade elasticities at the aggregate level. Furthermore, recent contributions in international macroeconomics suggest that low (implied) values of the trade elasticity of substitution may play an important role in understanding the disconnect between international prices and real variables. However, a standard model of the international business cycle displays multiple locally isolated equilibria if the trade elasticity of substitution is sufficiently low. The main contribution of this paper is to compute and characterize some dynamic properties of these equilibria. While multiple steady states clearly signal equilibrium multiplicity in the dynamic setup, this is not a necessary condition. Solutions based on log-linearization around a deterministic steady state are of limited to no help in computing the true dynamics. However, the log-linear solution can hint at the presence of multiple dynamic equilibria.