We apply recent stability and bifurcation results to provide an analytical characterization of Paul de Grauwe’s chaotic exchange rate model. We prove that the model’s fundamental steady state becomes unstable due to a Neimark-Sacker bifurcation when chartists extrapolate past exchange rate trends too strongly, a phenomenon that gives rise to cyclical exchange rate dynamics. In contrast, fundamentalists’ mean reversion strength only has a stabilizing effect on the model’s dynamics when the exchange rate is out of equilibrium. We also show that agent-based versions of Paul de Grauwe’s exchange rate model may produce endogenous exchange rate dynamics, too.