It is often argued that exchanged rates volatility during the 1980s was too excessive to be attributed only to market fundamentals. This paper investigates for speculative bubles in the franc–mark exchange rate applying direct tests for determinate bubbles and indirect ones(according to the issues of integration and cointegration)for stochastic bubbles, in the context of a sticky price monetary model. No clear-cut conclusions can be drawn from these tests although all of them indicate that the no-bubble hypothesis cannot be easily accepted. However, any evidence for bubbles should be interpreted with caution, since a possible misspecification of the model may produce misleading inferences.